
	Hinweise fuer den Gebrauch von KEYWORDS
	---------------------------------------

	Das vorliegende Verzeichnis soll das schnelle Auffinden von
	Funktionen, die bei der Loesung gegebener Probleme von Nutzen
	sein koennen, ermoeglichen. Es enthaelt Angaben zu allen
	SIMATH-Funktionen, und zwar:
	      - den Funktionsnamen samt Parameterliste,
	      - den ausfuehrlichen Namen (in Englisch),
	      - ob die Funktion rekursiv ist,
	      - ob die Funktion durch ein Macro realisiert ist.
	Der Funktionsname und (fast alle) Woerter des ausfuehrlichen
	Namens einer Funktion bilden die Schluesselwoerter, unter denen
	die Funktion im Verzeichnis zu finden ist. Das Verzeichnis ist
	nach den Schluesselwoertern alphabetisch sortiert (erste Spalte).


	Beispiel:
	Man moechte den groessten gemeinsamen Teiler (Englisch: "greatest
	common divisor") ueber den ganzen Zahlen berechnen; also wird man
	nachsehen, ob unter den Schluesselwoertern die Worte "greatest",
	"common" oder "divisor" vorkommen und wenn ja, ob unter diesen
	Schluesselwoertern geeignete Funktionen aufgefuehrt sind.

	Die Angaben zu einem Schluesselwort sind folgendermassen zu lesen:
	Man suche zunaechst den Funktionsnamen (kenntlich an der in Klammern
	gesetzten Parameterliste) auf und beginne von dort an die Zeile(n)
	zu lesen, bis man an das Ende der zu einem Schluesselwort gehoerenden
	Angaben angelangt ist; dann lese man mit dem Schluesselwort weiter
	bis zum Funktionsnamen.
	Die Angabe

"greatest                common divisor and cofactors
			 pigcdcf(r,P1,P2,pQ1,pQ2) polynomial over integers"
 
	ist also zu lesen als:

	"pigcdcf(r,P1,P2,pQ1,pQ2) polynomial over integers greatest common
	divisor and cofactors"



'rank'-th               derivative ecrlserrkd(E) elliptic curve over the 
			rationals, L-series, 
10                      ilog10(n) integer logarithm, base 
2^m-th                  power of variable, polynomial, remainder 
			upgf22pvprem(G,m,P) univariate polynomial over 
			Galois-field with characteristic 2, 
2x2                     product i22prod(A,B) integer 
Atkin                   primality test (rekursiv) igkapt(n,msg) integer 
			Goldwasser Kilian 
Ben-Or                  factorization upgf2bofact(G,P) univariate 
			polynomial over Galois-field with characteristic 2, 
Ben-Or                  factorization upgfsbofact(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic, 
Ben-Or                  factorization upmibofact(ip,P) univariate 
			polynomial over modular integers 
Ben-Or                  factorization, special upgf2bofacts(G,P) univariate 
			polynomial over Galois-field with characteristic 2 
Ben-Or                  factorization, special upgfsbofacts(p,AL,P) 
			univariate polynomial over Galois-field with single 
			characteristic, 
Ben-Or                  factorization, special upmibofacts(ip,P) univariate 
			polynomial over modular integers 
Berlekamp               Q polynomials construction upgf2bqp(G,P) univariate 
			polynomial over Galois-field with characteristic 2 
Berlekamp               Q polynomials construction upgfsbqp(p,AL,P) 
			univariate polynomial over Galois-field with single 
			characteristic 
Berlekamp               Q polynomials construction upmibqp(ip,P) univariate 
			polynomial over modular integers, 
Berlekamp               Q polynomials construction upmsbqp(p,A) univariate 
			polynomial over modular singles, 
Berlekamp               algorithm upmibfact(ip,P,d) univariate polynomial 
			over modular integers factorization, 
Berlekamp               algorithm upmsbfact(p,A,d) univariate polynomial 
			over modular singles factorization, 
Berlekamp               factorization upgfsbfact(p,AL,P,d) univariate 
			polynomial over Galois-field with single 
			characteristic 
Berlekamp               factorization, Zassenhaus method 
			upgfsbfzm(p,AL,s,P,G) univariate polynomial over 
			Galois-field with single characteristic 
Berlekamp               factorization, Zassenhaus method upmibfzm(ip,s,P,G) 
			univariate polynomial over modular integers, 
Berlekamp               factorization, Zassenhaus method upmsbfzm(m,s,P,G) 
			univariate polynomial over modular singles, 
Berlekamp               factorization, last step upgfsbfls(p,AL,P,B,d) 
			univariate polynomial over Galois-field with single 
			characteristic 
Berlekamp               factorization, last step upmibfls(ip,P,B,d) 
			univariate polynomial over modular integers 
Berlekamp               factorization, last step upmsbfls(m,P,B,d) 
			univariate polynomial over modular singles 
Bezout                  algorithm piresbez(r,P1,P2) polynomial over 
			integers resultant, 
Bezout-matrix           pibezout(r,P1,P2) polynomial over integers 
Bezout-matrix           pmibezout(r,m,P1,P2) polynomial over modular 
			integers 
Bezout-matrix           pmsbezout(r,m,P1,P2) polynomial over modular 
			singles 
C-floating              point fltoCfl(f) floating point to 
C-floating              point to floating point Cfltofl(x) 
Cfltofl(x)              C-floating point to floating point 
Collins                 algorithm (rekursiv) pmirescoll(r,m,P1,P2) 
			polynomial over modular integers resultant, 
Collins                 algorithm (rekursiv) pmsrescoll(r,m,P1,P2) 
			polynomial over modular singles resultant, 
Collins                 algorithm pirescoll(r,P1,P2,n) polynomial over 
			integers resultant, 
Collins                 algorithm special pirescspec(r,P1,P2,n) polynomial 
			over the integers resultant, 
Collins                 algorithm, version1 nfespecmpc1(F,a) number field 
			element special minimal polynomial, 
Collins                 algorithm, version2 nfespecmpc2(F,a) number field 
			element special minimal polynomial, 
Dedekind                eta function special cdedeetas(q,ln_q) complex 
Dedekind                maximality test oupidedekmt(M,P) order of an 
			univariate polynomial over the integers, 
Dedekind                maximality test ouspprmsp1dm(p,P,F) order of an 
			univariate separable polynomial over polynomial 
			ring over modular single prime, transcendence 
			degree 1, 
Dirichlet               character qnfdirchar(D,z) quadratic number field 
Earith()                Essen arithmetic package 
Essen                   arithmetic package Earith() 
Essen                   integer itoE(A,e) ( SIMATH ) integer to 
Essen                   integer to SIMATH integer Etoi(e) 
Essen                   integer to SIMATH integer negation Etoineg(e) 
Essen                   integer with upper bound itoEb(A,e,grenze) ( SIMATH 
			) integer to 
Essen                   integer, sign and upper bound itoEsb(A,e,grenze) ( 
			SIMATH ) integer to 
Etoi(e)                 Essen integer to SIMATH integer 
Etoineg(e)              Essen integer to SIMATH integer negation 
Euklid                  norm (rekursiv) pieuklnorm(r,P) polynomial over 
			integers 
Euklid-                 Gauss- step for columns maiegsc(M,A,B) matrix of 
			integers 
Euklid-                 Gauss- step for columns maupmipegsc(p,M,A,B) matrix 
			of univariate polynomials over modular integer 
			primes 
Euklid-                 Gauss- step for columns maupmspegsc(p,M,A,B) matrix 
			of univariate polynomials over modular single 
			primes 
Euklid-                 Gauss- step for columns maupregsc(M,A,B) matrix of 
			univariate polynomials over rationals 
Euklid-                 Gauss- step for rows maiegsr(M,A,B) matrix of 
			integers 
Euklid-                 Gauss- step for rows maupmipegsr(p,M,A,B) matrix of 
			univariate polynomials over modular integer primes 
Euklid-                 Gauss- step for rows maupmspegsr(p,M,A,B) matrix of 
			univariate polynomials over modular single primes 
Euklid-                 Gauss- step for rows maupregsr(M,A,B) matrix of 
			univariate polynomials over rationals 
Fermat                  residue ? ismifr(M,A,B) is modular integer 
Fermat                  residue list ifrl(N,pm) integer 
Fermat                  residue list msfrl(m,a) modular single 
Fermat's                theorem primality test iftpt(n,L,anz) integer 
Fourier                 expansion of the L-series ecrfelser(E,A,z,result) 
			elliptic curve over rational numbers, 
Galois                  field with characteristic 2 isomorphic embedding of 
			subfield gf2ies(Gm,Gn,n) 
Galois                  field with characteristic 2, combined Schoof- 
			Shanks- algorithm ecgf2cssa(G,a6,s,pl,ts) elliptic 
			curve over 
Galois                  field with characteristic 2, number of points after 
			field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
			curve over 
Galois-field            fputpgfs(r,p,AL,P,V,Vgfs,pf) file put polynomial 
			over 
Galois-field            putpgfs(r,p,AL,P,V,Vgfs) (MACRO) put polynomial 
			over 
Galois-field            with characteristic 2 (rekursiv) pgfstopgf2(r,G,P) 
			polynomial over Galois-field with single 
			characteristic to polynomial over 
Galois-field            with characteristic 2 (rekursiv) pm2topgf2(r,P) 
			polynomial over modular 2 to polynomial over 
Galois-field            with characteristic 2 ? 
			iselecgf2(G,a1,a2,a3,a4,a6,P) is element of an 
			elliptic curve over 
Galois-field            with characteristic 2 Ben-Or factorization, special 
			upgf2bofacts(G,P) univariate polynomial over 
Galois-field            with characteristic 2 Berlekamp Q polynomials 
			construction upgf2bqp(G,P) univariate polynomial 
			over 
Galois-field            with characteristic 2 arithmetic list generator 
			gf2algen(n,H) 
Galois-field            with characteristic 2 derivation, main variable 
			pgf2deriv(r,G,P) polynomial over 
Galois-field            with characteristic 2 derivation, specified 
			variable (rekursiv) pgf2derivsv(r,G,P,i) polynomial 
			over 
Galois-field            with characteristic 2 difference gf2dif(G,a,b) 
			(MACRO) 
Galois-field            with characteristic 2 difference pgf2dif(r,G,P1,P2) 
			(MACRO) polynomial over 
Galois-field            with characteristic 2 distinct degree factorization 
			upgf2ddfact(G,P) univariate polynomial over 
Galois-field            with characteristic 2 element ? isgf2el(G,a) 
			(MACRO) is 
Galois-field            with characteristic 2 element evaluation first 
			variable special version (rekursiv) 
			pigf2evalfvs(r,G,P) polynomial over integers 
Galois-field            with characteristic 2 element fgetgf2el(G,V,pf) 
			file get 
Galois-field            with characteristic 2 element fputgf2el(G,a,V,pf) 
			file put 
Galois-field            with characteristic 2 element getgf2el(G,V) (MACRO) 
			get 
Galois-field            with characteristic 2 element gfseltogf2el(G,a) 
			Galois-field with single characteristic element to 
Galois-field            with characteristic 2 element product (rekursiv) 
			pgf2gf2prod(r,G,P,a) polynomial over Galois-field 
			with characteristic 2, 
Galois-field            with characteristic 2 element putgf2el(G,a,V) 
			(MACRO) put 
Galois-field            with characteristic 2 element randomize 
			gf2elrand(G) 
Galois-field            with characteristic 2 element to Galois-field with 
			single characteristic element gf2eltogfsel(G,a) 
			(MACRO) 
Galois-field            with characteristic 2 element to univariate dense 
			polynomial over modular 2 gf2eltoudpm2(G,a) 
Galois-field            with characteristic 2 element udpm2togf2el(G,P) 
			univariate dense polynomial over modular 2 to 
Galois-field            with characteristic 2 elements ? islistgf2(G,L) is 
			list of 
Galois-field            with characteristic 2 elements scalar product 
			vecgf2sprod(G,V,W) vector of 
Galois-field            with characteristic 2 embedding in field extension 
			(rekursiv) pgf2efe(r,GmtoGn,P) polynomial over 
Galois-field            with characteristic 2 embedding in field extension 
			gf2efe(GmtoGn,gm) 
Galois-field            with characteristic 2 equal ? isppecgf2eq(p,P1,P2) 
			is projective point of an elliptic curve over 
Galois-field            with characteristic 2 evaluation upgf2eval(G,P,a) 
			polynomial over 
Galois-field            with characteristic 2 evaluation, main variable 
			pgf2eval(r,G,P,a) polynomial over 
Galois-field            with characteristic 2 exponentiation gf2exp(G,a,m) 
Galois-field            with characteristic 2 exponentiation 
			pgf2exp(r,G,P,n) polynomial over 
Galois-field            with characteristic 2 fgetpgf2(r,G,V,Vgf2,pf) file 
			get polynomial over 
Galois-field            with characteristic 2 fputpgf2(r,G,P,V,Vgf2,pf) 
			file put polynomial over 
Galois-field            with characteristic 2 getpgf2(r,G,V,Vgf2) (MACRO) 
			get polynomial over 
Galois-field            with characteristic 2 greatest common divisor 
			upgf2gcd(G,P1,P2) univariate polynomial over 
Galois-field            with characteristic 2 inverse gf2inv(G,a) 
Galois-field            with characteristic 2 irreducible and monic 
			polynomial in special bit-representation ? 
			isgf2impsb(G) is 
Galois-field            with characteristic 2 irreducible and monic 
			polynomial in special bit-representation generator 
			gf2impsbgen(n,H) 
Galois-field            with characteristic 2 monic pgf2monic(r,G,P) 
			polynomial over 
Galois-field            with characteristic 2 negation gf2neg(G,a) (MACRO) 
Galois-field            with characteristic 2 negation pgf2neg(r,G,P) 
			(MACRO) polynomial over 
Galois-field            with characteristic 2 point at infinity ? 
			isppecgf2pai(G,P) is projective point of an 
			elliptic curve over 
Galois-field            with characteristic 2 product (rekursiv) 
			pgf2prod(r,G,P1,P2) polynomial over 
Galois-field            with characteristic 2 product gf2prod(G,a,b) 
Galois-field            with characteristic 2 product with arithmetic list 
			gf2prodAL(AL,a,b) 
Galois-field            with characteristic 2 putpgf2(r,G,P,V,Vgf2) (MACRO) 
			put polynomial over 
Galois-field            with characteristic 2 quotient and remainder 
			(rekursiv) pgf2qrem(r,G,P1,P2,pR) polynomial over 
Galois-field            with characteristic 2 quotient gf2quot(G,a,b) 
Galois-field            with characteristic 2 quotient pgf2quot(r,G,P1,P2) 
			(MACRO) polynomial over 
Galois-field            with characteristic 2 remainder pgf2rem(r,G,P1,P2) 
			(MACRO) polynomial over 
Galois-field            with characteristic 2 remainder, special version 
			udpgf2remsp(G,P1,P2,ilc) univariate dense 
			polynomial over 
Galois-field            with characteristic 2 square (rekursiv) 
			pgf2square(r,G,P) polynomial over 
Galois-field            with characteristic 2 square gf2squ(G,a) 
Galois-field            with characteristic 2 square with arithmetic list 
			gf2squAL(AL,a) 
Galois-field            with characteristic 2 squarefree factorization 
			(rekursiv) upgf2sfact(G,P) univariate polynomial 
			over 
Galois-field            with characteristic 2 sum (rekursiv) 
			pgf2sum(r,G,P1,P2) polynomial over 
Galois-field            with characteristic 2 sum gf2sum(G,a,b) 
Galois-field            with characteristic 2 to polynomial over 
			Galois-field with single characteristic (rekursiv) 
			pgf2topgfs(r,G,P) polynomial over 
Galois-field            with characteristic 2 transformation 
			pgf2transf(r1,G,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over 
Galois-field            with characteristic 2, 2^m-th power of variable, 
			polynomial, remainder upgf22pvprem(G,m,P) 
			univariate polynomial over 
Galois-field            with characteristic 2, Ben-Or factorization 
			upgf2bofact(G,P) univariate polynomial over 
Galois-field            with characteristic 2, Galois-field with 
			characteristic 2 element product (rekursiv) 
			pgf2gf2prod(r,G,P,a) polynomial over 
Galois-field            with characteristic 2, Tate's values b2, b4, b6 
			ecgf2tavb6(G,a1,a2,a3,a4,a6) elliptic curve over 
Galois-field            with characteristic 2, Tate's values b2, b4, b6, b8 
			ecgf2tavb8(G,a1,a2,a3,a4,a6) elliptic curve over 
Galois-field            with characteristic 2, Tate's values c4, c6 
			ecgf2tavc6(G,a1,a2,a3,a4,a6) elliptic curve over 
Galois-field            with characteristic 2, birational transformation of 
			coefficients ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) 
			elliptic curve over 
Galois-field            with characteristic 2, construction of division 
			polynomials ecgf2cdivp(G,a6,m) elliptic curve over 
Galois-field            with characteristic 2, counting algorithm 
			ecgf2npca(G,a6) elliptic curve over 
Galois-field            with characteristic 2, discriminant 
			ecgf2disc(G,a1,a2,a3,a4,a6) elliptic curve over 
Galois-field            with characteristic 2, exponentiation, polynomial 
			remainder pgf2expprem(r,G,F,E,M) polynomial over 
Galois-field            with characteristic 2, find point 
			ecgf2fp(G,a1,a2,a3,a4,a6) elliptic curve over 
Galois-field            with characteristic 2, finding a multiple of the 
			order of a point with the Pollard Lambda method 
			ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) elliptic curve 
			over 
Galois-field            with characteristic 2, j-invariant 
			ecgf2jinv(G,a1,a2,a3,a4,a6) elliptic curve over 
Galois-field            with characteristic 2, line through points 
			ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
Galois-field            with characteristic 2, modified Shanks' algorithm, 
			first part ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) 
			elliptic curve over 
Galois-field            with characteristic 2, modular exponentiation, 
			special version upgf2modexps(G,F,m,P,pM) univariate 
			polynomial over 
Galois-field            with characteristic 2, monomial, polynomial, 
			remainder upgf2mprem(G,a,T,P) univariate polynomial 
			over 
Galois-field            with characteristic 2, multiple of the order of a 
			point to exact order of the point 
			ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve 
			over 
Galois-field            with characteristic 2, multiplication-map 
			ecgf2mul(G,a1,a2,a3,a4,a6,k,P1) elliptic curve 
Galois-field            with characteristic 2, negative point 
			ecgf2neg(G,a1,a2,a3,a4,a6,P) elliptic curve over 
Galois-field            with characteristic 2, number of points modulo a 
			power of 2 ecgf2npmp2(G,a6,c,L) elliptic curve over 
Galois-field            with characteristic 2, number of points modulo a 
			single prime determined with the Schoof algorithm, 
			version 1 ecgf2npmspv1(G,a6,p,L) elliptic curve 
			over 
Galois-field            with characteristic 2, number of points modulo a 
			single prime determined with the Schoof algorithm, 
			version 2 ecgf2npmspv2(G,a6,p,L) elliptic curve 
			over 
Galois-field            with characteristic 2, number of points modulo an 
			integer determined with the Schoof algorithm 
			ecgf2npmi(G,a6,S,v,pM) elliptic curve over 
Galois-field            with characteristic 2, random generator 
			upgf2gen(G,m) univariate polynomial over 
Galois-field            with characteristic 2, separate factor of equal 
			degree upgf2sfed(G,H,d) univariate polynomial over 
Galois-field            with characteristic 2, special form, 
			multiplication-map, special version 
			ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve over 
Galois-field            with characteristic 2, special form, sum of points, 
			special version ecgf2sfsums(G,a6,x1,y1,x2,y2) 
			elliptic curve over 
Galois-field            with characteristic 2, standard representation of 
			projective point ecgf2srpp(G,P) elliptic curve over 
Galois-field            with characteristic 2, sum of points 
			ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve 
			over 
Galois-field            with characteristic 2, trace function, special 
			upgf2tf(G,F,d,M) polynomial over 
Galois-field            with single characteristic (rekursiv) 
			pgf2topgfs(r,G,P) polynomial over Galois-field with 
			characteristic 2 to polynomial over 
Galois-field            with single characteristic (rekursiv) 
			pmstopgfs(r,p,P) polynomial over modular singles to 
			polynomial over 
Galois-field            with single characteristic ? (rekursiv) 
			ispgfs(r,p,AL,P) is polynomial over 
Galois-field            with single characteristic ? ismapgfs(r,p,AL,M) 
			(MACRO) is matrix of polynomials over 
Galois-field            with single characteristic ? isvecpgfs(r,p,AL,V) 
			(MACRO) is vector of polynomials over 
Galois-field            with single characteristic Berlekamp Q polynomials 
			construction upgfsbqp(p,AL,P) univariate polynomial 
			over 
Galois-field            with single characteristic Berlekamp factorization 
			upgfsbfact(p,AL,P,d) univariate polynomial over 
Galois-field            with single characteristic Berlekamp factorization, 
			Zassenhaus method upgfsbfzm(p,AL,s,P,G) univariate 
			polynomial over 
Galois-field            with single characteristic Berlekamp factorization, 
			last step upgfsbfls(p,AL,P,B,d) univariate 
			polynomial over 
Galois-field            with single characteristic Groebner basis 
			augmentation dipgfsgba(r,p,AL,PL,P) distributive 
			polynomial over 
Galois-field            with single characteristic Groebner basis 
			dipgfsgb(r,p,AL,PL) distributive polynomial over 
Galois-field            with single characteristic Groebner basis recursion 
			dipgfsgbr(r,p,AL,PL) distributive polynomial over 
Galois-field            with single characteristic S-polynomial 
			dipgfssp(r,p,AL,P1,P2) distributive polynomial over 
Galois-field            with single characteristic arithmetic list ? 
			isgfsal(p,AL) is 
Galois-field            with single characteristic arithmetic list 
			generator gfsalgen(p,n,G) 
Galois-field            with single characteristic arithmetic list 
			generator isomorphic embedding of subfield 
			gfsalgenies(p,m,n,ALn) 
Galois-field            with single characteristic characteristic 
			polynomial mapgfschpol(r,p,AL,M) (MACRO) matrix of 
			polynomials over 
Galois-field            with single characteristic complete factorization 
			special upgfscfacts(p,AL,P) univariate polynomial 
			over 
Galois-field            with single characteristic complete factorization 
			upgfscfact(p,AL,P) univariate polynomial over 
Galois-field            with single characteristic construction 1 
			mapgfscons1(r,p,AL,n) (MACRO) matrix of polynomials 
			over 
Galois-field            with single characteristic derivation, main 
			variable pgfsderiv(r,p,AL,P) polynomial over 
Galois-field            with single characteristic derivation, specified 
			variable (rekursiv) pgfsderivsv(r,p,AL,P,i) 
			polynomial over 
Galois-field            with single characteristic determinant 
			mapgfsdet(r,p,AL,M) matrix of polynomials over 
Galois-field            with single characteristic difference (rekursiv) 
			pgfsdif(r,p,AL,P1,P2) polynomial over 
Galois-field            with single characteristic difference 
			dipgfsdif(r,p,AL,P1,P2) distributive polynomial 
			over 
Galois-field            with single characteristic difference 
			gfsdif(p,AL,a,b) (MACRO) 
Galois-field            with single characteristic difference 
			mapgfsdif(r,p,AL,M,N) (MACRO) matrix of polynomials 
			over 
Galois-field            with single characteristic difference 
			vecpgfsdif(r,p,AL,U,V) (MACRO) vector of 
			polynomials over 
Galois-field            with single characteristic distinct degree 
			factorization upgfsddfact(p,AL,P) univariate 
			polynomial over 
Galois-field            with single characteristic eigenvalues and 
			irreducible factors of the characteristic 
			polynomial magfsevifcp(p,AL,M,pL) matrix over 
Galois-field            with single characteristic element ? 
			isgfsel(p,AL,a) is 
Galois-field            with single characteristic element evaluation first 
			variable special version (rekursiv) 
			pigfsevalfvs(r,p,AL,P) polynomial over integers 
Galois-field            with single characteristic element evaluation first 
			variable special version mapigfsevfvs(r,p,AL,M) 
			matrix over polynomials over integers 
Galois-field            with single characteristic element evaluation first 
			variable special version vecpigfsefvs(r,p,AL,V) 
			vector over polynomials over integers 
Galois-field            with single characteristic element 
			fgetgfsel(p,AL,V,pf) file get 
Galois-field            with single characteristic element 
			fputgfsel(p,AL,a,V,pf) file put 
Galois-field            with single characteristic element getgfsel(p,AL,V) 
			(MACRO) get 
Galois-field            with single characteristic element 
			gf2eltogfsel(G,a) (MACRO) Galois-field with 
			characteristic 2 element to 
Galois-field            with single characteristic element one ? 
			isgfsone(p,AL,a) is 
Galois-field            with single characteristic element product 
			(rekursiv) pgfsgfsprod(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic, 
Galois-field            with single characteristic element product 
			dipgfsgfprod(r,p,AL,P,a) distributive polynomial 
			over Galois-field with single characteristic, 
Galois-field            with single characteristic element 
			putgfsel(p,AL,a,V) (MACRO) put 
Galois-field            with single characteristic element quotient 
			(rekursiv) pgfsgfsquot(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic, 
Galois-field            with single characteristic element to Galois-field 
			with characteristic 2 element gfseltogf2el(G,a) 
Galois-field            with single characteristic elements ? 
			islistgfs(p,AL,L) is list of 
Galois-field            with single characteristic elements ? 
			ismagfs(p,AL,M) (MACRO) is matrix of 
Galois-field            with single characteristic elements ? 
			isvecgfs(p,AL,A) (MACRO) is vector of 
Galois-field            with single characteristic elements characteristic 
			polynomial magfschpol(p,AL,M) (MACRO) matrix of 
Galois-field            with single characteristic elements construction 1 
			magfscons1(p,AL,n) (MACRO) matrix of 
Galois-field            with single characteristic elements determinant 
			magfsdet(p,AL,M) matrix of 
Galois-field            with single characteristic elements difference 
			magfsdif(p,AL,M,N) (MACRO) matrix of 
Galois-field            with single characteristic elements difference 
			vecgfsdif(p,AL,U,V) (MACRO) vector of 
Galois-field            with single characteristic elements exponentiation 
			magfsexp(p,AL,M,n) matrix of 
Galois-field            with single characteristic elements 
			fgetmagfs(p,AL,V,pf) (MACRO) file get matrix of 
Galois-field            with single characteristic elements 
			fgetvecgfs(p,AL,VL,pf) (MACRO) file get vector of 
Galois-field            with single characteristic elements 
			fputmagfs(p,AL,M,V,pf) (MACRO) file put matrix of 
Galois-field            with single characteristic elements 
			fputvecgfs(p,AL,V,VL,pf) (MACRO) file put vector of 
Galois-field            with single characteristic elements 
			getmagfs(p,AL,V) (MACRO) get matrix of 
Galois-field            with single characteristic elements 
			getvecgfs(p,AL,VL) (MACRO) get vector of 
Galois-field            with single characteristic elements inverse 
			magfsinv(p,AL,M) matrix of 
Galois-field            with single characteristic elements linear 
			combination vecgfslc(p,AL,s1,s2,L1,L2) vector of 
Galois-field            with single characteristic elements negation 
			magfsneg(p,AL,M) (MACRO) matrix of 
Galois-field            with single characteristic elements negation 
			vecgfsneg(p,AL,V) (MACRO) vector of 
Galois-field            with single characteristic elements product 
			magfsprod(p,AL,M,N) (MACRO) matrix of 
Galois-field            with single characteristic elements 
			putmagfs(p,AL,M,V) (MACRO) put matrix of 
Galois-field            with single characteristic elements 
			putvecgfs(p,AL,V,VL) (MACRO) put vector of 
Galois-field            with single characteristic elements rank 
			magfsrk(p,AL,M) matrix of 
Galois-field            with single characteristic elements scalar 
			multiplication magfssmul(p,AL,M,el) matrix of 
Galois-field            with single characteristic elements scalar 
			multiplication vecgfssmul(p,AL,V,el) vector of 
Galois-field            with single characteristic elements scalar product 
			vecgfssprod(p,AL,V,W) vector of 
Galois-field            with single characteristic elements solution of a 
			system of linear equations 
			magfsssle(p,AL,A,b,pX,pN) matrix of 
Galois-field            with single characteristic elements sum 
			magfssum(p,AL,M,N) (MACRO) matrix of 
Galois-field            with single characteristic elements sum 
			vecgfssum(p,AL,U,V) (MACRO) vector of 
Galois-field            with single characteristic elements vector 
			multiplication magfsvecmul(p,AL,A,x) (MACRO) matrix 
			of 
Galois-field            with single characteristic elements, null space 
			basis magfsnsb(p,AL,M) matrix of 
Galois-field            with single characteristic embedding in field 
			extension (rekursiv) pgfsefe(r,p,ALm,P,g) 
			polynomial over 
Galois-field            with single characteristic embedding in field 
			extension gfsefe(p,ALm,a,g) 
Galois-field            with single characteristic embedding in field 
			extension magfsefe(p,ALm,M,g) matrix over 
Galois-field            with single characteristic embedding in field 
			extension mapgfsefe(r,p,ALm,M,g) matrix over 
			polynomials over 
Galois-field            with single characteristic embedding in field 
			extension vecgfsefe(p,ALm,V,g) vector over 
Galois-field            with single characteristic embedding in field 
			extension vecpgfsefe(r,p,ALm,V,g) vector over 
			polynomials over 
Galois-field            with single characteristic evaluation, main 
			variable pgfseval(r,p,AL,P,a) polynomial over 
Galois-field            with single characteristic evaluation, specified 
			variable (rekursiv) pgfsevalsv(r,p,AL,P,d,a) 
			polynomial over 
Galois-field            with single characteristic exponentiation 
			gfsexp(p,AL,a,m) 
Galois-field            with single characteristic exponentiation 
			mapgfsexp(r,p,AL,M,n) matrix of polynomials over 
Galois-field            with single characteristic exponentiation 
			pgfsexp(r,p,AL,P,m) polynomial over 
Galois-field            with single characteristic extended greatest common 
			divisor upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate 
			polynomial over 
Galois-field            with single characteristic 
			fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get 
			matrix of polynomials over 
Galois-field            with single characteristic 
			fgetpgfs(r,p,AL,V,Vgfs,pf) file get polynomial over 
Galois-field            with single characteristic 
			fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get vector 
			of polynomials over 
Galois-field            with single characteristic 
			fputmapgfs(r,p,AL,M,V,Vgfs,pf) (MACRO) file put 
			matrix of polynomials over 
Galois-field            with single characteristic 
			fputvpgfs(r,p,AL,W,V,Vgfs,pf) (MACRO) file put 
			vector of polynomials over 
Galois-field            with single characteristic getmapgfs(r,p,AL,V,Vgfs) 
			(MACRO) get matrix of polynomials over 
Galois-field            with single characteristic getpgfs(r,p,AL,V,Vgfs) 
			(MACRO) get polynomial over 
Galois-field            with single characteristic getvpgfs(r,p,AL,V,Vgfs) 
			(MACRO) get vector of polynomials over 
Galois-field            with single characteristic greatest common divisor 
			upgfsgcd(p,AL,P1,P2) univariate polynomial over 
Galois-field            with single characteristic greatest squarefree 
			divisor (rekursiv) upgfsgsd(p,AL,P) univariate 
			polynomial over 
Galois-field            with single characteristic half extended greatest 
			common divisor upgfshegcd(p,AL,P1,P2,pP3) 
			univariate polynomial over 
Galois-field            with single characteristic in graduated 
			lexicographical order dipgfslotglo(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over 
Galois-field            with single characteristic in lexicographical order 
			to distributive polynomial over Galois-field with 
			single characteristic in graduated lexicographical 
			order dipgfslotglo(r,p,AL,P) distributive 
			polynomial over 
Galois-field            with single characteristic in lexicographical order 
			to distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over 
Galois-field            with single characteristic in lexicographical order 
			to distributive polynomial over Galois-field with 
			single characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) distributive polynomial over 
Galois-field            with single characteristic in lexicographical order 
			with inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over 
Galois-field            with single characteristic inverse gfsinv(p,AL,a) 
Galois-field            with single characteristic inverse 
			mapgfsinv(r,p,AL,M) matrix of polynomials over 
Galois-field            with single characteristic linear combination 
			vecpgfslc(r,p,AL,s1,s2,L1,L2) vector of polynomials 
			over 
Galois-field            with single characteristic list 
			fgetdipgfsl(r,p,AL,VL,Vgfs,pf) file get 
			distributive polynomial over 
Galois-field            with single characteristic list 
			fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put 
			distributive polynomial over 
Galois-field            with single characteristic list 
			getdipgfsl(r,p,AL,VL,Vgfs) (MACRO) get distributive 
			polynomial over 
Galois-field            with single characteristic list 
			putdipgfsl(r,p,AL,PL,VL,Vgfs) (MACRO) put 
			distributive polynomial over 
Galois-field            with single characteristic maitomagfs(p,M) matrix 
			over integers to matrix over 
Galois-field            with single characteristic monic 
			dipgfsmonic(r,p,AL,P) distributive polynomial over 
Galois-field            with single characteristic monic 
			pgfsmonic(r,p,AL,P) polynomial over 
Galois-field            with single characteristic mpgfstompmp(r,p,AL,P,M) 
			matrix of polynomials over Galois-field with single 
			characteristic to matrix of polynomials modulo 
			polynomial over 
Galois-field            with single characteristic mpmstompgfs(r,p,M) 
			matrix of polynomials over modular singles to 
			matrix of polynomials over 
Galois-field            with single characteristic negation (rekursiv) 
			pgfsneg(r,p,AL,P) polynomial over 
Galois-field            with single characteristic negation as function 
			gfsnegf(p,AL,a) 
Galois-field            with single characteristic negation 
			dipgfsneg(r,p,AL,P) distributive polynomial over 
Galois-field            with single characteristic negation gfsneg(p,AL,a) 
			(MACRO) 
Galois-field            with single characteristic negation 
			mapgfsneg(r,p,AL,M) (MACRO) matrix of polynomials 
			over 
Galois-field            with single characteristic negation 
			vecpgfsneg(r,p,AL,V) (MACRO) vector of polynomials 
			over 
Galois-field            with single characteristic number of irreducible 
			factors upgfsnif(p,AL,P) univariate polynomial over 
Galois-field            with single characteristic product (rekursiv) 
			pgfsprod(r,p,AL,P1,P2) polynomial over 
Galois-field            with single characteristic product 
			dipgfsprod(r,p,AL,P1,P2) distributive polynomial 
			over 
Galois-field            with single characteristic product 
			gfsprod(p,AL,a,b) 
Galois-field            with single characteristic product 
			mapgfsprod(r,p,AL,M,N) (MACRO) matrix of 
			polynomials over 
Galois-field            with single characteristic 
			putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) put matrix of 
			polynomials over 
Galois-field            with single characteristic 
			putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) put vector of 
			polynomials over 
Galois-field            with single characteristic quotient and remainder 
			(rekursiv) pgfsqrem(r,p,AL,P1,P2,pR) polynomial 
			over 
Galois-field            with single characteristic quotient 
			gfsquot(p,AL,a,b) 
Galois-field            with single characteristic quotient 
			pgfsquot(r,p,AL,P1,P2) (MACRO) polynomial over 
Galois-field            with single characteristic randomize 
			upgfsrand(p,AL,m) univariate polynomial over 
Galois-field            with single characteristic randomize, positive 
			degree upgfsrandpd(p,AL,m) univariate polynomial 
			over 
Galois-field            with single characteristic relative prime 
			factorization upgfsrelpfac(p,AL,P,Fak,pA2) 
			univariate polynomial over 
Galois-field            with single characteristic remainder 
			pgfsrem(r,p,AL,P1,P2) (MACRO) polynomial over 
Galois-field            with single characteristic resultant 
			pgfsres(r,p,AL,P1,P2) polynomial over 
Galois-field            with single characteristic root finding (rekursiv) 
			upgfsrf(p,AL,P) univariate polynomial over 
Galois-field            with single characteristic scalar multiplication 
			mapgfssmul(r,p,AL,M,el) matrix of polynomials over 
Galois-field            with single characteristic scalar multiplication 
			vecpgfssmul(r,p,AL,V,el) vector of polynomials over 
Galois-field            with single characteristic scalar product 
			vpgfssprod(r,p,AL,V,W) vector of polynomials over 
Galois-field            with single characteristic squarefree factorization 
			(rekursiv) upgfssfact(p,AL,P) univariate polynomial 
			over 
Galois-field            with single characteristic squarefree part 
			upgfssfp(p,AL,P) univariate polynomial over 
Galois-field            with single characteristic sum (rekursiv) 
			pgfssum(r,p,AL,P1,P2) polynomial over 
Galois-field            with single characteristic sum as function 
			gfssumf(p,AL,a,b) 
Galois-field            with single characteristic sum 
			dipgfssum(r,p,AL,P1,P2) distributive polynomial 
			over 
Galois-field            with single characteristic sum gfssum(p,AL,a,b) 
			(MACRO) 
Galois-field            with single characteristic sum 
			mapgfssum(r,p,AL,M,N) (MACRO) matrix of polynomials 
			over 
Galois-field            with single characteristic sum 
			vecpgfssum(r,p,AL,U,V) (MACRO) vector of 
			polynomials over 
Galois-field            with single characteristic to matrix of polynomials 
			modulo polynomial over Galois-field with single 
			characteristic mpgfstompmp(r,p,AL,P,M) matrix of 
			polynomials over 
Galois-field            with single characteristic to polynomial over 
			Galois-field with characteristic 2 (rekursiv) 
			pgfstopgf2(r,G,P) polynomial over 
Galois-field            with single characteristic to vector of polynomials 
			modulo polynomial over Galois-field with single 
			characteristic vpgfstovpmp(r,p,AL,P,V) vector of 
			polynomials over 
Galois-field            with single characteristic transformation 
			mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) matrix 
			of polynomials over 
Galois-field            with single characteristic transformation 
			pgfstransf(r1,p,AL,P1,V1,r2,P2,V2,Vn,pV3) 
			polynomial over 
Galois-field            with single characteristic transformation 
			vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) vector 
			of polynomials over 
Galois-field            with single characteristic vecitovecgfs(p,V) vector 
			over integers to vector over 
Galois-field            with single characteristic vector multiplication 
			mapgfsvmul(r,p,AL,A,x) (MACRO) matrix of 
			polynomials over 
Galois-field            with single characteristic vpgfstovpmp(r,p,AL,P,V) 
			vector of polynomials over Galois-field with single 
			characteristic to vector of polynomials modulo 
			polynomial over 
Galois-field            with single characteristic vpmstovpgfs(r,p,V) 
			vector of polynomials over modular singles to 
			vector of polynomials over 
Galois-field            with single characteristic with total degree 
			ordering dipgfslottdo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over 
Galois-field            with single characteristic, Ben-Or factorization 
			upgfsbofact(p,AL,P) univariate polynomial over 
Galois-field            with single characteristic, Ben-Or factorization, 
			special upgfsbofacts(p,AL,P) univariate polynomial 
			over 
Galois-field            with single characteristic, Galois-field with 
			single characteristic element product (rekursiv) 
			pgfsgfsprod(r,p,AL,P,a) polynomial over 
Galois-field            with single characteristic, Galois-field with 
			single characteristic element product 
			dipgfsgfprod(r,p,AL,P,a) distributive polynomial 
			over 
Galois-field            with single characteristic, Galois-field with 
			single characteristic element quotient (rekursiv) 
			pgfsgfsquot(r,p,AL,P,a) polynomial over 
Galois-field            with single characteristic, element randomize 
			gfselrand(p,AL) 
Galois-field            with single characteristic, exponentiation, 
			polynomial remainder pgfsexpprem(r,p,AL,F,E,M) 
			polynomial over 
Galois-field            with single characteristic, separate factors of 
			equal degree upgfssfed(p,AL,G,d) univariate 
			polynomial over 
Galois-field            with single characteristic, trace function 
			upgfstf(p,AL,G,d,M) univariate polynomial over 
Galois-field,           monomial, integer exponentiation, polynomial, 
			remainder upgfsmieprem(p,AL,a,t,P) univariate 
			polynomial over 
Galois-field,           monomial, polynomial, remainder 
			upgfsmprem(p,AL,a,T,P) univariate polynomial over 
Gauss-                  step for columns maiegsc(M,A,B) matrix of integers 
			Euklid- 
Gauss-                  step for columns maupmipegsc(p,M,A,B) matrix of 
			univariate polynomials over modular integer primes 
			Euklid- 
Gauss-                  step for columns maupmspegsc(p,M,A,B) matrix of 
			univariate polynomials over modular single primes 
			Euklid- 
Gauss-                  step for columns maupregsc(M,A,B) matrix of 
			univariate polynomials over rationals Euklid- 
Gauss-                  step for rows maiegsr(M,A,B) matrix of integers 
			Euklid- 
Gauss-                  step for rows maupmipegsr(p,M,A,B) matrix of 
			univariate polynomials over modular integer primes 
			Euklid- 
Gauss-                  step for rows maupmspegsr(p,M,A,B) matrix of 
			univariate polynomials over modular single primes 
			Euklid- 
Gauss-                  step for rows maupregsr(M,A,B) matrix of univariate 
			polynomials over rationals Euklid- 
Gelfond-factor          coefficient bound pigfcb(r,P) polynomial over 
			integers 
Goldwasser              Kilian Atkin primality test (rekursiv) 
			igkapt(n,msg) integer 
Groebner                basis augmentation dipgfsgba(r,p,AL,PL,P) 
			distributive polynomial over Galois-field with 
			single characteristic 
Groebner                basis augmentation dipigba(r,PL,P) distributive 
			polynomial over integers 
Groebner                basis augmentation dipmipgba(r,p,PL,P) distributive 
			polynomial over modular integer primes 
Groebner                basis augmentation dipmspgba(r,p,PL,P) distributive 
			polynomial over modular single primes 
Groebner                basis augmentation dipnfgba(r,F,PL,P) distributive 
			polynomial over number field 
Groebner                basis augmentation dippigba(r1,r2,PL,P) 
			distributive polynomial over polynomials over 
			integers 
Groebner                basis augmentation diprfrgba(r1,r2,PL,P) 
			distributive polynomial over rational functions 
			over the rationals 
Groebner                basis augmentation diprgba(r,PL,P) distributive 
			polynomial over rationals 
Groebner                basis dipgfsgb(r,p,AL,PL) distributive polynomial 
			over Galois-field with single characteristic 
Groebner                basis dipigb(r,PL) distributive polynomial over 
			integers 
Groebner                basis dipmipgb(r,p,PL) distributive polynomial over 
			modular integer primes 
Groebner                basis dipmspgb(r,p,PL) distributive polynomial over 
			modular single primes 
Groebner                basis dipnfgb(r,F,PL) distributive polynomial over 
			number field 
Groebner                basis 
			dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers comprehensive 
Groebner                basis dippigb(r1,r2,PL) distributive polynomial 
			over polynomials over integers 
Groebner                basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers reduced comprehensive 
Groebner                basis diprfrgb(r1,r2,PL) distributive polynomial 
			over rational functions over the rationals 
Groebner                basis diprgb(r,PL) distributive polynomial over 
			rationals 
Groebner                basis fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file 
			put distributive polynomial over polynomials over 
			integers comprehensive 
Groebner                basis putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers comprehensive 
Groebner                basis recursion dipgfsgbr(r,p,AL,PL) distributive 
			polynomial over Galois-field with single 
			characteristic 
Groebner                basis recursion dipigbr(r,PL) distributive 
			polynomial over integers 
Groebner                basis recursion dipmipgbr(r,p,PL) distributive 
			polynomial over modular integer primes 
Groebner                basis recursion dipmspgbr(r,p,PL) distributive 
			polynomial over modular single primes 
Groebner                basis recursion dipnfgbr(r,F,PL) distributive 
			polynomial over number field 
Groebner                basis recursion dippigbr(r1,r2,PL) distributive 
			polynomial over polynomials over integers 
Groebner                basis recursion diprfrgbr(r1,r2,PL) distributive 
			polynomial over rational functions over the 
			rationals 
Groebner                basis recursion diprgbr(r,PL) distributive 
			polynomial over rationals 
Groebner                system fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file 
			put distributive polynomial over polynomials over 
			integers 
Groebner                system putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) put 
			distributive polynomial over polynomials over 
			integers 
Groebner                test dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) 
			distributive polynomial over polynomials over 
			integers 
Groebner                test fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) 
			file put distributive polynomial over polynomials 
			over integers 
Groebner                test putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) 
			(MACRO) put distributive polynomial over 
			polynomials over integers 
HDiadd()                Heidelberg arithmetic package: integer addition 
HDidigit()              Heidelberg arithmetic package: digit functions 
HDidigitvec()           Heidelberg arithmetic package: vector functions 
HDidiv()                Heidelberg arithmetic package: integer division 
HDigcd()                Heidelberg arithmetic package: greatest common 
			divisor 
HDiio()                 Heidelberg arithmetic package: I/O functions 
HDimem()                Heidelberg arithmetic package: memory management 
HDimul()                Heidelberg arithmetic package: integer 
			multiplication 
HDiutil()               Heidelberg arithmetic package: utilities 
Hankel                  matrix pmidiscrhank(r,M,P) polynomial over modular 
			integers discriminant via 
Hankel-                 matrix pidiscrhank(r,P) polynomial over integers 
			discriminant via 
Heidelberg              ) Integer itoI(A,h) ( SIMATH ) integer to ( 
Heidelberg              ) Integer special version itoI_sp(A,lA,h) ( SIMATH 
			) integer to ( 
Heidelberg              ) Integer to ( SIMATH ) integer Itoi(h) ( 
Heidelberg              arithmetic functions 
			iHDfu(func,anzahlargs,arg1,arg2) integer using 
Heidelberg              arithmetic package: I/O functions HDiio() 
Heidelberg              arithmetic package: digit functions HDidigit() 
Heidelberg              arithmetic package: greatest common divisor 
			HDigcd() 
Heidelberg              arithmetic package: integer addition HDiadd() 
Heidelberg              arithmetic package: integer division HDidiv() 
Heidelberg              arithmetic package: integer multiplication HDimul() 
Heidelberg              arithmetic package: memory management HDimem() 
Heidelberg              arithmetic package: utilities HDiutil() 
Heidelberg              arithmetic package: vector functions HDidigitvec() 
Hensel                  factorization approximation upprmsp1hfa(p,F,P,L,k) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
Hensel                  lemma factorization approximation 
			pihlfa(r,p,L,M,S,P) polynomial over integers, 
Hensel                  lemma factorization approximation upihlfa(p,P,L,k) 
			univariate polynomial over the integers, 
Hensel                  lemma factorization approximation with respect to 
			integer prime upihlfaip(p,P,L,k) univariate 
			polynomial over integers, 
Hensel                  lemma initialization upihli(p,P,L) univariate 
			polynomial over integers, 
Hensel                  lemma initialization upprmsp1hli(p,F,P,L) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
Hensel                  lemma initialization with respect to integer prime 
			upihliip(P,F,L) univariate polynomial over 
			integers, 
Hensel                  lemma quadratic step on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
			modular integers, modular ideal, 
Hensel                  lemma quadratic step 
			pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial over 
			integers, modular ideal, 
Hensel                  lemma quadratic step 
			pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial 
			over modular integers, modular ideal, 
Hensel                  lemma quadratic step upihlqs(p,p_k,p_l,P,L1,L2,A) 
			univariate polynomial over integers, 
Hensel                  lemma quadratic step with respect to integer prime 
			upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over integers, 
Hensel                  quadratic step upprmsp1hqs(p,F,T,L1,L2,A) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
Hermite                 normal form ( lower triangular form with negative 
			entries ) maihermltne(A) (MACRO) matrix of integers 
Hermite                 normal form ( lower triangular form with positive 
			entries ) maihermltpe(A) (MACRO) matrix of integers 
Hermite                 normal form maiherm(A,ne) matrix of integers 
I/O                     functions HDiio() Heidelberg arithmetic package: 
I/O-functions           PAFio() Papanikolaou floating point package: 
I/O-operations          errmsgio(name,errno) error message, 
Integer                 itoI(A,h) ( SIMATH ) integer to ( Heidelberg ) 
Integer                 special version itoI_sp(A,lA,h) ( SIMATH ) integer 
			to ( Heidelberg ) 
Integer                 to ( SIMATH ) integer Itoi(h) ( Heidelberg ) 
Itoi(h)                 ( Heidelberg ) Integer to ( SIMATH ) integer 
Jacobi-symbol           ( Legendre-symbol ) ipjacsym(a,p) integer prime 
Jacobi-symbol           ( lists only ) ijacsym_lo(A,B) integer 
Jacobi-symbol           ijacsym(A,B) integer 
Jacobi-symbol           udpmijacsym(m,P1,P2) univariate dense polynomial 
			over modular integers 
Jacobi-symbol           udpmsjacsym(m,P1,P2) univariate dense polynomial 
			over modular singles 
Jacobi-symbol           upmijacsym(m,P1,P2) univariate polynomial over 
			modular integers 
Jacobi-symbol           upmsjacsym(m,P1,P2) univariate polynomial over 
			modular singles 
Jacobi-symbols          udpmssumjs(m,P,n) univariate dense polynomial over 
			modular singles, summation over 
Kant                    StoK(D,struc,data,type,digits) SIMATH to 
Kant                    string StoKstr(str,D,typ,prec) SIMATH to 
Kant                    string to SIMATH KstrtoS(a) 
Kant                    to SIMATH KtoS(struc,data,type) 
Kilian                  Atkin primality test (rekursiv) igkapt(n,msg) 
			integer Goldwasser 
KstrtoS(a)              Kant string to SIMATH 
KtoS(struc,data,type)   Kant to SIMATH 
L-                      series ecrclser(E,A,n) elliptic curve over the 
			rationals, coefficients of 
L-series                ecrfelser(E,A,z,result) elliptic curve over 
			rational numbers, Fourier expansion of the 
L-series                ecrlser(E) elliptic curve over rational numbers, 
L-series,               'rank'-th derivative ecrlserrkd(E) elliptic curve 
			over the rationals, 
L-series,               first derivative ecrlserfd(E) elliptic curve over 
			rational numbers, 
L-series,               first derivative, special version 
			ecrlserfds(E,A,result) elliptic curve over the 
			rationals, 
L-series,               higher derivative ecrlserhd(E,r) elliptic curve 
			over rational numbers, 
L-series,               higher derivative, large conductor 
			ecrlserhdlc(E,A,s,result) elliptic curve over the 
			rationals, 
L-series,               higher derivative, small conductor 
			ecrlserhdsc(E,A,r,result) elliptic curve over 
			rational numbers, 
L-series,               special version ecrlsers(E,A,result) elliptic curve 
			over the rationals, 
LLL                     - reduced ? isbasilllred(bas) is basis over the 
			integers 
LLL                     reduction marlllred(bas) matrix of rationals, 
LLL                     reduction modilllred(bas) module over the integers, 
Lambda                  method ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) 
			elliptic curve over Galois-field with 
			characteristic 2, finding a multiple of the order 
			of a point with the Pollard 
Lambda                  method ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve 
			over modular primes, short normal form, finding a 
			multiple of the order of a point with the Pollard 
Landau-                 Mignotte- factor coefficient bound pilmfcb(r,P) 
			polynomial over integers 
Laska's                 algorithm ) ecractoecimin(E) elliptic curve over 
			rational numbers, actual curve to global minimal 
			model ( 
Legendre-symbol         ) ipjacsym(a,p) integer prime Jacobi-symbol ( 
Manin                   algorithm ecrmaninalg(E) elliptic curve over 
			rational numbers, 
Mignotte-               factor coefficient bound pilmfcb(r,P) polynomial 
			over integers Landau- 
Mordell-Weil-group,     base eciminmwgbase(E) elliptic curve with integer 
			coefficients, minimal model, 
Mordell-Weil-group,     base ecisnfmwgbase(E) elliptic curve with integer 
			coefficients, short normal form, 
Mordell-Weil-group,     base ecracmwgbase(E) elliptic curve over the 
			rational numbers, actual curve, 
NTH_EPS                 eciminntheps(E,d) elliptic curve with integer 
			coefficients, minimal model, set 
Neron-Tate              height ecimindwhnth(E) elliptic curve with integer 
			coefficients, minimal model, difference between 
			Weil height and 
Neron-Tate              height eciminnetahe(E,P) elliptic curve with 
			integer coefficients, minimal model, 
Neron-Tate              height ecisnfdwhnth(E) elliptic curve with integer 
			coefficients, short normal form, difference between 
			Weil height and 
Neron-Tate              pairing eciminnetapa(E,P,Q) elliptic curve with 
			integer coefficients, minimal model, 
ORDMAX,                 Ordmax, ordmax, integral basis ) ouspibasisic(F,pL) 
			order of an univariate separable polynomial over 
			the integers basis of the integral closure ( 
Ordmax,                 ordmax, integral basis ) ouspibasisic(F,pL) order 
			of an univariate separable polynomial over the 
			integers basis of the integral closure ( ORDMAX, 
P-adic                  factorization uspprmsp1apf(p,P,F,k) univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			approximation of 
P-adic                  valuation of an element of the polynomial order of 
			a univariate separable polynomial over the 
			polynomial ring over modular single prime, 
			transcendence degree 1 vepepuspmsp1(p,F,a,P,k,v) 
			values of the extensions of the 
P-part                  with respect to an integer intppint(P,A) integer 
P-primality             test and factorization of the defining polynomial 
			or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
			modular single prime, transcendence degree 1, 
P-primary               number field element, core algorithm with respect 
			to integer primes ippnfecalip(F,P,Q,mp) integral 
P-star                  valuation iafmsp1psval(p,P,A) integral algebraic 
			function over modular single prime, transcendence 
			degree 1, 
P-star                  value afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) 
			algebraic function over modular single primes, 
			transcendence degree 1, increasing the denominator 
			of the 
PAFadd()                Papanikolaou floating point package: addition 
PAFassign()             Papanikolaou floating point package: assignments 
PAFcomp()               Papanikolaou floating point package: comparisons 
PAFcon()                Papanikolaou floating point package: construction 
PAFdiv()                Papanikolaou floating point package: division 
PAFglob()               Papanikolaou floating point package: globals 
PAFio()                 Papanikolaou floating point package: I/O-functions 
PAFmul()                Papanikolaou floating point package: multiplication 
PAFshift()              Papanikolaou floating point package: shiftings 
PAFsub()                Papanikolaou floating point package: subtraction 
PAFtofl(x)              Papanikolaou floating point to ( SIMATH ) floating 
			point 
PAFtrans1()             Papanikolaou floating point package: transcendental 
			functions 1 
PAFtrans2()             Papanikolaou floating point package: transcendental 
			functions 2 
PAFtrans3()             Papanikolaou floating point package: transcendental 
			functions 3 
PAFtype()               Papanikolaou floating point package: typer 
PAFutil()               Papanikolaou floating point package: utilities 
Papanikolaou            floating point fltoPAF(f,x) ( SIMATH ) floating 
			point to 
Papanikolaou            floating point functions 
			flPAFfu(func,anzahlargs,arg1,arg2) floating point 
			using 
Papanikolaou            floating point package: I/O-functions PAFio() 
Papanikolaou            floating point package: addition PAFadd() 
Papanikolaou            floating point package: assignments PAFassign() 
Papanikolaou            floating point package: comparisons PAFcomp() 
Papanikolaou            floating point package: construction PAFcon() 
Papanikolaou            floating point package: division PAFdiv() 
Papanikolaou            floating point package: globals PAFglob() 
Papanikolaou            floating point package: multiplication PAFmul() 
Papanikolaou            floating point package: shiftings PAFshift() 
Papanikolaou            floating point package: subtraction PAFsub() 
Papanikolaou            floating point package: transcendental functions 1 
			PAFtrans1() 
Papanikolaou            floating point package: transcendental functions 2 
			PAFtrans2() 
Papanikolaou            floating point package: transcendental functions 3 
			PAFtrans3() 
Papanikolaou            floating point package: typer PAFtype() 
Papanikolaou            floating point package: utilities PAFutil() 
Papanikolaou            floating point to ( SIMATH ) floating point 
			PAFtofl(x) 
Pi                      flPi() floating point 
Pollard                 Lambda method ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) 
			elliptic curve over Galois-field with 
			characteristic 2, finding a multiple of the order 
			of a point with the 
Pollard                 Lambda method ecmpsnffmopl(p,a4,a6,P,L,N) elliptic 
			curve over modular primes, short normal form, 
			finding a multiple of the order of a point with the 
Pollard                 Rho method ecmpsnffmopr(p,a4,a6,P,k) elliptic curve 
			over modular primes, short normal form, finding a 
			multiple of the order of a point with the 
Pollard                 divisor search ( lists only ) rhopds_lo(N,b,z) rho- 
			method by 
Pollard                 divisor search rhofrpds(N,b,z) rho- method ( fast 
			reduction ) by 
Pollard                 divisor search rhopds(N,b,z) rho- method by 
Rho                     method ecmpsnffmopr(p,a4,a6,P,k) elliptic curve 
			over modular primes, short normal form, finding a 
			multiple of the order of a point with the Pollard 
S-polynomial            dipgfssp(r,p,AL,P1,P2) distributive polynomial over 
			Galois-field with single characteristic 
S-polynomial            dipisp(r,P1,P2) distributive polynomial over 
			integers 
S-polynomial            dipmipsp(r,p,P1,P2) distributive polynomial over 
			modular integer primes 
S-polynomial            dipmspsp(r,p,P1,P2) distributive polynomial over 
			modular single primes 
S-polynomial            dipnfsp(r,F,P1,P2) distributive polynomial over 
			number field 
S-polynomial            dippisp(r1,r2,P1,P2) distributive polynomial over 
			polynomials over integers 
S-polynomial            diprfrsp(r1,r2,P1,P2) distributive polynomial over 
			rational functions over the rationals 
S-polynomial            diprsp(r,P1,P2) distributive polynomial over 
			rationals 
SIMATH                  ) floating point PAFtofl(x) Papanikolaou floating 
			point to ( 
SIMATH                  ) floating point to Papanikolaou floating point 
			fltoPAF(f,x) ( 
SIMATH                  ) integer Itoi(h) ( Heidelberg ) Integer to ( 
SIMATH                  ) integer to ( Heidelberg ) Integer itoI(A,h) ( 
SIMATH                  ) integer to ( Heidelberg ) Integer special version 
			itoI_sp(A,lA,h) ( 
SIMATH                  ) integer to Essen integer itoE(A,e) ( 
SIMATH                  ) integer to Essen integer with upper bound 
			itoEb(A,e,grenze) ( 
SIMATH                  ) integer to Essen integer, sign and upper bound 
			itoEsb(A,e,grenze) ( 
SIMATH                  KstrtoS(a) Kant string to 
SIMATH                  KtoS(struc,data,type) Kant to 
SIMATH                  divs(A,B) (MACRO) division with reference to 
SIMATH                  integer Etoi(e) Essen integer to 
SIMATH                  integer negation Etoineg(e) Essen integer to 
SIMATH                  mods(A,B) (MACRO) modulo with reference to 
SIMATH                  to Kant StoK(D,struc,data,type,digits) 
SIMATH                  to Kant string StoKstr(str,D,typ,prec) 
SPACE                   setspace(anz) set 
STACK                   ? isbound(pL) is bound in 
STACK                   setstack(anz) set 
Schoof                  algorithm ecgf2npmi(G,a6,S,v,pM) elliptic curve 
			over Galois-field with characteristic 2, number of 
			points modulo an integer determined with the 
Schoof                  algorithm ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve 
			over modular primes, short normal form, number of 
			points modulo an integer determined with the 
Schoof                  algorithm ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve 
			over modular primes, short normal form, number of 
			points modulo a single prime determined with the 
Schoof                  algorithm, version 1 ecgf2npmspv1(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, number of points modulo a single 
			prime determined with the 
Schoof                  algorithm, version 2 ecgf2npmspv2(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, number of points modulo a single 
			prime determined with the 
Schoof-                 Shanks- algorithm ecgf2cssa(G,a6,s,pl,ts) elliptic 
			curve over Galois field with characteristic 2, 
			combined 
Schoof-                 Shanks- algorithm ecmpsnfcssa(p,a4,a6,s,pl,ts) 
			elliptic curve over modular primes, short normal 
			form, combined 
Selfridge               primality test ispt(M,M1,F) integer 
Shafarevic              group ecrordtsg(E) elliptic curve over the rational 
			numbers, order of Tate- 
Shanks'                 algorithm ecmspsnfsha(p,a4,a6) (MACRO) elliptic 
			curve over modular single primes, short normal 
			form, 
Shanks'                 algorithm, first part 
			ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) elliptic 
			curve over Galois-field with characteristic 2, 
			modified 
Shanks'                 algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over modular primes, short normal form, modified 
Shanks-                 algorithm ecgf2cssa(G,a6,s,pl,ts) elliptic curve 
			over Galois field with characteristic 2, combined 
			Schoof- 
Shanks-                 algorithm ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic 
			curve over modular primes, short normal form, 
			combined Schoof- 
StoK(D,struc,data,type,digits) SIMATH to Kant 
StoKstr(str,D,typ,prec) SIMATH to Kant string 
Sylvester               algorithm piressylv(r,P1,P2) polynomial over 
			integers resultant, 
Sylvester               algorithm pprmsp1ress(r,p,P1,P2) polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, resultant, 
Sylvester               algorithm upprmsp1ress(p,P1,P2) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, resultant, 
Sylvester               matrix psylvester(r,P1,P2) polynomial 
Tate                    value b2 ecqnfacb2(E) elliptic curve over quadratic 
			number field, actual model, 
Tate                    value b4 ecqnfacb4(E) elliptic curve over quadratic 
			number field, actual model, 
Tate                    value b6 ecqnfacb6(E) elliptic curve over quadratic 
			number field, actual model, 
Tate                    value b8 ecqnfacb8(E) elliptic curve over quadratic 
			number field, actual model, 
Tate                    value c4 ecqnfacc4(E) elliptic curve over quadratic 
			number field, actual model, 
Tate                    value c6 ecqnfacc6(E) elliptic curve over quadratic 
			number field, actual model, 
Tate's                  algorithm ecimintatealg(E,p,n) elliptic curve with 
			integer coefficients, minimal model, 
Tate's                  algorithm ecitatealg(a1,a2,a3,a4,a6,p,n) elliptic 
			curve with integer coefficients 
Tate's                  algorithm ecqnftatealg(D,LC,LTV,P,pi,z,n) elliptic 
			curve over quadratic number field, 
Tate's                  values b2, b4, b6 ecgf2tavb6(G,a1,a2,a3,a4,a6) 
			elliptic curve over Galois-field with 
			characteristic 2, 
Tate's                  values b2, b4, b6 ecmptavb6(p,a1,a2,a3,a4,a6) 
			elliptic curve over modular primes 
Tate's                  values b2, b4, b6 ecnftavb6(F,a1,a2,a3,a4,a6) 
			elliptic curve over number field 
Tate's                  values b2, b4, b6, b8 ecgf2tavb8(G,a1,a2,a3,a4,a6) 
			elliptic curve over Galois-field with 
			characteristic 2, 
Tate's                  values b2, b4, b6, b8 ecitavalb(a1,a2,a3,a4,a6) 
			elliptic curve with integer coefficients, 
Tate's                  values b2, b4, b6, b8 ecmptavb8(p,a1,a2,a3,a4,a6) 
			elliptic curve over modular primes 
Tate's                  values b2, b4, b6, b8 ecnftavb8(F,a1,a2,a3,a4,a6) 
			elliptic curve over number field 
Tate's                  values b2, b4, b6, b8 ecrtavalb(a1,a2,a3,a4,a6) 
			elliptic curve over rational numbers, 
Tate's                  values c4, c6 ecgf2tavc6(G,a1,a2,a3,a4,a6) elliptic 
			curve over Galois-field with characteristic 2, 
Tate's                  values c4, c6 ecitavalc(a1,a2,a3,a4,a6) elliptic 
			curve with integer coefficients, minimal model, 
Tate's                  values c4, c6 ecmptavc6(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular primes 
Tate's                  values c4, c6 ecnftavc6(F,a1,a2,a3,a4,a6) elliptic 
			curve over number field 
Tate's                  values c4, c6 ecrtavalc(a1,a2,a3,a4,a6) elliptic 
			curve over the rationals 
Tate-                   Shafarevic group ecrordtsg(E) elliptic curve over 
			the rational numbers, order of 
Weber                   function f cweberf(z) complex 
Weber                   function f1 cweberf1(z) complex 
Weber                   function f2 cweberf2(z) complex 
Weil                    height and Neron-Tate height ecimindwhnth(E) 
			elliptic curve with integer coefficients, minimal 
			model, difference between 
Weil                    height and Neron-Tate height ecisnfdwhnth(E) 
			elliptic curve with integer coefficients, short 
			normal form, difference between 
Weil                    height ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) 
			elliptic curve with integer coefficients, short 
			normal form, points of bounded 
Weil                    height ecracweilhe(E,P) elliptic curve over the 
			rational numbers, 
XOR                     product special sxprods(a,b) single 
XOR                     product sxprod(a,b,pc,pd) single 
XOR                     square sxsqu(a,pc,pd) single 
Z-module                homomorphism cdprzmodhom(P,M) common denominator 
			polynomial over the rationals 
Zassenhaus              method upgfsbfzm(p,AL,s,P,G) univariate polynomial 
			over Galois-field with single characteristic 
			Berlekamp factorization, 
Zassenhaus              method upmibfzm(ip,s,P,G) univariate polynomial 
			over modular integers, Berlekamp factorization, 
Zassenhaus              method upmsbfzm(m,s,P,G) univariate polynomial over 
			modular singles, Berlekamp factorization, 
____                    ? isma_(M,is,anzahlargs,arg1,arg2) is matrix of 
____                    ? isvec_(V,is,anzahlargs,arg1,arg2) is vector of 
____,                   special ? ismaspec_(M,is,anzahlargs,arg1,...,arg5) 
			is matrix of 
____,                   special ? isvecspec_(V,is,anzahlargs,arg1,...,arg5) 
			is vector of 
a1                      ecimina1(E) elliptic curve with integer 
			coefficients, minimal model, 
a1                      ecraca1(E) (MACRO) elliptic curve over rational 
			numbers, actual curve, 
a2                      ecimina2(E) elliptic curve with integer 
			coefficients, minimal model, 
a2                      ecraca2(E) (MACRO) elliptic curve over rational 
			numbers, actual curve, 
a3                      ecimina3(E) elliptic curve with integer 
			coefficients, minimal model, 
a3                      ecraca3(E) (MACRO) elliptic curve over rational 
			numbers, actual curve, 
a4                      ecimina4(E) elliptic curve with integer 
			coefficients, minimal model, 
a4                      ecisnfa4(E) elliptic curve with integer 
			coefficients, short normal form, 
a4                      ecraca4(E) (MACRO) elliptic curve over rational 
			numbers, actual curve, 
a6                      ecimina6(E) elliptic curve with integer 
			coefficients, minimal model, 
a6                      ecisnfa6(E) elliptic curve with integer 
			coefficients, short normal form, 
a6                      ecraca6(E) (MACRO) elliptic curve over rational 
			numbers, actual curve, 
abelian                 number field relative class number abnfrelcl(q,g) 
abelian                 number field relative class number modulo prime 
			abnfrelclmp(m,q,g) 
abnfrelcl(q,g)          abelian number field relative class number 
abnfrelclmp(m,q,g)      abelian number field relative class number modulo 
			prime 
absolute                height rabsheight(r) rational number 
absolute                value cabsv(z) complex 
absolute                value eciminlhaav(E,P) elliptic curve with integer 
			coefficients, minimal model, local height at the 
			archimedean 
absolute                value flabs(f) (MACRO) floating point 
absolute                value iabs(A) (MACRO) integer 
absolute                value piabs(r,P) polynomial over integers 
absolute                value rabs(R) (MACRO) rational number 
absolute                value sabs(a) (MACRO) single-precision 
absolute                values eciminlhnaav(E,P) elliptic curve with 
			integer coefficients, minimal model, local heights 
			at all non archimedean 
actual                  ( rational ) model eciminbtac(E) elliptic curve 
			with integer coefficients, minimal model, 
			birational transformation to 
actual                  ( rational ) model ecisnfbtac(E) elliptic curve 
			with integer coefficients, short normal form, 
			birational transformation to 
actual                  curve fputecrac(E,pf) file put elliptic curve over 
			rational numbers, 
actual                  curve putecrac(E) (MACRO) put elliptic curve over 
			rational numbers, 
actual                  curve to global minimal model ( Laska's algorithm ) 
			ecractoecimin(E) elliptic curve over rational 
			numbers, 
actual                  curve, Mordell-Weil-group, base ecracmwgbase(E) 
			elliptic curve over the rational numbers, 
actual                  curve, a1 ecraca1(E) (MACRO) elliptic curve over 
			rational numbers, 
actual                  curve, a2 ecraca2(E) (MACRO) elliptic curve over 
			rational numbers, 
actual                  curve, a3 ecraca3(E) (MACRO) elliptic curve over 
			rational numbers, 
actual                  curve, a4 ecraca4(E) (MACRO) elliptic curve over 
			rational numbers, 
actual                  curve, a6 ecraca6(E) (MACRO) elliptic curve over 
			rational numbers, 
actual                  curve, b2 ecracb2(E) elliptic curve over rational 
			numbers, 
actual                  curve, b4 ecracb4(E) elliptic curve over rational 
			numbers, 
actual                  curve, b6 ecracb6(E) elliptic curve over rational 
			numbers, 
actual                  curve, b8 ecracb8(E) elliptic curve over rational 
			numbers, 
actual                  curve, birational transformation to minimal model 
			ecracbtmin(E) elliptic curve over the rationals, 
actual                  curve, birational transformation to short normal 
			form ecracbtsnf(E) elliptic curve over rational 
			numbers, 
actual                  curve, c4 ecracc4(E) elliptic curve over rational 
			numbers, 
actual                  curve, c6 ecracc6(E) elliptic curve over rational 
			numbers, 
actual                  curve, difference of points ecracdif(E,P,Q) 
			elliptic curve with integer coefficients, 
actual                  curve, discriminant ecracdisc(E) elliptic curve 
			over rational numbers, 
actual                  curve, factorization of discriminant ecracfdisc(E) 
			elliptic curve over rational numbers, 
actual                  curve, generators of torsion group ecracgentor(E) 
			elliptic curve over rational numbers, 
actual                  curve, multiplication-map ecracmul(E,P,n) elliptic 
			curve over the rational numbers, 
actual                  curve, negative point ecracneg(E,P) elliptic curve 
			over the rational numbers, 
actual                  curve, sum of points ecracsum(E,P,Q) elliptic curve 
			over the rational numbers, 
actual                  curve, torsion group ecractorgr(E) elliptic curve 
			over rational numbers, 
actual                  model isponecrac(E,P) is point on elliptic curve 
			over rational numbers, 
actual                  model, Tate value b2 ecqnfacb2(E) elliptic curve 
			over quadratic number field, 
actual                  model, Tate value b4 ecqnfacb4(E) elliptic curve 
			over quadratic number field, 
actual                  model, Tate value b6 ecqnfacb6(E) elliptic curve 
			over quadratic number field, 
actual                  model, Tate value b8 ecqnfacb8(E) elliptic curve 
			over quadratic number field, 
actual                  model, Tate value c4 ecqnfacc4(E) elliptic curve 
			over quadratic number field, 
actual                  model, Tate value c6 ecqnfacc6(E) elliptic curve 
			over quadratic number field, 
actual                  model, discriminant ecqnfacdisc(E) elliptic curve 
			over quadratic number field, 
actual                  model, factorization of the norm of the 
			discriminant ecqnfacfndisc(E) elliptic curve over 
			quadratic number field, 
actual                  model, norm of the discriminant ecqnfacndisc(E) 
			elliptic curve over quadratic number field, 
actual                  model, prime ideal factorization of the 
			discriminant ecqnfacpifdi(E) elliptic curve over 
			quadratic number field, 
addition                HDiadd() Heidelberg arithmetic package: integer 
addition                PAFadd() Papanikolaou floating point package: 
additive                m-adic value iaval(m,A) integer 
additive                m-adic value raval(m,R) rational 
additive                valuation pfaval(p,a) p-adic field 
additive                valuation qnfaval(D,p,a) quadratic number field 
additive                valuation upmiaddval(p,P1,P) univariate polynomial 
			over modular integer prime 
additive                valuation upmsaddval(p,P1,P) univariate polynomial 
			over modular singles 
additive                value with respect to integer iavalint(M,I) integer 
additive                value with respect to integer ravalint(M,R) 
			rational 
adjoin                  matrix maam(M,el) matrix 
advance                 dipmoad(r,P,pLBC,pLEV) distributive polynomial 
			monomial 
affmsp1decl(p,F,P)      algebraic function field over modular single prime, 
			transcendence degree 1, decomposition law 
afmsp1coreal(p,F,P,Q,mp) algebraic function over modular single primes, 
			transcendence degree 1, core algorithm 
afmsp1expsp(p,F,a,e,M)  algebraic function over modular single prime, 
			transcendence degree 1, exponentiation special 
afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic function over modular 
			single primes, transcendence degree 1, increasing 
			the denominator of the P-star value 
afmsp1minpol(p,F,a)     algebraic function over modular single primes, 
			transcendence degree 1, minimal polynomial 
afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over modular single prime, 
			transcendence degree 1, P-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial 
afmsp1prodsp(p,F,a,b,M) algebraic function over modular single prime, 
			transcendence degree 1, product special 
afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) algebraic function over modular single 
			primes, transcendence degree 1, regulation 
after                   field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
			curve over Galois field with characteristic 2, 
			number of points 
algebraic               function field over modular single prime, 
			transcendence degree 1, decomposition law 
			affmsp1decl(p,F,P) 
algebraic               function over modular single prime, transcendence 
			degree 1, P-primality test and factorization of the 
			defining polynomial or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) 
algebraic               function over modular single prime, transcendence 
			degree 1, P-star valuation iafmsp1psval(p,P,A) 
			integral 
algebraic               function over modular single prime, transcendence 
			degree 1, evaluation special upprmsp1afes(p,F,P,a) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
algebraic               function over modular single prime, transcendence 
			degree 1, exponentiation special 
			afmsp1expsp(p,F,a,e,M) 
algebraic               function over modular single prime, transcendence 
			degree 1, product special afmsp1prodsp(p,F,a,b,M) 
algebraic               function over modular single primes, transcendence 
			degree 1, core algorithm afmsp1coreal(p,F,P,Q,mp) 
algebraic               function over modular single primes, transcendence 
			degree 1, increasing the denominator of the P-star 
			value afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) 
algebraic               function over modular single primes, transcendence 
			degree 1, minimal polynomial afmsp1minpol(p,F,a) 
algebraic               function over modular single primes, transcendence 
			degree 1, minimal polynomial iafmsp1mpol(p,F,a,Q) 
			integral 
algebraic               function over modular single primes, transcendence 
			degree 1, minimal polynomial modulo power of an 
			univariate prime polynomial over modular single 
			primes iafmsp1mpmpp(p,F,a,P,e,Q) integral 
algebraic               function over modular single primes, transcendence 
			degree 1, regulation 
			afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) 
alternative             version irand_2(u) integer randomize, 
approximation           of P-adic factorization uspprmsp1apf(p,P,F,k) 
			univariate separable polynomial over polynomial 
			ring over modular single prime, transcendence 
			degree 1, 
approximation           of p-adic factorization of the defining polynomial, 
			generators of p-maximal orders of the p-adic 
			divisors of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable polynomial over 
			the integers 
approximation           of p-adic factorization uspiapf(p,P,k) univariate 
			separable polynomial over the integers, 
approximation           pihlfa(r,p,L,M,S,P) polynomial over integers, 
			Hensel lemma factorization 
approximation           upihlfa(p,P,L,k) univariate polynomial over the 
			integers, Hensel lemma factorization 
approximation           upprmsp1hfa(p,F,P,L,k) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, Hensel factorization 
approximation           with respect to integer prime upihlfaip(p,P,L,k) 
			univariate polynomial over integers, Hensel lemma 
			factorization 
archimedean             absolute value eciminlhaav(E,P) elliptic curve with 
			integer coefficients, minimal model, local height 
			at the 
archimedean             absolute values eciminlhnaav(E,P) elliptic curve 
			with integer coefficients, minimal model, local 
			heights at all non 
arcus                   tangens special version flatn_sp(f) floating point 
area                    tangens hyperbolicus special version flath_sp(f) 
			floating point 
arguments               (rekursiv) micran(n,LM,LA) modular integer chinese 
			remainder algorithm, n 
arguments               (rekursiv) mscran(n,Lm,La) modular single chinese 
			remainder algorithm, n 
arithmetic              functions iHDfu(func,anzahlargs,arg1,arg2) integer 
			using Heidelberg 
arithmetic              list ? isgfsal(p,AL) is Galois-field with single 
			characteristic 
arithmetic              list generator gf2algen(n,H) Galois-field with 
			characteristic 2 
arithmetic              list generator gfsalgen(p,n,G) Galois-field with 
			single characteristic 
arithmetic              list generator isomorphic embedding of subfield 
			gfsalgenies(p,m,n,ALn) Galois-field with single 
			characteristic 
arithmetic              list gf2prodAL(AL,a,b) Galois-field with 
			characteristic 2 product with 
arithmetic              list gf2squAL(AL,a) Galois-field with 
			characteristic 2 square with 
arithmetic              package Earith() Essen 
arithmetic              package: I/O functions HDiio() Heidelberg 
arithmetic              package: digit functions HDidigit() Heidelberg 
arithmetic              package: greatest common divisor HDigcd() 
			Heidelberg 
arithmetic              package: integer addition HDiadd() Heidelberg 
arithmetic              package: integer division HDidiv() Heidelberg 
arithmetic              package: integer multiplication HDimul() Heidelberg 
arithmetic              package: memory management HDimem() Heidelberg 
arithmetic              package: utilities HDiutil() Heidelberg 
arithmetic              package: vector functions HDidigitvec() Heidelberg 
aritho-geometric        mean cagm(a,b) complex 
aritho-geometric        mean flagm(a,b) floating point 
assignments             PAFassign() Papanikolaou floating point package: 
atom                    ? isatom(a) (MACRO) is 
atom                    fgeta(pf) file get 
atom                    fputa(a,pf) file put 
atom                    geta() (MACRO) get 
atom                    puta(a) (MACRO) put 
atom                    sgeta(ps) string get 
atom                    sputa(a,str) (MACRO) string put 
augmentation            dipgfsgba(r,p,AL,PL,P) distributive polynomial over 
			Galois-field with single characteristic Groebner 
			basis 
augmentation            dipigba(r,PL,P) distributive polynomial over 
			integers Groebner basis 
augmentation            dipmipgba(r,p,PL,P) distributive polynomial over 
			modular integer primes Groebner basis 
augmentation            dipmspgba(r,p,PL,P) distributive polynomial over 
			modular single primes Groebner basis 
augmentation            dipnfgba(r,F,PL,P) distributive polynomial over 
			number field Groebner basis 
augmentation            dippigba(r1,r2,PL,P) distributive polynomial over 
			polynomials over integers Groebner basis 
augmentation            diprfrgba(r1,r2,PL,P) distributive polynomial over 
			rational functions over the rationals Groebner 
			basis 
augmentation            diprgba(r,PL,P) distributive polynomial over 
			rationals Groebner basis 
b2                      eciminb2(E) elliptic curve with integer 
			coefficients, minimal model, 
b2                      ecisnfb2(E) elliptic curve with integer 
			coefficients, short normal form, 
b2                      ecqnfacb2(E) elliptic curve over quadratic number 
			field, actual model, Tate value 
b2                      ecracb2(E) elliptic curve over rational numbers, 
			actual curve, 
b4                      eciminb4(E) elliptic curve with integer 
			coefficients, minimal model, 
b4                      ecisnfb4(E) elliptic curve with integer 
			coefficients, short normal form, 
b4                      ecqnfacb4(E) elliptic curve over quadratic number 
			field, actual model, Tate value 
b4                      ecracb4(E) elliptic curve over rational numbers, 
			actual curve, 
baby                    step - giant step version qffmsregbg(m,D) quadratic 
			function field over modular singles regulator, 
baby                    step - giant step version qffmsregobg(m,D) 
			quadratic function field over modular singles 
			regulator, original 
baby                    step - giant step version, first case 
			qffmsregbg1(m,D,s) quadratic function field over 
			modular singles regulator, 
baby                    step - giant step version, fourth case 
			qffmsregbg4(m,D,s) quadratic function field over 
			modular singles regulator, 
baby                    step - giant step version, second case 
			qffmsregbg2(m,D,s) quadratic function field over 
			modular singles regulator, 
baby                    step - giant step version, third case 
			qffmsregbg3(m,D,s) quadratic function field over 
			modular singles regulator, 
baby                    step version qffmsfubs(m,D) quadratic function 
			field over modular singles fundamental unit, 
baby                    step version qffmsregbs(m,D) quadratic function 
			field over modular singles regulator, 
baby                    step version qffmsregobs(m,D) quadratic function 
			field over modular singles regulator, original 
bad                     reduction type modulo prime eciminbrtmp(E,p,n) 
			elliptic curve with integer coefficients, minimal 
			model, 
ball                    ? iscinball(z,r,eps) is complex number in 
ball                    volunitball(r) volume of the unit 
base                    10 ilog10(n) integer logarithm, 
base                    2 ilog2(A) integer logarithm, 
base                    2 rlog2(R) rational number logarithm, 
base                    2 slog2(a) single-precision logarithm, 
base                    coefficient (rekursiv) ptbc(r,P) polynomial 
			trailing 
base                    coefficient diplbc(r,P) (MACRO) distributive 
			polynomial leading 
base                    coefficient udpmstbc(m,P) univariate dense 
			polynomial over modular single trailing 
base                    coefficient udptbc(P) univariate dense polynomial 
			trailing 
base                    coefficient, main variable plbc(r,P) polynomial 
			leading 
base                    eciminmwgbase(E) elliptic curve with integer 
			coefficients, minimal model, Mordell-Weil-group, 
base                    ecisnfmwgbase(E) elliptic curve with integer 
			coefficients, short normal form, 
			Mordell-Weil-group, 
base                    ecracmwgbase(E) elliptic curve over the rational 
			numbers, actual curve, Mordell-Weil-group, 
base                    variable pisign(r,P) polynomial over integers sign, 
basis                   ) ouspibasisic(F,pL) order of an univariate 
			separable polynomial over the integers basis of the 
			integral closure ( ORDMAX, Ordmax, ordmax, integral 
basis                   augmentation dipgfsgba(r,p,AL,PL,P) distributive 
			polynomial over Galois-field with single 
			characteristic Groebner 
basis                   augmentation dipigba(r,PL,P) distributive 
			polynomial over integers Groebner 
basis                   augmentation dipmipgba(r,p,PL,P) distributive 
			polynomial over modular integer primes Groebner 
basis                   augmentation dipmspgba(r,p,PL,P) distributive 
			polynomial over modular single primes Groebner 
basis                   augmentation dipnfgba(r,F,PL,P) distributive 
			polynomial over number field Groebner 
basis                   augmentation dippigba(r1,r2,PL,P) distributive 
			polynomial over polynomials over integers Groebner 
basis                   augmentation diprfrgba(r1,r2,PL,P) distributive 
			polynomial over rational functions over the 
			rationals Groebner 
basis                   augmentation diprgba(r,PL,P) distributive 
			polynomial over rationals Groebner 
basis                   dipgfsgb(r,p,AL,PL) distributive polynomial over 
			Galois-field with single characteristic Groebner 
basis                   dipigb(r,PL) distributive polynomial over integers 
			Groebner 
basis                   dipmipgb(r,p,PL) distributive polynomial over 
			modular integer primes Groebner 
basis                   dipmspgb(r,p,PL) distributive polynomial over 
			modular single primes Groebner 
basis                   dipnfgb(r,F,PL) distributive polynomial over number 
			field Groebner 
basis                   dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers comprehensive Groebner 
basis                   dippigb(r1,r2,PL) distributive polynomial over 
			polynomials over integers Groebner 
basis                   dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers reduced comprehensive Groebner 
basis                   diprfrgb(r1,r2,PL) distributive polynomial over 
			rational functions over the rationals Groebner 
basis                   diprgb(r,PL) distributive polynomial over rationals 
			Groebner 
basis                   fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers comprehensive Groebner 
basis                   from generators oibasisfgen(F,L) order over the 
			integers 
basis                   from generators oprmsp1basfg(p,F,L) order over 
			polynomial ring over modular single prime, 
			transcendence degree 1, 
basis                   magfsnsb(p,AL,M) matrix of Galois-field with single 
			characteristic elements, null space 
basis                   maminsb(P,M) matrix of modular integers, null space 
basis                   mamsnsb(p,A) (MACRO) matrix of modular singles null 
			space 
basis                   manfnsb(F,M) matrix of number field elements null 
			space 
basis                   manfsnsb(F,M) matrix of number field elements, 
			sparse representation, null space 
basis                   marfmsp1nsb(p,M) matrix of rational functions over 
			modular single primes, transcendence degree 1, null 
			space 
basis                   marfrnsb(r,M) matrix of rational functions over 
			rationals, null space 
basis                   marnsb(M) matrix of rationals null space 
basis                   modiorthobas(bas) module over the integers, 
			orthogonalized 
basis                   of a local maximal over-order ouspibaslmo(F,p,Q,pk) 
			order of an univariate separable polynomial over 
			the integers 
basis                   of a local maximal over-order 
			ouspprmsp1bl(p,F,P,Q,pk) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
basis                   of a local maximal over-order with respect to 
			integer primes ouspibaslmoi(F,P,Q,pk) order of an 
			univariate separable polynomial over the integers 
basis                   of the integral closure ( ORDMAX, Ordmax, ordmax, 
			integral basis ) ouspibasisic(F,pL) order of an 
			univariate separable polynomial over the integers 
basis                   ouspprmsp1ib(p,F,pL) order of an univariate 
			separable polynomial over the polynomial ring over 
			modular single prime, transcendence degree 1, 
			integral 
basis                   over the integers LLL - reduced ? isbasilllred(bas) 
			is 
basis                   putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers comprehensive Groebner 
basis                   qnfintbas(D) quadratic number field integral 
basis                   recursion dipgfsgbr(r,p,AL,PL) distributive 
			polynomial over Galois-field with single 
			characteristic Groebner 
basis                   recursion dipigbr(r,PL) distributive polynomial 
			over integers Groebner 
basis                   recursion dipmipgbr(r,p,PL) distributive polynomial 
			over modular integer primes Groebner 
basis                   recursion dipmspgbr(r,p,PL) distributive polynomial 
			over modular single primes Groebner 
basis                   recursion dipnfgbr(r,F,PL) distributive polynomial 
			over number field Groebner 
basis                   recursion dippigbr(r1,r2,PL) distributive 
			polynomial over polynomials over integers Groebner 
basis                   recursion diprfrgbr(r1,r2,PL) distributive 
			polynomial over rational functions over the 
			rationals Groebner 
basis                   recursion diprgbr(r,PL) distributive polynomial 
			over rationals Groebner 
between                 Weil height and Neron-Tate height ecimindwhnth(E) 
			elliptic curve with integer coefficients, minimal 
			model, difference 
between                 Weil height and Neron-Tate height ecisnfdwhnth(E) 
			elliptic curve with integer coefficients, short 
			normal form, difference 
binary                  quadratic forms iprpdbqf(D,h1,h2) integer primitive 
			reduced positive definite 
bind                    for global and static variables globbind(pL) 
binomial                coefficient ibinom(n,k) integer 
birational              transformation of coefficients 
			ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over Galois-field with characteristic 2, 
birational              transformation of coefficients eciminbtco(E,BT) 
			elliptic curve with integer coefficients, minimal 
			model, 
birational              transformation of coefficients ecisnfbtco(E,BT) 
			elliptic curve with integer coefficients, short 
			normal form, 
birational              transformation of coefficients 
			ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over modular primes, 
birational              transformation of coefficients 
			ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over number field 
birational              transformation of coefficients ecracbtco(E,BT) 
			elliptic curve over rational numbers, 
birational              transformation of coefficients ecrbtco(LC,BT) 
			elliptic curve over rational numbers, 
birational              transformation of list of points 
			ecrbtlistp(LP,BT,modus) elliptic curve over 
			rational numbers, 
birational              transformation of point ecrbtp(P,BT) elliptic curve 
			over rational numbers, 
birational              transformation to actual ( rational ) model 
			eciminbtac(E) elliptic curve with integer 
			coefficients, minimal model, 
birational              transformation to actual ( rational ) model 
			ecisnfbtac(E) elliptic curve with integer 
			coefficients, short normal form, 
birational              transformation to minimal model ecisnfbtmin(E) 
			elliptic curve with integer coefficients, short 
			normal form, 
birational              transformation to minimal model ecracbtmin(E) 
			elliptic curve over the rationals, actual curve, 
birational              transformation to short normal form eciminbtsnf(E) 
			elliptic curve with integer coefficients, minimal 
			model, 
birational              transformation to short normal form ecracbtsnf(E) 
			elliptic curve over rational numbers, actual curve, 
birational              transformation, concatenation of transformations 
			ecrbtconc(BT1,BT2) elliptic curve over rational 
			numbers, 
birational              transformation, inverse transformation ecrbtinv(BT) 
			elliptic curve over rational numbers, 
bit-representation      ? isgf2impsb(G) is Galois-field with characteristic 
			2 irreducible and monic polynomial in special 
bit-representation      ? isudpm2sb(A) is univariate dense polynomial over 
			modular 2 in special 
bit-representation      generator gf2impsbgen(n,H) Galois-field with 
			characteristic 2 irreducible and monic polynomial 
			in special 
bit-representation      to univariate dense polynomial over modular 2 
			sbtoudpm2(a) (MACRO) special 
bit-representation      udpm2tosb(P) univariate dense polynomial over 
			modular 2 to special 
bits                    fputbits(s,pf) file put 
bits                    putbits(s) (MACRO) put 
bivariate               polynomial over modular integers substitution with 
			respect to a cubic equation bpmisubcubeq(p,P,R) 
blanks                  fgetcb(pf) file get character, skipping 
blanks                  getcb() (MACRO) get character, skipping 
blanks                  sgetcb(pf) string get character, skipping 
blocks                  gcfree() garbage collector with freeing 
bound                   in STACK ? isbound(pL) is 
bound                   itoEb(A,e,grenze) ( SIMATH ) integer to Essen 
			integer with upper 
bound                   itoEsb(A,e,grenze) ( SIMATH ) integer to Essen 
			integer, sign and upper 
bound                   pifcb(L) polynomial over integers factor 
			coefficient 
bound                   pigfcb(r,P) polynomial over integers Gelfond-factor 
			coefficient 
bound                   pilmfcb(r,P) polynomial over integers Landau- 
			Mignotte- factor coefficient 
bounded                 Weil height ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) 
			elliptic curve with integer coefficients, short 
			normal form, points of 
bounded                 length lblength(L,b) list 
bpmisubcubeq(p,P,R)     bivariate polynomial over modular integers 
			substitution with respect to a cubic equation 
bubble                  merge sort lsbmsort(L) list of single precisions 
bubble                  sort dipbsort(r,P) distributive polynomial 
bubble                  sort libsort(L) list of integers 
bubble                  sort lsbsort(L) list of single precision 
bubble                  sort, special lpbsorts(r,L) list of polynomials 
c4                      eciminc4(E) elliptic curve with integer 
			coefficients, minimal model, 
c4                      ecisnfc4(E) elliptic curve with integer 
			coefficients, short normal form, 
c4                      ecqnfacc4(E) elliptic curve over quadratic number 
			field, actual model, Tate value 
c4                      ecracc4(E) elliptic curve over rational numbers, 
			actual curve, 
c_p-                    values ecrprodcp(E) elliptic curve over the 
			rationals, product over all 
cabsv(z)                complex absolute value 
cagm(a,b)               complex aritho-geometric mean 
case                    distinction fgetdippicd(r1,r2,VL1,VL2,fac,pf) file 
			get distributive polynomial over polynomials over 
			integers 
case                    distinction getdippicd(r1,r2,VL1,VL2,fac) (MACRO) 
			get distributive polynomial over polynomials over 
			integers 
case                    qffmsicggii(m,D,H,L,pIT) quadratic function field 
			over modular singles ideal class group generators 
			and isomorphy type, imaginary 
case                    qffmsicggir(m,D,d,H,L,pIT) quadratic function field 
			over modular singles ideal class group generators 
			and isomorphy type, real 
case                    qffmsicgri(m,D,pHid) quadratic function field over 
			modular singles ideal class group system of 
			representatives, imaginary 
case                    qffmsicgrr(m,D,d) quadratic function field over 
			modular singles ideal class group system of 
			representatives, real 
case                    qffmsicgsti(m,D,L) quadratic function field over 
			modular singles ideal class group structure, 
			imaginary 
case                    qffmsicgstr(m,D,d,LG,pHid) quadratic function field 
			over modular singles ideal class group structure, 
			real 
case                    qffmsordsici(m,D,Q,P,OS) quadratic function field 
			over modular singles order of one single ideal 
			class, imaginary 
case                    qffmsordsicr(m,D,d,LE,ID,OS) quadratic function 
			field over modular singles order of one single 
			ideal class, real 
case                    qffmsregbg1(m,D,s) quadratic function field over 
			modular singles regulator, baby step - giant step 
			version, first 
case                    qffmsregbg2(m,D,s) quadratic function field over 
			modular singles regulator, baby step - giant step 
			version, second 
case                    qffmsregbg3(m,D,s) quadratic function field over 
			modular singles regulator, baby step - giant step 
			version, third 
case                    qffmsregbg4(m,D,s) quadratic function field over 
			modular singles regulator, baby step - giant step 
			version, fourth 
case                    qffmszcgiti(m,D,LG,IT) quadratic function field 
			over modular singles zero class group isomorphy 
			type, imaginary 
case                    qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function 
			field over modular singles zero class group 
			isomorphy type, real 
case,                   primitive ideal reduction 
			qffmsipidred(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular singles, imaginary 
case,                   qffmspidgenr(m,D,Q,P,G,pB) quadratic function field 
			over modular singles, principal ideal generating 
			element, real 
case,                   reduction of a primitive ideal 
			qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real 
case,                   sparse representation, reduction of a primitive 
			ideal qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic 
			function field over modular singles, imaginary 
case,                   sparse representation, reduction of a primitive 
			ideal qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic 
			function field over modular singles, real 
ccomp(a,b)              (MACRO) complex comparison 
cconjug(v)              complex conjugation 
ccri(re,im)             (MACRO) complex construction from real and 
			imaginary part 
cdedeetas(q,ln_q)       complex Dedekind eta function special 
cdif(v,w)               complex difference 
cdmarfmsp1hr(p,M)       common denominator matrix of rational functions 
			over modular single prime, transcendence degree 1, 
			hermitian reduction 
cdmarfmsp1id(n)         common denominator matrix of rational functions 
			over modular single prime, transcendence degree 1, 
			identity construction 
cdmarhermred(M)         common denominator matrix of rationals, hermitian 
			reduction 
cdmarid(n)              common denominator matrix of rationals, identity 
			construction 
cdprfcl(L)              common denominator polynomial over the rationals 
			from coefficient list 
cdprfmsp1fcl(L,p)       common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, from coefficient list 
cdprfmsp1fup(p,P)       common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, from univariate polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 
cdprfmsp1inv(p,F,A)     common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, inverse 
cdprfmsp1lfm(M,p)       common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, list from common denominator matrix of 
			rational functions over modular single prime, 
			transcendence degree 1 
cdprfmsp1mh(p,P,M)      common denominator polynomial over rational 
			functions over modular single primes, transcendence 
			degree 1, module homomorphism 
cdprfmsp1sum(p,P1,P2)   common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, sum 
cdprfmsp1upq(p,F,P)     common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, univariate polynomial over modular single 
			prime quotient 
cdprfupr(P)             common denominator polynomial over the rationals 
			from univariate polynomial over the rationals 
cdprinv(F,A)            common denominator polynomial over the rationals 
			inverse 
cdpriquot(P,I)          common denominator polynomial over the rationals 
			integer quotient 
cdprlfcdmar(M)          common denominator polynomial over the rationals 
			list from common denominator matrix of rationals 
cdprsum(P1,P2)          common denominator polynomial over the rationals 
			sum 
cdprzmodhom(P,M)        common denominator polynomial over the rationals 
			Z-module homomorphism 
ceiling                 rceil(R) rational number 
cexp(z)                 complex exponential function 
cexpsv(z,n)             complex exponential function special version 
character               fgetc(pf) (MACRO) file get 
character               fputc(c,pf) (MACRO) file put 
character               getc(pf) (MACRO) get 
character               getchar() (MACRO) get 
character               putc(c,pf) (MACRO) put 
character               putchar(c) (MACRO) put 
character               qnfdirchar(D,z) quadratic number field Dirichlet 
character               sgetc(ps) string get 
character               to floating point chartofl(A) 
character               unsgetc(c,ps) undo string get 
character,              skipping blanks fgetcb(pf) file get 
character,              skipping blanks getcb() (MACRO) get 
character,              skipping blanks sgetcb(pf) string get 
character,              skipping space fgetcs(pf) file get 
character,              skipping space getcs() (MACRO) get 
character,              skipping space sgetcs(ps) string get 
characteristic          (rekursiv) pgf2topgfs(r,G,P) polynomial over 
			Galois-field with characteristic 2 to polynomial 
			over Galois-field with single 
characteristic          (rekursiv) pmstopgfs(r,p,P) polynomial over modular 
			singles to polynomial over Galois-field with single 
characteristic          2 (rekursiv) pgfstopgf2(r,G,P) polynomial over 
			Galois-field with single characteristic to 
			polynomial over Galois-field with 
characteristic          2 (rekursiv) pm2topgf2(r,P) polynomial over modular 
			2 to polynomial over Galois-field with 
characteristic          2 ? iselecgf2(G,a1,a2,a3,a4,a6,P) is element of an 
			elliptic curve over Galois-field with 
characteristic          2 Ben-Or factorization, special upgf2bofacts(G,P) 
			univariate polynomial over Galois-field with 
characteristic          2 Berlekamp Q polynomials construction 
			upgf2bqp(G,P) univariate polynomial over 
			Galois-field with 
characteristic          2 arithmetic list generator gf2algen(n,H) 
			Galois-field with 
characteristic          2 derivation, main variable pgf2deriv(r,G,P) 
			polynomial over Galois-field with 
characteristic          2 derivation, specified variable (rekursiv) 
			pgf2derivsv(r,G,P,i) polynomial over Galois-field 
			with 
characteristic          2 difference gf2dif(G,a,b) (MACRO) Galois-field 
			with 
characteristic          2 difference pgf2dif(r,G,P1,P2) (MACRO) polynomial 
			over Galois-field with 
characteristic          2 distinct degree factorization upgf2ddfact(G,P) 
			univariate polynomial over Galois-field with 
characteristic          2 element ? isgf2el(G,a) (MACRO) is Galois-field 
			with 
characteristic          2 element evaluation first variable special version 
			(rekursiv) pigf2evalfvs(r,G,P) polynomial over 
			integers Galois-field with 
characteristic          2 element fgetgf2el(G,V,pf) file get Galois-field 
			with 
characteristic          2 element fputgf2el(G,a,V,pf) file put Galois-field 
			with 
characteristic          2 element getgf2el(G,V) (MACRO) get Galois-field 
			with 
characteristic          2 element gfseltogf2el(G,a) Galois-field with 
			single characteristic element to Galois-field with 
characteristic          2 element product (rekursiv) pgf2gf2prod(r,G,P,a) 
			polynomial over Galois-field with characteristic 2, 
			Galois-field with 
characteristic          2 element putgf2el(G,a,V) (MACRO) put Galois-field 
			with 
characteristic          2 element randomize gf2elrand(G) Galois-field with 
characteristic          2 element to Galois-field with single 
			characteristic element gf2eltogfsel(G,a) (MACRO) 
			Galois-field with 
characteristic          2 element to univariate dense polynomial over 
			modular 2 gf2eltoudpm2(G,a) Galois-field with 
characteristic          2 element udpm2togf2el(G,P) univariate dense 
			polynomial over modular 2 to Galois-field with 
characteristic          2 elements ? islistgf2(G,L) is list of Galois-field 
			with 
characteristic          2 elements scalar product vecgf2sprod(G,V,W) vector 
			of Galois-field with 
characteristic          2 embedding in field extension (rekursiv) 
			pgf2efe(r,GmtoGn,P) polynomial over Galois-field 
			with 
characteristic          2 embedding in field extension gf2efe(GmtoGn,gm) 
			Galois-field with 
characteristic          2 equal ? isppecgf2eq(p,P1,P2) is projective point 
			of an elliptic curve over Galois-field with 
characteristic          2 evaluation upgf2eval(G,P,a) polynomial over 
			Galois-field with 
characteristic          2 evaluation, main variable pgf2eval(r,G,P,a) 
			polynomial over Galois-field with 
characteristic          2 exponentiation gf2exp(G,a,m) Galois-field with 
characteristic          2 exponentiation pgf2exp(r,G,P,n) polynomial over 
			Galois-field with 
characteristic          2 fgetpgf2(r,G,V,Vgf2,pf) file get polynomial over 
			Galois-field with 
characteristic          2 fputpgf2(r,G,P,V,Vgf2,pf) file put polynomial 
			over Galois-field with 
characteristic          2 getpgf2(r,G,V,Vgf2) (MACRO) get polynomial over 
			Galois-field with 
characteristic          2 greatest common divisor upgf2gcd(G,P1,P2) 
			univariate polynomial over Galois-field with 
characteristic          2 inverse gf2inv(G,a) Galois-field with 
characteristic          2 irreducible and monic polynomial in special 
			bit-representation ? isgf2impsb(G) is Galois-field 
			with 
characteristic          2 irreducible and monic polynomial in special 
			bit-representation generator gf2impsbgen(n,H) 
			Galois-field with 
characteristic          2 isomorphic embedding of subfield gf2ies(Gm,Gn,n) 
			Galois field with 
characteristic          2 monic pgf2monic(r,G,P) polynomial over 
			Galois-field with 
characteristic          2 negation gf2neg(G,a) (MACRO) Galois-field with 
characteristic          2 negation pgf2neg(r,G,P) (MACRO) polynomial over 
			Galois-field with 
characteristic          2 point at infinity ? isppecgf2pai(G,P) is 
			projective point of an elliptic curve over 
			Galois-field with 
characteristic          2 product (rekursiv) pgf2prod(r,G,P1,P2) polynomial 
			over Galois-field with 
characteristic          2 product gf2prod(G,a,b) Galois-field with 
characteristic          2 product with arithmetic list gf2prodAL(AL,a,b) 
			Galois-field with 
characteristic          2 putpgf2(r,G,P,V,Vgf2) (MACRO) put polynomial over 
			Galois-field with 
characteristic          2 quotient and remainder (rekursiv) 
			pgf2qrem(r,G,P1,P2,pR) polynomial over Galois-field 
			with 
characteristic          2 quotient gf2quot(G,a,b) Galois-field with 
characteristic          2 quotient pgf2quot(r,G,P1,P2) (MACRO) polynomial 
			over Galois-field with 
characteristic          2 remainder pgf2rem(r,G,P1,P2) (MACRO) polynomial 
			over Galois-field with 
characteristic          2 remainder, special version 
			udpgf2remsp(G,P1,P2,ilc) univariate dense 
			polynomial over Galois-field with 
characteristic          2 square (rekursiv) pgf2square(r,G,P) polynomial 
			over Galois-field with 
characteristic          2 square gf2squ(G,a) Galois-field with 
characteristic          2 square with arithmetic list gf2squAL(AL,a) 
			Galois-field with 
characteristic          2 squarefree factorization (rekursiv) 
			upgf2sfact(G,P) univariate polynomial over 
			Galois-field with 
characteristic          2 sum (rekursiv) pgf2sum(r,G,P1,P2) polynomial over 
			Galois-field with 
characteristic          2 sum gf2sum(G,a,b) Galois-field with 
characteristic          2 to polynomial over Galois-field with single 
			characteristic (rekursiv) pgf2topgfs(r,G,P) 
			polynomial over Galois-field with 
characteristic          2 transformation 
			pgf2transf(r1,G,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over Galois-field with 
characteristic          2, 2^m-th power of variable, polynomial, remainder 
			upgf22pvprem(G,m,P) univariate polynomial over 
			Galois-field with 
characteristic          2, Ben-Or factorization upgf2bofact(G,P) univariate 
			polynomial over Galois-field with 
characteristic          2, Galois-field with characteristic 2 element 
			product (rekursiv) pgf2gf2prod(r,G,P,a) polynomial 
			over Galois-field with 
characteristic          2, Tate's values b2, b4, b6 
			ecgf2tavb6(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with 
characteristic          2, Tate's values b2, b4, b6, b8 
			ecgf2tavb8(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with 
characteristic          2, Tate's values c4, c6 
			ecgf2tavc6(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with 
characteristic          2, birational transformation of coefficients 
			ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over Galois-field with 
characteristic          2, combined Schoof- Shanks- algorithm 
			ecgf2cssa(G,a6,s,pl,ts) elliptic curve over Galois 
			field with 
characteristic          2, construction of division polynomials 
			ecgf2cdivp(G,a6,m) elliptic curve over Galois-field 
			with 
characteristic          2, counting algorithm ecgf2npca(G,a6) elliptic 
			curve over Galois-field with 
characteristic          2, discriminant ecgf2disc(G,a1,a2,a3,a4,a6) 
			elliptic curve over Galois-field with 
characteristic          2, exponentiation, polynomial remainder 
			pgf2expprem(r,G,F,E,M) polynomial over Galois-field 
			with 
characteristic          2, find point ecgf2fp(G,a1,a2,a3,a4,a6) elliptic 
			curve over Galois-field with 
characteristic          2, finding a multiple of the order of a point with 
			the Pollard Lambda method 
			ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) elliptic curve 
			over Galois-field with 
characteristic          2, j-invariant ecgf2jinv(G,a1,a2,a3,a4,a6) elliptic 
			curve over Galois-field with 
characteristic          2, line through points 
			ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
			Galois-field with 
characteristic          2, modified Shanks' algorithm, first part 
			ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) elliptic 
			curve over Galois-field with 
characteristic          2, modular exponentiation, special version 
			upgf2modexps(G,F,m,P,pM) univariate polynomial over 
			Galois-field with 
characteristic          2, monomial, polynomial, remainder 
			upgf2mprem(G,a,T,P) univariate polynomial over 
			Galois-field with 
characteristic          2, multiple of the order of a point to exact order 
			of the point ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) 
			elliptic curve over Galois-field with 
characteristic          2, multiplication-map 
			ecgf2mul(G,a1,a2,a3,a4,a6,k,P1) elliptic curve 
			Galois-field with 
characteristic          2, negative point ecgf2neg(G,a1,a2,a3,a4,a6,P) 
			elliptic curve over Galois-field with 
characteristic          2, number of points after field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
			curve over Galois field with 
characteristic          2, number of points modulo a power of 2 
			ecgf2npmp2(G,a6,c,L) elliptic curve over 
			Galois-field with 
characteristic          2, number of points modulo a single prime 
			determined with the Schoof algorithm, version 1 
			ecgf2npmspv1(G,a6,p,L) elliptic curve over 
			Galois-field with 
characteristic          2, number of points modulo a single prime 
			determined with the Schoof algorithm, version 2 
			ecgf2npmspv2(G,a6,p,L) elliptic curve over 
			Galois-field with 
characteristic          2, number of points modulo an integer determined 
			with the Schoof algorithm ecgf2npmi(G,a6,S,v,pM) 
			elliptic curve over Galois-field with 
characteristic          2, random generator upgf2gen(G,m) univariate 
			polynomial over Galois-field with 
characteristic          2, separate factor of equal degree upgf2sfed(G,H,d) 
			univariate polynomial over Galois-field with 
characteristic          2, special form, multiplication-map, special 
			version ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve 
			over Galois-field with 
characteristic          2, special form, sum of points, special version 
			ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic curve over 
			Galois-field with 
characteristic          2, standard representation of projective point 
			ecgf2srpp(G,P) elliptic curve over Galois-field 
			with 
characteristic          2, sum of points ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over Galois-field with 
characteristic          2, trace function, special upgf2tf(G,F,d,M) 
			polynomial over Galois-field with 
characteristic          ? (rekursiv) ispgfs(r,p,AL,P) is polynomial over 
			Galois-field with single 
characteristic          ? ismapgfs(r,p,AL,M) (MACRO) is matrix of 
			polynomials over Galois-field with single 
characteristic          ? isvecpgfs(r,p,AL,V) (MACRO) is vector of 
			polynomials over Galois-field with single 
characteristic          Berlekamp Q polynomials construction 
			upgfsbqp(p,AL,P) univariate polynomial over 
			Galois-field with single 
characteristic          Berlekamp factorization upgfsbfact(p,AL,P,d) 
			univariate polynomial over Galois-field with single 
characteristic          Berlekamp factorization, Zassenhaus method 
			upgfsbfzm(p,AL,s,P,G) univariate polynomial over 
			Galois-field with single 
characteristic          Berlekamp factorization, last step 
			upgfsbfls(p,AL,P,B,d) univariate polynomial over 
			Galois-field with single 
characteristic          Groebner basis augmentation dipgfsgba(r,p,AL,PL,P) 
			distributive polynomial over Galois-field with 
			single 
characteristic          Groebner basis dipgfsgb(r,p,AL,PL) distributive 
			polynomial over Galois-field with single 
characteristic          Groebner basis recursion dipgfsgbr(r,p,AL,PL) 
			distributive polynomial over Galois-field with 
			single 
characteristic          S-polynomial dipgfssp(r,p,AL,P1,P2) distributive 
			polynomial over Galois-field with single 
characteristic          arithmetic list ? isgfsal(p,AL) is Galois-field 
			with single 
characteristic          arithmetic list generator gfsalgen(p,n,G) 
			Galois-field with single 
characteristic          arithmetic list generator isomorphic embedding of 
			subfield gfsalgenies(p,m,n,ALn) Galois-field with 
			single 
characteristic          characteristic polynomial mapgfschpol(r,p,AL,M) 
			(MACRO) matrix of polynomials over Galois-field 
			with single 
characteristic          complete factorization special upgfscfacts(p,AL,P) 
			univariate polynomial over Galois-field with single 
characteristic          complete factorization upgfscfact(p,AL,P) 
			univariate polynomial over Galois-field with single 
characteristic          construction 1 mapgfscons1(r,p,AL,n) (MACRO) matrix 
			of polynomials over Galois-field with single 
characteristic          derivation, main variable pgfsderiv(r,p,AL,P) 
			polynomial over Galois-field with single 
characteristic          derivation, specified variable (rekursiv) 
			pgfsderivsv(r,p,AL,P,i) polynomial over 
			Galois-field with single 
characteristic          determinant mapgfsdet(r,p,AL,M) matrix of 
			polynomials over Galois-field with single 
characteristic          difference (rekursiv) pgfsdif(r,p,AL,P1,P2) 
			polynomial over Galois-field with single 
characteristic          difference dipgfsdif(r,p,AL,P1,P2) distributive 
			polynomial over Galois-field with single 
characteristic          difference gfsdif(p,AL,a,b) (MACRO) Galois-field 
			with single 
characteristic          difference mapgfsdif(r,p,AL,M,N) (MACRO) matrix of 
			polynomials over Galois-field with single 
characteristic          difference vecpgfsdif(r,p,AL,U,V) (MACRO) vector of 
			polynomials over Galois-field with single 
characteristic          distinct degree factorization upgfsddfact(p,AL,P) 
			univariate polynomial over Galois-field with single 
characteristic          eigenvalues and irreducible factors of the 
			characteristic polynomial magfsevifcp(p,AL,M,pL) 
			matrix over Galois-field with single 
characteristic          element ? isgfsel(p,AL,a) is Galois-field with 
			single 
characteristic          element evaluation first variable special version 
			(rekursiv) pigfsevalfvs(r,p,AL,P) polynomial over 
			integers Galois-field with single 
characteristic          element evaluation first variable special version 
			mapigfsevfvs(r,p,AL,M) matrix over polynomials over 
			integers Galois-field with single 
characteristic          element evaluation first variable special version 
			vecpigfsefvs(r,p,AL,V) vector over polynomials over 
			integers Galois-field with single 
characteristic          element fgetgfsel(p,AL,V,pf) file get Galois-field 
			with single 
characteristic          element fputgfsel(p,AL,a,V,pf) file put 
			Galois-field with single 
characteristic          element getgfsel(p,AL,V) (MACRO) get Galois-field 
			with single 
characteristic          element gf2eltogfsel(G,a) (MACRO) Galois-field with 
			characteristic 2 element to Galois-field with 
			single 
characteristic          element one ? isgfsone(p,AL,a) is Galois-field with 
			single 
characteristic          element product (rekursiv) pgfsgfsprod(r,p,AL,P,a) 
			polynomial over Galois-field with single 
			characteristic, Galois-field with single 
characteristic          element product dipgfsgfprod(r,p,AL,P,a) 
			distributive polynomial over Galois-field with 
			single characteristic, Galois-field with single 
characteristic          element putgfsel(p,AL,a,V) (MACRO) put Galois-field 
			with single 
characteristic          element quotient (rekursiv) pgfsgfsquot(r,p,AL,P,a) 
			polynomial over Galois-field with single 
			characteristic, Galois-field with single 
characteristic          element to Galois-field with characteristic 2 
			element gfseltogf2el(G,a) Galois-field with single 
characteristic          elements ? islistgfs(p,AL,L) is list of 
			Galois-field with single 
characteristic          elements ? ismagfs(p,AL,M) (MACRO) is matrix of 
			Galois-field with single 
characteristic          elements ? isvecgfs(p,AL,A) (MACRO) is vector of 
			Galois-field with single 
characteristic          elements characteristic polynomial 
			magfschpol(p,AL,M) (MACRO) matrix of Galois-field 
			with single 
characteristic          elements construction 1 magfscons1(p,AL,n) (MACRO) 
			matrix of Galois-field with single 
characteristic          elements determinant magfsdet(p,AL,M) matrix of 
			Galois-field with single 
characteristic          elements difference magfsdif(p,AL,M,N) (MACRO) 
			matrix of Galois-field with single 
characteristic          elements difference vecgfsdif(p,AL,U,V) (MACRO) 
			vector of Galois-field with single 
characteristic          elements exponentiation magfsexp(p,AL,M,n) matrix 
			of Galois-field with single 
characteristic          elements fgetmagfs(p,AL,V,pf) (MACRO) file get 
			matrix of Galois-field with single 
characteristic          elements fgetvecgfs(p,AL,VL,pf) (MACRO) file get 
			vector of Galois-field with single 
characteristic          elements fputmagfs(p,AL,M,V,pf) (MACRO) file put 
			matrix of Galois-field with single 
characteristic          elements fputvecgfs(p,AL,V,VL,pf) (MACRO) file put 
			vector of Galois-field with single 
characteristic          elements getmagfs(p,AL,V) (MACRO) get matrix of 
			Galois-field with single 
characteristic          elements getvecgfs(p,AL,VL) (MACRO) get vector of 
			Galois-field with single 
characteristic          elements inverse magfsinv(p,AL,M) matrix of 
			Galois-field with single 
characteristic          elements linear combination 
			vecgfslc(p,AL,s1,s2,L1,L2) vector of Galois-field 
			with single 
characteristic          elements negation magfsneg(p,AL,M) (MACRO) matrix 
			of Galois-field with single 
characteristic          elements negation vecgfsneg(p,AL,V) (MACRO) vector 
			of Galois-field with single 
characteristic          elements product magfsprod(p,AL,M,N) (MACRO) matrix 
			of Galois-field with single 
characteristic          elements putmagfs(p,AL,M,V) (MACRO) put matrix of 
			Galois-field with single 
characteristic          elements putvecgfs(p,AL,V,VL) (MACRO) put vector of 
			Galois-field with single 
characteristic          elements rank magfsrk(p,AL,M) matrix of 
			Galois-field with single 
characteristic          elements scalar multiplication magfssmul(p,AL,M,el) 
			matrix of Galois-field with single 
characteristic          elements scalar multiplication 
			vecgfssmul(p,AL,V,el) vector of Galois-field with 
			single 
characteristic          elements scalar product vecgfssprod(p,AL,V,W) 
			vector of Galois-field with single 
characteristic          elements solution of a system of linear equations 
			magfsssle(p,AL,A,b,pX,pN) matrix of Galois-field 
			with single 
characteristic          elements sum magfssum(p,AL,M,N) (MACRO) matrix of 
			Galois-field with single 
characteristic          elements sum vecgfssum(p,AL,U,V) (MACRO) vector of 
			Galois-field with single 
characteristic          elements vector multiplication 
			magfsvecmul(p,AL,A,x) (MACRO) matrix of 
			Galois-field with single 
characteristic          elements, null space basis magfsnsb(p,AL,M) matrix 
			of Galois-field with single 
characteristic          embedding in field extension (rekursiv) 
			pgfsefe(r,p,ALm,P,g) polynomial over Galois-field 
			with single 
characteristic          embedding in field extension gfsefe(p,ALm,a,g) 
			Galois-field with single 
characteristic          embedding in field extension magfsefe(p,ALm,M,g) 
			matrix over Galois-field with single 
characteristic          embedding in field extension mapgfsefe(r,p,ALm,M,g) 
			matrix over polynomials over Galois-field with 
			single 
characteristic          embedding in field extension vecgfsefe(p,ALm,V,g) 
			vector over Galois-field with single 
characteristic          embedding in field extension 
			vecpgfsefe(r,p,ALm,V,g) vector over polynomials 
			over Galois-field with single 
characteristic          evaluation, main variable pgfseval(r,p,AL,P,a) 
			polynomial over Galois-field with single 
characteristic          evaluation, specified variable (rekursiv) 
			pgfsevalsv(r,p,AL,P,d,a) polynomial over 
			Galois-field with single 
characteristic          exponentiation gfsexp(p,AL,a,m) Galois-field with 
			single 
characteristic          exponentiation mapgfsexp(r,p,AL,M,n) matrix of 
			polynomials over Galois-field with single 
characteristic          exponentiation pgfsexp(r,p,AL,P,m) polynomial over 
			Galois-field with single 
characteristic          extended greatest common divisor 
			upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate polynomial 
			over Galois-field with single 
characteristic          fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get 
			matrix of polynomials over Galois-field with single 
characteristic          fgetpgfs(r,p,AL,V,Vgfs,pf) file get polynomial over 
			Galois-field with single 
characteristic          fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get vector 
			of polynomials over Galois-field with single 
characteristic          fputmapgfs(r,p,AL,M,V,Vgfs,pf) (MACRO) file put 
			matrix of polynomials over Galois-field with single 
characteristic          fputvpgfs(r,p,AL,W,V,Vgfs,pf) (MACRO) file put 
			vector of polynomials over Galois-field with single 
characteristic          getmapgfs(r,p,AL,V,Vgfs) (MACRO) get matrix of 
			polynomials over Galois-field with single 
characteristic          getpgfs(r,p,AL,V,Vgfs) (MACRO) get polynomial over 
			Galois-field with single 
characteristic          getvpgfs(r,p,AL,V,Vgfs) (MACRO) get vector of 
			polynomials over Galois-field with single 
characteristic          greatest common divisor upgfsgcd(p,AL,P1,P2) 
			univariate polynomial over Galois-field with single 
characteristic          greatest squarefree divisor (rekursiv) 
			upgfsgsd(p,AL,P) univariate polynomial over 
			Galois-field with single 
characteristic          half extended greatest common divisor 
			upgfshegcd(p,AL,P1,P2,pP3) univariate polynomial 
			over Galois-field with single 
characteristic          in graduated lexicographical order 
			dipgfslotglo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single 
characteristic          in lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
			graduated lexicographical order 
			dipgfslotglo(r,p,AL,P) distributive polynomial over 
			Galois-field with single 
characteristic          in lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
			lexicographical order with inverse exponent vector 
			dipgfslotlio(r,p,AL,P) distributive polynomial over 
			Galois-field with single 
characteristic          in lexicographical order to distributive polynomial 
			over Galois-field with single characteristic with 
			total degree ordering dipgfslottdo(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single 
characteristic          in lexicographical order with inverse exponent 
			vector dipgfslotlio(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single 
characteristic          inverse gfsinv(p,AL,a) Galois-field with single 
characteristic          inverse mapgfsinv(r,p,AL,M) matrix of polynomials 
			over Galois-field with single 
characteristic          linear combination vecpgfslc(r,p,AL,s1,s2,L1,L2) 
			vector of polynomials over Galois-field with single 
characteristic          list fgetdipgfsl(r,p,AL,VL,Vgfs,pf) file get 
			distributive polynomial over Galois-field with 
			single 
characteristic          list fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put 
			distributive polynomial over Galois-field with 
			single 
characteristic          list getdipgfsl(r,p,AL,VL,Vgfs) (MACRO) get 
			distributive polynomial over Galois-field with 
			single 
characteristic          list putdipgfsl(r,p,AL,PL,VL,Vgfs) (MACRO) put 
			distributive polynomial over Galois-field with 
			single 
characteristic          maitomagfs(p,M) matrix over integers to matrix over 
			Galois-field with single 
characteristic          monic dipgfsmonic(r,p,AL,P) distributive polynomial 
			over Galois-field with single 
characteristic          monic pgfsmonic(r,p,AL,P) polynomial over 
			Galois-field with single 
characteristic          mpgfstompmp(r,p,AL,P,M) matrix of polynomials over 
			Galois-field with single characteristic to matrix 
			of polynomials modulo polynomial over Galois-field 
			with single 
characteristic          mpmstompgfs(r,p,M) matrix of polynomials over 
			modular singles to matrix of polynomials over 
			Galois-field with single 
characteristic          negation (rekursiv) pgfsneg(r,p,AL,P) polynomial 
			over Galois-field with single 
characteristic          negation as function gfsnegf(p,AL,a) Galois-field 
			with single 
characteristic          negation dipgfsneg(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
characteristic          negation gfsneg(p,AL,a) (MACRO) Galois-field with 
			single 
characteristic          negation mapgfsneg(r,p,AL,M) (MACRO) matrix of 
			polynomials over Galois-field with single 
characteristic          negation vecpgfsneg(r,p,AL,V) (MACRO) vector of 
			polynomials over Galois-field with single 
characteristic          number of irreducible factors upgfsnif(p,AL,P) 
			univariate polynomial over Galois-field with single 
characteristic          polynomial 
			machpol(M,det,minusEins,anzahlargs,arg1,arg2) 
			matrix 
characteristic          polynomial magfschpol(p,AL,M) (MACRO) matrix of 
			Galois-field with single characteristic elements 
characteristic          polynomial magfsevifcp(p,AL,M,pL) matrix over 
			Galois-field with single characteristic eigenvalues 
			and irreducible factors of the 
characteristic          polynomial maichpol(M) (MACRO) matrix of integers 
characteristic          polynomial maievifcp(M,pL) matrix of integers 
			eigenvalues and irreducible factors of the 
characteristic          polynomial mamichpol(m,M) (MACRO) matrix of modular 
			integers 
characteristic          polynomial mamievifcp(p,M,pL) matrix of modular 
			integers eigenvalues and irreducible factors of the 
characteristic          polynomial mamschpol(m,M) (MACRO) matrix of modular 
			singles 
characteristic          polynomial mamsevifcp(p,M,pL) matrix of modular 
			singles eigenvalues and irreducible factors of the 
characteristic          polynomial manfchpol(F,M) (MACRO) matrix of number 
			field elements 
characteristic          polynomial mapgfschpol(r,p,AL,M) (MACRO) matrix of 
			polynomials over Galois-field with single 
			characteristic 
characteristic          polynomial mapichpol(r,M) (MACRO) matrix of 
			polynomials over integers 
characteristic          polynomial mapmichpol(r,m,M) (MACRO) matrix of 
			polynomials over modular integers 
characteristic          polynomial mapmschpol(r,m,M) (MACRO) matrix of 
			polynomials over modular singles 
characteristic          polynomial mapnfchpol(r,F,M) (MACRO) matrix of 
			polynomials over number field 
characteristic          polynomial maprchpol(r,M) (MACRO) matrix of 
			polynomials over rationals 
characteristic          polynomial marchpol(M) (MACRO) matrix of rationals 
characteristic          polynomial marevifcp(M,*pL) matrix of rationals 
			eigenvalues and irreducible factors of the 
characteristic          polynomial marfrchpol(r,M) matrix of rational 
			functions over rationals 
characteristic          polynomial nf3chpol(F,el) number field of degree 3 
characteristic          polynomial special 
			machpolspec(M,det,minusEins,anzahlargs,arg1,...,arg5) 
			matrix 
characteristic          product (rekursiv) pgfsprod(r,p,AL,P1,P2) 
			polynomial over Galois-field with single 
characteristic          product dipgfsprod(r,p,AL,P1,P2) distributive 
			polynomial over Galois-field with single 
characteristic          product gfsprod(p,AL,a,b) Galois-field with single 
characteristic          product mapgfsprod(r,p,AL,M,N) (MACRO) matrix of 
			polynomials over Galois-field with single 
characteristic          putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) put matrix of 
			polynomials over Galois-field with single 
characteristic          putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) put vector of 
			polynomials over Galois-field with single 
characteristic          quotient and remainder (rekursiv) 
			pgfsqrem(r,p,AL,P1,P2,pR) polynomial over 
			Galois-field with single 
characteristic          quotient gfsquot(p,AL,a,b) Galois-field with single 
characteristic          quotient pgfsquot(r,p,AL,P1,P2) (MACRO) polynomial 
			over Galois-field with single 
characteristic          randomize upgfsrand(p,AL,m) univariate polynomial 
			over Galois-field with single 
characteristic          randomize, positive degree upgfsrandpd(p,AL,m) 
			univariate polynomial over Galois-field with single 
characteristic          relative prime factorization 
			upgfsrelpfac(p,AL,P,Fak,pA2) univariate polynomial 
			over Galois-field with single 
characteristic          remainder pgfsrem(r,p,AL,P1,P2) (MACRO) polynomial 
			over Galois-field with single 
characteristic          resultant pgfsres(r,p,AL,P1,P2) polynomial over 
			Galois-field with single 
characteristic          root finding (rekursiv) upgfsrf(p,AL,P) univariate 
			polynomial over Galois-field with single 
characteristic          scalar multiplication mapgfssmul(r,p,AL,M,el) 
			matrix of polynomials over Galois-field with single 
characteristic          scalar multiplication vecpgfssmul(r,p,AL,V,el) 
			vector of polynomials over Galois-field with single 
characteristic          scalar product vpgfssprod(r,p,AL,V,W) vector of 
			polynomials over Galois-field with single 
characteristic          set from partition csetpart(L) 
characteristic          set intersection csetinter(S,T) 
characteristic          set union csetunion(S,T) 
characteristic          squarefree factorization (rekursiv) 
			upgfssfact(p,AL,P) univariate polynomial over 
			Galois-field with single 
characteristic          squarefree part upgfssfp(p,AL,P) univariate 
			polynomial over Galois-field with single 
characteristic          sum (rekursiv) pgfssum(r,p,AL,P1,P2) polynomial 
			over Galois-field with single 
characteristic          sum as function gfssumf(p,AL,a,b) Galois-field with 
			single 
characteristic          sum dipgfssum(r,p,AL,P1,P2) distributive polynomial 
			over Galois-field with single 
characteristic          sum gfssum(p,AL,a,b) (MACRO) Galois-field with 
			single 
characteristic          sum mapgfssum(r,p,AL,M,N) (MACRO) matrix of 
			polynomials over Galois-field with single 
characteristic          sum vecpgfssum(r,p,AL,U,V) (MACRO) vector of 
			polynomials over Galois-field with single 
characteristic          to matrix of polynomials modulo polynomial over 
			Galois-field with single characteristic 
			mpgfstompmp(r,p,AL,P,M) matrix of polynomials over 
			Galois-field with single 
characteristic          to polynomial over Galois-field with characteristic 
			2 (rekursiv) pgfstopgf2(r,G,P) polynomial over 
			Galois-field with single 
characteristic          to vector of polynomials modulo polynomial over 
			Galois-field with single characteristic 
			vpgfstovpmp(r,p,AL,P,V) vector of polynomials over 
			Galois-field with single 
characteristic          transformation 
			mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) matrix 
			of polynomials over Galois-field with single 
characteristic          transformation 
			pgfstransf(r1,p,AL,P1,V1,r2,P2,V2,Vn,pV3) 
			polynomial over Galois-field with single 
characteristic          transformation 
			vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) vector 
			of polynomials over Galois-field with single 
characteristic          vecitovecgfs(p,V) vector over integers to vector 
			over Galois-field with single 
characteristic          vector multiplication mapgfsvmul(r,p,AL,A,x) 
			(MACRO) matrix of polynomials over Galois-field 
			with single 
characteristic          vpgfstovpmp(r,p,AL,P,V) vector of polynomials over 
			Galois-field with single characteristic to vector 
			of polynomials modulo polynomial over Galois-field 
			with single 
characteristic          vpmstovpgfs(r,p,V) vector of polynomials over 
			modular singles to vector of polynomials over 
			Galois-field with single 
characteristic          with total degree ordering dipgfslottdo(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single 
characteristic,         Ben-Or factorization upgfsbofact(p,AL,P) univariate 
			polynomial over Galois-field with single 
characteristic,         Ben-Or factorization, special upgfsbofacts(p,AL,P) 
			univariate polynomial over Galois-field with single 
characteristic,         Galois-field with single characteristic element 
			product (rekursiv) pgfsgfsprod(r,p,AL,P,a) 
			polynomial over Galois-field with single 
characteristic,         Galois-field with single characteristic element 
			product dipgfsgfprod(r,p,AL,P,a) distributive 
			polynomial over Galois-field with single 
characteristic,         Galois-field with single characteristic element 
			quotient (rekursiv) pgfsgfsquot(r,p,AL,P,a) 
			polynomial over Galois-field with single 
characteristic,         element randomize gfselrand(p,AL) Galois-field with 
			single 
characteristic,         exponentiation, polynomial remainder 
			pgfsexpprem(r,p,AL,F,E,M) polynomial over 
			Galois-field with single 
characteristic,         separate factors of equal degree 
			upgfssfed(p,AL,G,d) univariate polynomial over 
			Galois-field with single 
characteristic,         trace function upgfstf(p,AL,G,d,M) univariate 
			polynomial over Galois-field with single 
chartofl(A)             character to floating point 
chinese                 remainder algorithm (rekursiv) picra(r,P1,P2,M,m,a) 
			polynomial over integers 
chinese                 remainder algorithm micra(M1,M2,N1,A1,A2) modular 
			integer 
chinese                 remainder algorithm milcra(m1,m2,L1,L2) modular 
			integer list 
chinese                 remainder algorithm miscra(M,m,m1,A,a) modular 
			integer single 
chinese                 remainder algorithm mscra(m1,m2,n1,a1,a2) modular 
			single 
chinese                 remainder algorithm mslcra(m1,m2,L1,L2) modular 
			single list 
chinese                 remainder algorithm, n arguments (rekursiv) 
			micran(n,LM,LA) modular integer 
chinese                 remainder algorithm, n arguments (rekursiv) 
			mscran(n,Lm,La) modular single 
choice                  of evaluation points picevalp(r,P,sA) polynomial 
			over integers 
cimag(z)                (MACRO) complex imaginary part 
ciprod(v,i)             complex integer product 
ciquot(v,i)             complex integer quotient 
class                   equation sdisccleq(D,L) single discriminant 
class                   fields qnfdegrescf(D,p) quadratic number field 
			degrees of the residue 
class                   group generators and isomorphy type, imaginary case 
			qffmsicggii(m,D,H,L,pIT) quadratic function field 
			over modular singles ideal 
class                   group generators and isomorphy type, real case 
			qffmsicggir(m,D,d,H,L,pIT) quadratic function field 
			over modular singles ideal 
class                   group isomorphy type, imaginary case 
			qffmszcgiti(m,D,LG,IT) quadratic function field 
			over modular singles zero 
class                   group isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function 
			field over modular singles zero 
class                   group structure, imaginary case qffmsicgsti(m,D,L) 
			quadratic function field over modular singles ideal 
class                   group structure, real case 
			qffmsicgstr(m,D,d,LG,pHid) quadratic function field 
			over modular singles ideal 
class                   group system of representatives 
			qffmsicgrep(m,D,pHid) quadratic function field over 
			modular singles ideal 
class                   group system of representatives, imaginary case 
			qffmsicgri(m,D,pHid) quadratic function field over 
			modular singles ideal 
class                   group system of representatives, real case 
			qffmsicgrr(m,D,d) quadratic function field over 
			modular singles ideal 
class                   number abnfrelcl(q,g) abelian number field relative 
class                   number modulo prime abnfrelclmp(m,q,g) abelian 
			number field relative 
class                   number qffmsdcn(m,P) quadratic function field over 
			modular singles divisor 
class                   number qffmsicn(m,P) quadratic function field over 
			modular singles ideal 
class                   number subroutine 1 qffmsdcns1(m,P) quadratic 
			function field over modular singles divisor 
class                   number subroutine 2 qffmsdcns2(m,P) quadratic 
			function field over modular singles divisor 
class                   number subroutine 3 qffmsdcns3(m,P) quadratic 
			function field over modular singles divisor 
class                   qffmsiselic(m,D,L,Q,P) quadratic function field 
			over modular singles is element of an ideal 
class,                  imaginary case qffmsordsici(m,D,Q,P,OS) quadratic 
			function field over modular singles order of one 
			single ideal 
class,                  real case qffmsordsicr(m,D,d,LE,ID,OS) quadratic 
			function field over modular singles order of one 
			single ideal 
clfcdpr(P,n)            coefficient list from common denominator polynomial 
			over the rationals 
clfcdprfmsp1(P,n)       coefficient list from common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1 
closure                 ( ORDMAX, Ordmax, ordmax, integral basis ) 
			ouspibasisic(F,pL) order of an univariate separable 
			polynomial over the integers basis of the integral 
cmodinv(q,ln_q)         complex modular invariant j 
coefficient             (rekursiv) ptbc(r,P) polynomial trailing base 
coefficient             bound pifcb(L) polynomial over integers factor 
coefficient             bound pigfcb(r,P) polynomial over integers 
			Gelfond-factor 
coefficient             bound pilmfcb(r,P) polynomial over integers Landau- 
			Mignotte- factor 
coefficient             diplbc(r,P) (MACRO) distributive polynomial leading 
			base 
coefficient             ibinom(n,k) integer binomial 
coefficient             list cdprfcl(L) common denominator polynomial over 
			the rationals from 
coefficient             list cdprfmsp1fcl(L,p) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, from 
coefficient             list from common denominator polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1 clfcdprfmsp1(P,n) 
coefficient             list from common denominator polynomial over the 
			rationals clfcdpr(P,n) 
coefficient             list from univariate polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 sclfuprfmsp1(P,n) special 
coefficient             list from univariate polynomial over the integers 
			sclfupi(P,n) special 
coefficient             list upifscl(L) univariate polynomial over the 
			integers from special 
coefficient             list uprfmsp1fscl(L) univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, from special 
coefficient             udpmstbc(m,P) univariate dense polynomial over 
			modular single trailing base 
coefficient             udptbc(P) univariate dense polynomial trailing base 
coefficient,            main variable plbc(r,P) polynomial leading base 
coefficient,            main variable plc(r,P) (MACRO) polynomial leading 
coefficients            Tate's algorithm ecitatealg(a1,a2,a3,a4,a6,p,n) 
			elliptic curve with integer 
coefficients            ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over Galois-field with characteristic 2, birational 
			transformation of 
coefficients            eciminbtco(E,BT) elliptic curve with integer 
			coefficients, minimal model, birational 
			transformation of 
coefficients            ecisnfbtco(E,BT) elliptic curve with integer 
			coefficients, short normal form, birational 
			transformation of 
coefficients            ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over modular primes, birational transformation of 
coefficients            ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over number field birational transformation of 
coefficients            ecqnftoeci(D,L) elliptic curve over quadratic 
			number field to elliptic curve with integral 
coefficients            ecracbtco(E,BT) elliptic curve over rational 
			numbers, birational transformation of 
coefficients            ecrbtco(LC,BT) elliptic curve over rational 
			numbers, birational transformation of 
coefficients            of L- series ecrclser(E,A,n) elliptic curve over 
			the rationals, 
coefficients            of univariate polynomials macup(n,L) matrix of 
coefficients,           Tate's values b2, b4, b6, b8 
			ecitavalb(a1,a2,a3,a4,a6) elliptic curve with 
			integer 
coefficients,           actual curve, difference of points ecracdif(E,P,Q) 
			elliptic curve with integer 
coefficients,           minimal model fputecimin(E,pf) file put elliptic 
			curve with integer 
coefficients,           minimal model isecimintorp(E,P) is torsion point on 
			elliptic curve with integer 
coefficients,           minimal model isineciminpl(E,P,h,PL) is in list of 
			points on elliptic curve with integer 
coefficients,           minimal model isponecimin(E,P) is point on elliptic 
			curve with integer 
coefficients,           minimal model putecimin(E) (MACRO) put elliptic 
			curve with integer 
coefficients,           minimal model to short normal form ecimintosnf(E) 
			elliptic curve with integer 
coefficients,           minimal model, Mordell-Weil-group, base 
			eciminmwgbase(E) elliptic curve with integer 
coefficients,           minimal model, Neron-Tate height eciminnetahe(E,P) 
			elliptic curve with integer 
coefficients,           minimal model, Neron-Tate pairing 
			eciminnetapa(E,P,Q) elliptic curve with integer 
coefficients,           minimal model, Tate's algorithm 
			ecimintatealg(E,p,n) elliptic curve with integer 
coefficients,           minimal model, Tate's values c4, c6 
			ecitavalc(a1,a2,a3,a4,a6) elliptic curve with 
			integer 
coefficients,           minimal model, a1 ecimina1(E) elliptic curve with 
			integer 
coefficients,           minimal model, a2 ecimina2(E) elliptic curve with 
			integer 
coefficients,           minimal model, a3 ecimina3(E) elliptic curve with 
			integer 
coefficients,           minimal model, a4 ecimina4(E) elliptic curve with 
			integer 
coefficients,           minimal model, a6 ecimina6(E) elliptic curve with 
			integer 
coefficients,           minimal model, b2 eciminb2(E) elliptic curve with 
			integer 
coefficients,           minimal model, b4 eciminb4(E) elliptic curve with 
			integer 
coefficients,           minimal model, b6 eciminb6(E) elliptic curve with 
			integer 
coefficients,           minimal model, b8 eciminb8(E) elliptic curve with 
			integer 
coefficients,           minimal model, bad reduction type modulo prime 
			eciminbrtmp(E,p,n) elliptic curve with integer 
coefficients,           minimal model, birational transformation of 
			coefficients eciminbtco(E,BT) elliptic curve with 
			integer 
coefficients,           minimal model, birational transformation to actual 
			( rational ) model eciminbtac(E) elliptic curve 
			with integer 
coefficients,           minimal model, birational transformation to short 
			normal form eciminbtsnf(E) elliptic curve with 
			integer 
coefficients,           minimal model, c4 eciminc4(E) elliptic curve with 
			integer 
coefficients,           minimal model, c6 eciminc6(E) elliptic curve with 
			integer 
coefficients,           minimal model, difference between Weil height and 
			Neron-Tate height ecimindwhnth(E) elliptic curve 
			with integer 
coefficients,           minimal model, difference of points 
			ecimindif(E,P,Q) elliptic curve with integer 
coefficients,           minimal model, difference of points 
			ecisnfdif(E,P,Q) elliptic curve with integer 
coefficients,           minimal model, discriminant ecimindisc(E) elliptic 
			curve with integer 
coefficients,           minimal model, division by 2 of a point 
			ecimindivby2(E,P,h,PL,H) elliptic curve with 
			integer 
coefficients,           minimal model, division of a point by an integer 
			ecimindiv(E,P,n) elliptic curve with integer 
coefficients,           minimal model, division of a point by an integer, 
			special version ecimindivs(E,P,h,ug,PL,n) elliptic 
			curve with integer 
coefficients,           minimal model, double of a point ecimindouble(E,P) 
			elliptic curve with integer 
coefficients,           minimal model, factorization of discriminant 
			eciminfdisc(E) elliptic curve with integer 
coefficients,           minimal model, generators of torsion group 
			ecimingentor(E) elliptic curve with integer 
coefficients,           minimal model, local height at the archimedean 
			absolute value eciminlhaav(E,P) elliptic curve with 
			integer 
coefficients,           minimal model, local heights at all non archimedean 
			absolute values eciminlhnaav(E,P) elliptic curve 
			with integer 
coefficients,           minimal model, multiplication-map eciminmul(E,P,n) 
			elliptic curve with integer 
coefficients,           minimal model, multiplicative reduction type modulo 
			prime eciminmrtmp(E,p) elliptic curve with integer 
coefficients,           minimal model, negative point eciminneg(E,P) 
			elliptic curve with integer 
coefficients,           minimal model, point comparison modulo torsion 
			eciminpcompmt(E,P1,P2) elliptic curve with integer 
coefficients,           minimal model, point list union 
			eciminplunion(E,L1,L2,modus) elliptic curve with 
			integer 
coefficients,           minimal model, point list, insert point 
			eciminplinsp(P,h,PL) elliptic curve with integer 
coefficients,           minimal model, reduction type eciminredtype(E) 
			elliptic curve with integer 
coefficients,           minimal model, regulator eciminreg(E,LP,n,modus) 
			elliptic curve with integer 
coefficients,           minimal model, set NTH_EPS eciminntheps(E,d) 
			elliptic curve with integer 
coefficients,           minimal model, sum of points eciminsum(E,P,Q) 
			elliptic curve with integer 
coefficients,           minimal model, torsion group ecimintorgr(E) 
			elliptic curve with integer 
coefficients,           model in short normal form isponecisnf(E,P) is 
			point on elliptic curve with integer 
coefficients,           point normalization ecipnorm(P) elliptic curve with 
			integer 
coefficients,           short normal form fputecisnf(E,*pf) file put 
			elliptic curve with integer 
coefficients,           short normal form putecisnf(E) (MACRO) put elliptic 
			curve with integer 
coefficients,           short normal form, Mordell-Weil-group, base 
			ecisnfmwgbase(E) elliptic curve with integer 
coefficients,           short normal form, a4 ecisnfa4(E) elliptic curve 
			with integer 
coefficients,           short normal form, a6 ecisnfa6(E) elliptic curve 
			with integer 
coefficients,           short normal form, b2 ecisnfb2(E) elliptic curve 
			with integer 
coefficients,           short normal form, b4 ecisnfb4(E) elliptic curve 
			with integer 
coefficients,           short normal form, b6 ecisnfb6(E) elliptic curve 
			with integer 
coefficients,           short normal form, b8 ecisnfb8(E) elliptic curve 
			with integer 
coefficients,           short normal form, birational transformation of 
			coefficients ecisnfbtco(E,BT) elliptic curve with 
			integer 
coefficients,           short normal form, birational transformation to 
			actual ( rational ) model ecisnfbtac(E) elliptic 
			curve with integer 
coefficients,           short normal form, birational transformation to 
			minimal model ecisnfbtmin(E) elliptic curve with 
			integer 
coefficients,           short normal form, c4 ecisnfc4(E) elliptic curve 
			with integer 
coefficients,           short normal form, c6 ecisnfc6(E) elliptic curve 
			with integer 
coefficients,           short normal form, difference between Weil height 
			and Neron-Tate height ecisnfdwhnth(E) elliptic 
			curve with integer 
coefficients,           short normal form, discriminant ecisnfdisc(E) 
			elliptic curve with integer 
coefficients,           short normal form, double of point 
			ecisnfdouble(E,P) elliptic curve with integer 
coefficients,           short normal form, elliptic logarithm of point 
			ecisnfelogp(E,P,n) elliptic curve with integer 
coefficients,           short normal form, factorization of discriminant 
			ecisnffdisc(E) elliptic curve with integer 
coefficients,           short normal form, generators of the torsion group 
			ecisnfgentor(E) elliptic curve with integer 
coefficients,           short normal form, multiplication-map 
			ecisnfmul(E,P,n) elliptic curve with integer 
coefficients,           short normal form, negative of point ecisnfneg(E,P) 
			elliptic curve with integer 
coefficients,           short normal form, points of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve 
			with integer 
coefficients,           short normal form, sum of points ecisnfsum(E,P,Q) 
			elliptic curve with integer 
coefficients,           short normal form, torsion group ecisnftorgr(E) 
			elliptic curve with integer 
cofactor                of resultant equation upiresulc(P1,P2,pB) 
			univariate polynomial over the integers resultant 
			and 
cofactor                of resultant equation upmiresulc(m,P1,P2,pC) 
			univariate polynomial over modular integers 
			resultant and 
cofactor                of resultant equation upmsresulc(m,P1,P2,pC) 
			univariate polynomial over modular singles 
			resultant and 
cofactors               (rekursiv) pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial 
			over modular integers greatest common divisor and 
cofactors               (rekursiv) pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial 
			over modular singles greatest common divisor and 
cofactors               igcdcf(A,B,pU,pV) integer greatest common divisor 
			and 
cofactors               maiedfcf(M,pA,pB) matrix of integers elementary 
			divisor form and 
cofactors               maupmipedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over modular integer primes elementary 
			divisor form and 
cofactors               maupmspedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over modular single primes elementary 
			divisor form and 
cofactors               maupredfcf(M,pA,pB) matrix of univariate 
			polynomials over rationals elementary divisor form 
			and 
cofactors               pigcdcf(r,P1,P2,pQ1,pQ2) polynomial over integers 
			greatest common divisor and 
cofactors               upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate polynomial 
			over number field greatest common divisor and 
collector               gc() garbage 
collector               reinitialization gcreinit(bls,blnrm) garbage 
collector               with freeing blocks gcfree() garbage 
collector:              compressing gccpr() garbage 
column                  madel1rc(pM,i,j) matrix delete 1 row and 1 
columns                 madelsc(pM,I) matrix delete several 
columns                 madelsrc(pM,I,J) (MACRO) matrix delete several rows 
			and 
columns                 maiegsc(M,A,B) matrix of integers Euklid- Gauss- 
			step for 
columns                 manrcol(M) (MACRO) matrix number of 
columns                 maupmipegsc(p,M,A,B) matrix of univariate 
			polynomials over modular integer primes Euklid- 
			Gauss- step for 
columns                 maupmspegsc(p,M,A,B) matrix of univariate 
			polynomials over modular single primes Euklid- 
			Gauss- step for 
columns                 maupregsc(M,A,B) matrix of univariate polynomials 
			over rationals Euklid- Gauss- step for 
combination             ilcomb(A,B,m,n) integer linear 
combination             vecgfslc(p,AL,s1,s2,L1,L2) vector of Galois-field 
			with single characteristic elements linear 
combination             vecilc(s1,s2,V1,V2) vector of integers linear 
combination             vecmilc(M,S1,S2,L1,L2) vector of modular integers 
			linear 
combination             vecmslc(m,s1,s2,L1,L2) vector of modular singles 
			linear 
combination             vecnflc(F,s1,s2,L1,L2) vector of number field 
			elements linear 
combination             vecnfslc(F,s1,s2,L1,L2) vector of number field 
			elements, sparse representation, linear 
combination             vecpgfslc(r,p,AL,s1,s2,L1,L2) vector of polynomials 
			over Galois-field with single characteristic linear 
combination             vecpilc(r,P1,P2,V1,V2) vector of polynomials over 
			integers linear 
combination             vecpmilc(r,m,P1,P2,V1,V2) vector of polynomials 
			over modular integers linear 
combination             vecpmslc(r,m,P1,P2,V1,V2) vector of polynomials 
			over modular singles linear 
combination             vecpnflc(r,F,s1,s2,L1,L2) vector of polynomials 
			over number field linear 
combination             vecprlc(r,P1,P2,V1,V2) vector of polynomials over 
			rationals linear 
combination             vecrfmsp1lc(p,F1,F2,V1,V2) vector of rational 
			functions over modular single primes, transcendence 
			degree 1, linear 
combination             vecrfrlc(r,F1,F2,V1,V2) vector of rational 
			functions over rationals linear 
combination             vecrlc(s1,s2,V1,V2) vector of rationals linear 
combined                Schoof- Shanks- algorithm ecgf2cssa(G,a6,s,pl,ts) 
			elliptic curve over Galois field with 
			characteristic 2, 
combined                Schoof- Shanks- algorithm 
			ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic curve over 
			modular primes, short normal form, 
common                  denominator matrix of rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, list from 
common                  denominator matrix of rational functions over 
			modular single prime, transcendence degree 1, 
			hermitian reduction cdmarfmsp1hr(p,M) 
common                  denominator matrix of rational functions over 
			modular single prime, transcendence degree 1, 
			identity construction cdmarfmsp1id(n) 
common                  denominator matrix of rationals cdprlfcdmar(M) 
			common denominator polynomial over the rationals 
			list from 
common                  denominator matrix of rationals, hermitian 
			reduction cdmarhermred(M) 
common                  denominator matrix of rationals, identity 
			construction cdmarid(n) 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			clfcdprfmsp1(P,n) coefficient list from 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, from 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			coefficient list cdprfmsp1fcl(L,p) 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, 
			inverse cdprfmsp1inv(p,F,A) 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, list 
			from common denominator matrix of rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1lfm(M,p) 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, sum 
			cdprfmsp1sum(p,P1,P2) 
common                  denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, 
			univariate polynomial over modular single prime 
			quotient cdprfmsp1upq(p,F,P) 
common                  denominator polynomial over rational functions over 
			modular single primes, transcendence degree 1, 
			module homomorphism cdprfmsp1mh(p,P,M) 
common                  denominator polynomial over the rationals Z-module 
			homomorphism cdprzmodhom(P,M) 
common                  denominator polynomial over the rationals 
			clfcdpr(P,n) coefficient list from 
common                  denominator polynomial over the rationals from 
			coefficient list cdprfcl(L) 
common                  denominator polynomial over the rationals from 
			univariate polynomial over the rationals 
			cdprfupr(P) 
common                  denominator polynomial over the rationals integer 
			quotient cdpriquot(P,I) 
common                  denominator polynomial over the rationals inverse 
			cdprinv(F,A) 
common                  denominator polynomial over the rationals list from 
			common denominator matrix of rationals 
			cdprlfcdmar(M) 
common                  denominator polynomial over the rationals sum 
			cdprsum(P1,P2) 
common                  denominator polynomial over the rationals 
			uprfcdpr(PC) univariate polynomial over the 
			rationals from 
common                  divisor HDigcd() Heidelberg arithmetic package: 
			greatest 
common                  divisor and cofactors (rekursiv) 
			pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
			integers greatest 
common                  divisor and cofactors (rekursiv) 
			pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
			singles greatest 
common                  divisor and cofactors igcdcf(A,B,pU,pV) integer 
			greatest 
common                  divisor and cofactors pigcdcf(r,P1,P2,pQ1,pQ2) 
			polynomial over integers greatest 
common                  divisor and cofactors upnfgcdcf(F,P1,P2,pQ1,pQ2) 
			univariate polynomial over number field greatest 
common                  divisor iegcd(A,B,pU,pV) integer extended greatest 
common                  divisor igcd(A,B) integer greatest 
common                  divisor ihegcd(A,B,pV) integer half extended 
			greatest 
common                  divisor segcd(a,b,pu,pv) single-precision extended 
			greatest 
common                  divisor sgcd(a,b) single-precision greatest 
common                  divisor udpmiegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over modular integers extended greatest 
common                  divisor udpmigcd(m,P1,P2) univariate dense 
			polynomial over modular integers greatest 
common                  divisor udpmihegcd(m,P1,P2,pP3) univariate dense 
			polynomial over modular integers half extended 
			greatest 
common                  divisor udpmsegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over modular singles extended greatest 
common                  divisor udpmsgcd(m,P1,P2) univariate dense 
			polynomial over modular singles greatest 
common                  divisor udpmshegcd(m,P1,P2,pP3) univariate dense 
			polynomial over modular singles half extended 
			greatest 
common                  divisor upgf2gcd(G,P1,P2) univariate polynomial 
			over Galois-field with characteristic 2 greatest 
common                  divisor upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate 
			polynomial over Galois-field with single 
			characteristic extended greatest 
common                  divisor upgfsgcd(p,AL,P1,P2) univariate polynomial 
			over Galois-field with single characteristic 
			greatest 
common                  divisor upgfshegcd(p,AL,P1,P2,pP3) univariate 
			polynomial over Galois-field with single 
			characteristic half extended greatest 
common                  divisor upmiegcd(P,P1,P2,pP3,pP4) univariate 
			polynomial over modular integers extended greatest 
common                  divisor upmigcd(ip,P1,P2) univariate polynomial 
			over modular integers greatest 
common                  divisor upmihegcd(P,P1,P2,pP3) univariate 
			polynomial over modular integers half extended 
			greatest 
common                  divisor upmsegcd(m,P1,P2,pP3,pP4) univariate 
			polynomial over modular singles extended greatest 
common                  divisor upmsgcd(m,P1,P2) univariate polynomial over 
			modular singles greatest 
common                  divisor upmshegcd(m,P1,P2,pP3) univariate 
			polynomial over modular singles half extended 
			greatest 
common                  divisor upnfgcd(F,P1,P2) univariate polynomial over 
			number field greatest 
common                  divisor uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, extended 
			greatest 
common                  divisor, lists only igcd_lo(A,B) integer greatest 
common                  multiple dipevlcm(r,EV1,EV2) distributive 
			polynomial exponent vector least 
common                  multiple ilcm(A,B) integer least 
compare                 dipevcomp(r,EV1,EV2) distributive polynomial 
			exponent vector 
comparison              ccomp(a,b) (MACRO) complex 
comparison              ecrpcomp(P1,P2) elliptic curve over rational 
			numbers, point 
comparison              flcomp(f,g) floating point 
comparison              icomp(A,B) integer 
comparison              inocmp(dk1,dk2) i-node 
comparison              modulo torsion eciminpcompmt(E,P1,P2) elliptic 
			curve with integer coefficients, minimal model, 
			point 
comparison              qnfelcomp(D,A,B) quadratic number field element 
comparison              qnfidcomp(D,A,B) quadratic number field ideal 
comparison              rcomp(R,S) rational number 
comparison              special version lscomps(L1,L2) list of singles 
comparison              vncomp(Vn1,Vn2) variable name 
comparison,             lexicographical order lscomp(L1,L2) list of singles 
comparisons             PAFcomp() Papanikolaou floating point package: 
complete                factorization special upgfscfacts(p,AL,P) 
			univariate polynomial over Galois-field with single 
			characteristic 
complete                factorization special upmicfacts(P,F) univariate 
			polynomial over modular integers, 
complete                factorization special upmscfacts(p,A) univariate 
			polynomial over modular single prime, 
complete                factorization upgfscfact(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic 
complete                factorization upmicfact(ip,P) univariate polynomial 
			over modular integers 
complete                factorization upmscfact(p,A) univariate polynomial 
			over modular singles 
complex                 Dedekind eta function special cdedeetas(q,ln_q) 
complex                 Weber function f cweberf(z) 
complex                 Weber function f1 cweberf1(z) 
complex                 Weber function f2 cweberf2(z) 
complex                 absolute value cabsv(z) 
complex                 aritho-geometric mean cagm(a,b) 
complex                 comparison ccomp(a,b) (MACRO) 
complex                 conjugation cconjug(v) 
complex                 construction from real and imaginary part 
			ccri(re,im) (MACRO) 
complex                 difference cdif(v,w) 
complex                 exponential function cexp(z) 
complex                 exponential function special version cexpsv(z,n) 
complex                 imaginary part cimag(z) (MACRO) 
complex                 integer product ciprod(v,i) 
complex                 integer quotient ciquot(v,i) 
complex                 modular invariant j cmodinv(q,ln_q) 
complex                 number fputcn(a,v,n,pf) file put 
complex                 number in ball ? iscinball(z,r,eps) is 
complex                 number putcn(a,v,n) (MACRO) put 
complex                 period ecrcperiod(E) elliptic curve over the 
			rational numbers, 
complex                 product cprod(v,w) 
complex                 quotient cquot(v,w) 
complex                 real part creal(z) (MACRO) 
complex                 single exponentiation csexp(v,n) 
complex                 square csqr(v) 
complex                 square root csqrt(z) 
complex                 sum csum(v,w) 
composition             lcomp(a,L) list 
composition,            2 objects lcomp2(a,b,L) (MACRO) list 
composition,            3 objects lcomp3(a,b,c,L) (MACRO) list 
composition,            4 objects lcomp4(a,b,c,d,L) (MACRO) list 
composition,            5 objects lcomp5(a,b,c,d,e,L) (MACRO) list 
composition,            6 objects lcomp6(a,b,c,d,e,f,L) (MACRO) list 
comprehensive           Groebner basis 
			dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers 
comprehensive           Groebner basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers reduced 
comprehensive           Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers 
comprehensive           Groebner basis putdippicgb(r1,r2,CGBL,i,VL1,VL2) 
			(MACRO) put distributive polynomial over 
			polynomials over integers 
compressing             gccpr() garbage collector: 
concatenation           lcconc(L1,L2) list constructive 
concatenation           lconc(L1,L2) list 
concatenation           llconc(L) list of lists 
concatenation           macconc(M,N) matrix constructive 
concatenation           maconc(M,N) matrix 
concatenation           of transformations ecrbtconc(BT1,BT2) elliptic 
			curve over rational numbers, birational 
			transformation, 
conductor               ecqnfcond(E) elliptic curve over quadratic number 
			field, 
conductor               ecrcond(E) elliptic curve over rational numbers, 
conductor               ecrfcond(E) elliptic curve over rational numbers, 
			factorization of 
conductor               ecrlserhdlc(E,A,s,result) elliptic curve over the 
			rationals, L-series, higher derivative, large 
conductor               ecrlserhdsc(E,A,r,result) elliptic curve over 
			rational numbers, L-series, higher derivative, 
			small 
conjugate               element qnfconj(D,a) quadratic number field 
conjugation             cconjug(v) complex 
constant                ? ispconst(r,P,pC) is polynomial 
construction            1 magfscons1(p,AL,n) (MACRO) matrix of Galois-field 
			with single characteristic elements 
construction            1 maicons1(n) (MACRO) matrix of integers 
construction            1 mamicons1(m,n) (MACRO) matrix of modular integers 
construction            1 mamscons1(m,n) (MACRO) matrix of modular singles 
construction            1 manfcons1(F,n) (MACRO) matrix of number field 
			elements 
construction            1 manfscons1(F,n) (MACRO) matrix of number field 
			elements, sparse representation, 
construction            1 mapgfscons1(r,p,AL,n) (MACRO) matrix of 
			polynomials over Galois-field with single 
			characteristic 
construction            1 mapicons1(r,n) (MACRO) matrix of polynomials over 
			integers 
construction            1 mapmicons1(r,m,n) (MACRO) matrix of polynomials 
			over modular integers 
construction            1 mapmscons1(r,m,n) (MACRO) matrix of polynomials 
			over modular singles 
construction            1 mapnfcons1(r,F,n) (MACRO) matrix of polynomials 
			over number field 
construction            1 maprcons1(r,n) (MACRO) matrix of polynomials over 
			rationals 
construction            1 marcons1(n) (MACRO) matrix of rationals 
construction            1 marfmsp1c1(p,n) (MACRO) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, 
construction            1 marfrcons1(r,n) (MACRO) matrix of rational 
			functions over rationals 
construction            PAFcon() Papanikolaou floating point package: 
construction            by cutting flcut(A,e,lA) floating point 
construction            cdmarfmsp1id(n) common denominator matrix of 
			rational functions over modular single prime, 
			transcendence degree 1, identity 
construction            cdmarid(n) common denominator matrix of rationals, 
			identity 
construction            diagonal-matrix maconsdiag(n,el) matrix 
construction            flcons(A,e,lA) floating point 
construction            from real and imaginary part ccri(re,im) (MACRO) 
			complex 
construction            iprimeconstr(bits,f,pL,n) integer prime 
construction            of division polynomials ecgf2cdivp(G,a6,m) elliptic 
			curve over Galois-field with characteristic 2, 
construction            of division polynomials ecmpsnfcdivp(P,a4,a6,n) 
			elliptic curve over modular primes, short normal 
			form, 
construction            rcons(A,B) rational number 
construction            rfrcons(r,P1,P2) rational function over the 
			rationals 
construction            upgf2bqp(G,P) univariate polynomial over 
			Galois-field with characteristic 2 Berlekamp Q 
			polynomials 
construction            upgfsbqp(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic Berlekamp Q 
			polynomials 
construction            upmibqp(ip,P) univariate polynomial over modular 
			integers, Berlekamp Q polynomials 
construction            upmsbqp(p,A) univariate polynomial over modular 
			singles, Berlekamp Q polynomials 
construction            zero maconszero(m,n) matrix 
construction,           transcendence degree 1 rfmsp1cons(p,P1,P2) rational 
			function over modular single prime 
constructive            concatenation lcconc(L1,L2) list 
constructive            concatenation macconc(M,N) matrix 
constructive            delete lecdel(L,n) list element 
constructive            insert lecins(L,k,a) list element 
constructive            inverse lcinv(L) list 
constructive            transpose mactransp(M) matrix 
content                 (rekursiv) piicont(r,P) polynomial over integers 
			integer 
content                 (rekursiv) pmiucont(r,m,P) polynomial over modular 
			integers univariate 
content                 (rekursiv) pmsucont(r,m,P) polynomial over modular 
			singles univariate 
content                 and primitive part dipicp(r,P,pPP) distributive 
			polynomial over integers 
content                 and primitive part dippicp(r1,r2,P,pPP) 
			distributive polynomial over polynomials over 
			integers 
content                 and primitive part picontpp(r,P,pPP) polynomial 
			over integers 
content                 and primitive part udpicontpp(P,pPP) univariate 
			dense polynomial over integers 
content                 of resultant equation upireddiscc(P,pc) univariate 
			polynomial over the integers reduced discriminant 
			and 
content                 picont(r,P) polynomial over integers 
continued               fraction expansion ifactcfe(n,Large_P,K,mode) 
			integer factorization 
copy                    (rekursiv) lcopy(L) list 
copy                    macopy(M) matrix 
core                    algorithm afmsp1coreal(p,F,P,Q,mp) algebraic 
			function over modular single primes, transcendence 
			degree 1, 
core                    algorithm ippnfecoreal(F,p,Q,mp) integral p-primary 
			number field element, 
core                    algorithm with respect to integer primes 
			ippnfecalip(F,P,Q,mp) integral P-primary number 
			field element, 
cornaccia               cornaccia(m,q,x0,pX,pY) determine a solution of the 
			diophantine equation x^2+q*y^2=m using the 
			algorithm of 
cornaccia(m,q,x0,pX,pY) determine a solution of the diophantine equation 
			x^2+q*y^2=m using the algorithm of cornaccia 
cosinus                 flcos(a) floating point 
cosinus                 special version flcos_sp(f) floating point 
counting                algorithm ecgf2npca(G,a6) elliptic curve over 
			Galois-field with characteristic 2, 
cprod(v,w)              complex product 
cquot(v,w)              complex quotient 
creal(z)                (MACRO) complex real part 
csetinter(S,T)          characteristic set intersection 
csetpart(L)             characteristic set from partition 
csetunion(S,T)          characteristic set union 
csexp(v,n)              complex single exponentiation 
csqr(v)                 complex square 
csqrt(z)                complex square root 
csum(v,w)               complex sum 
cubic                   equation bpmisubcubeq(p,P,R) bivariate polynomial 
			over modular integers substitution with respect to 
			a 
cubic                   resolvent upid4cubres(P) univariate polynomial over 
			integers of degree 4 
curve                   Galois-field with characteristic 2, 
			multiplication-map ecgf2mul(G,a1,a2,a3,a4,a6,k,P1) 
			elliptic 
curve                   fast divisor search elcfds(N,b,e) elliptic 
curve                   find point iecfindp(p,a,b) integer elliptic 
curve                   fputecr(E,pf) file put elliptic 
curve                   fputecrac(E,pf) file put elliptic curve over 
			rational numbers, actual 
curve                   j-invariant to equation iecjtoeq(p,j) integer 
			elliptic 
curve                   j-invariant to equation special version 
			iecjtoeqsv(p,j,pi) integer elliptic 
curve                   of given number of points, j-invariant 
			iecgnpj(p,m,h1,h2,D) integer elliptic 
curve                   over Galois field with characteristic 2, combined 
			Schoof- Shanks- algorithm ecgf2cssa(G,a6,s,pl,ts) 
			elliptic 
curve                   over Galois field with characteristic 2, number of 
			points after field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
curve                   over Galois-field with characteristic 2 ? 
			iselecgf2(G,a1,a2,a3,a4,a6,P) is element of an 
			elliptic 
curve                   over Galois-field with characteristic 2 equal ? 
			isppecgf2eq(p,P1,P2) is projective point of an 
			elliptic 
curve                   over Galois-field with characteristic 2 point at 
			infinity ? isppecgf2pai(G,P) is projective point of 
			an elliptic 
curve                   over Galois-field with characteristic 2, Tate's 
			values b2, b4, b6 ecgf2tavb6(G,a1,a2,a3,a4,a6) 
			elliptic 
curve                   over Galois-field with characteristic 2, Tate's 
			values b2, b4, b6, b8 ecgf2tavb8(G,a1,a2,a3,a4,a6) 
			elliptic 
curve                   over Galois-field with characteristic 2, Tate's 
			values c4, c6 ecgf2tavc6(G,a1,a2,a3,a4,a6) elliptic 
curve                   over Galois-field with characteristic 2, birational 
			transformation of coefficients 
			ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) elliptic 
curve                   over Galois-field with characteristic 2, 
			construction of division polynomials 
			ecgf2cdivp(G,a6,m) elliptic 
curve                   over Galois-field with characteristic 2, counting 
			algorithm ecgf2npca(G,a6) elliptic 
curve                   over Galois-field with characteristic 2, 
			discriminant ecgf2disc(G,a1,a2,a3,a4,a6) elliptic 
curve                   over Galois-field with characteristic 2, find point 
			ecgf2fp(G,a1,a2,a3,a4,a6) elliptic 
curve                   over Galois-field with characteristic 2, finding a 
			multiple of the order of a point with the Pollard 
			Lambda method ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) 
			elliptic 
curve                   over Galois-field with characteristic 2, 
			j-invariant ecgf2jinv(G,a1,a2,a3,a4,a6) elliptic 
curve                   over Galois-field with characteristic 2, line 
			through points ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) 
			elliptic 
curve                   over Galois-field with characteristic 2, modified 
			Shanks' algorithm, first part 
			ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) elliptic 
curve                   over Galois-field with characteristic 2, multiple 
			of the order of a point to exact order of the point 
			ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic 
curve                   over Galois-field with characteristic 2, negative 
			point ecgf2neg(G,a1,a2,a3,a4,a6,P) elliptic 
curve                   over Galois-field with characteristic 2, number of 
			points modulo a power of 2 ecgf2npmp2(G,a6,c,L) 
			elliptic 
curve                   over Galois-field with characteristic 2, number of 
			points modulo a single prime determined with the 
			Schoof algorithm, version 1 ecgf2npmspv1(G,a6,p,L) 
			elliptic 
curve                   over Galois-field with characteristic 2, number of 
			points modulo a single prime determined with the 
			Schoof algorithm, version 2 ecgf2npmspv2(G,a6,p,L) 
			elliptic 
curve                   over Galois-field with characteristic 2, number of 
			points modulo an integer determined with the Schoof 
			algorithm ecgf2npmi(G,a6,S,v,pM) elliptic 
curve                   over Galois-field with characteristic 2, special 
			form, multiplication-map, special version 
			ecgf2sfmuls(p,a6,x1,y1,n) elliptic 
curve                   over Galois-field with characteristic 2, special 
			form, sum of points, special version 
			ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic 
curve                   over Galois-field with characteristic 2, standard 
			representation of projective point ecgf2srpp(G,P) 
			elliptic 
curve                   over Galois-field with characteristic 2, sum of 
			points ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) elliptic 
curve                   over modular integer primes short normal form 
			number of points special version 
			ecmipsnfnpsv(p,a4,a6) elliptic 
curve                   over modular primes ? iselecmp(p,a1,a2,a3,a4,a6,P) 
			is element of an elliptic 
curve                   over modular primes Tate's values b2, b4, b6 
			ecmptavb6(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes Tate's values b2, b4, b6, b8 
			ecmptavb8(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes Tate's values c4, c6 
			ecmptavc6(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes equal ? isppecmpeq(p,P1,P2) is 
			projective point of an elliptic 
curve                   over modular primes multiplication-map 
			ecmpmul(p,a1,a2,a3,a4,a6,n,P1) elliptic 
curve                   over modular primes negative point 
			ecmpneg(p,a1,a2,a3,a4,a6,P) elliptic 
curve                   over modular primes point at infinity ? 
			isppecmppai(p,P) is projective point of an elliptic 
curve                   over modular primes to short normal form 
			ecmptosnf(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes, birational transformation of 
			coefficients ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) 
			elliptic 
curve                   over modular primes, discriminant 
			ecmpdisc(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes, find point 
			ecmpfp(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes, j-invariant 
			ecmpjinv(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular primes, line through points 
			ecmplp(p,a1,a2,a3,a4,a6,P1,P2) elliptic 
curve                   over modular primes, short normal form ? 
			iselecmpsnf(p,a,b,P) is element of an elliptic 
curve                   over modular primes, short normal form, combined 
			Schoof- Shanks- algorithm 
			ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic 
curve                   over modular primes, short normal form, 
			construction of division polynomials 
			ecmpsnfcdivp(P,a4,a6,n) elliptic 
curve                   over modular primes, short normal form, 
			discriminant ecmpsnfdisc(p,a4,a6) elliptic 
curve                   over modular primes, short normal form, find point 
			ecmpsnffp(p,a4,a6) elliptic 
curve                   over modular primes, short normal form, finding a 
			multiple of the order of a point with the Pollard 
			Lambda method ecmpsnffmopl(p,a4,a6,P,L,N) elliptic 
curve                   over modular primes, short normal form, finding a 
			multiple of the order of a point with the Pollard 
			Rho method ecmpsnffmopr(p,a4,a6,P,k) elliptic 
curve                   over modular primes, short normal form, j-invariant 
			ecmpsnfjinv(p,a4,a6) elliptic 
curve                   over modular primes, short normal form, line 
			through points ecmpsnflp(p,a4,a6,P1,P2) elliptic 
curve                   over modular primes, short normal form, modified 
			Shanks' algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic 
curve                   over modular primes, short normal form, multiple of 
			the order of a point to exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic 
curve                   over modular primes, short normal form, 
			multiplication-map ecmpsnfmul(p,a4,a6,n,P1) 
			elliptic 
curve                   over modular primes, short normal form, 
			multiplication-map, special version 
			ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic 
curve                   over modular primes, short normal form, negative 
			point ecmpsnfneg(p,a4,a6,P) elliptic 
curve                   over modular primes, short normal form, number of 
			points modulo 2 ecmpsnfnpm2(P,a4,a6) elliptic 
curve                   over modular primes, short normal form, number of 
			points modulo a single prime determined with the 
			Schoof algorithm ecmpsnfnpmsp(P,a4,a6,p,L) elliptic 
curve                   over modular primes, short normal form, number of 
			points modulo an integer determined with the Schoof 
			algorithm ecmpsnfnpmi(P,a4,a6,S,pM) elliptic 
curve                   over modular primes, short normal form, sum of 
			points ecmpsnfsum(p,a4,a6,P1,P2) elliptic 
curve                   over modular primes, short normal form, sum of 
			points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic 
curve                   over modular primes, standard representation of 
			projective point ecmpsrpp(p,P) elliptic 
curve                   over modular primes, sum of points 
			ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) elliptic 
curve                   over modular single prime, number of points 
			ecmspnp(p,a1,a2,a3,a4,a6) elliptic 
curve                   over modular single primes, short normal form, 
			Shanks' algorithm ecmspsnfsha(p,a4,a6) (MACRO) 
			elliptic 
curve                   over modular single primes, short normal form, 
			number of points ecmspsnfnp(p,a4,a6) elliptic 
curve                   over number field ? iselecnf(F,a1,a2,a3,a4,a6,P) is 
			element of an elliptic 
curve                   over number field Tate's values b2, b4, b6 
			ecnftavb6(F,a1,a2,a3,a4,a6) elliptic 
curve                   over number field Tate's values b2, b4, b6, b8 
			ecnftavb8(F,a1,a2,a3,a4,a6) elliptic 
curve                   over number field Tate's values c4, c6 
			ecnftavc6(F,a1,a2,a3,a4,a6) elliptic 
curve                   over number field birational transformation of 
			coefficients ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) 
			elliptic 
curve                   over number field discriminant 
			ecnfdisc(F,a1,a2,a3,a4,a6) elliptic 
curve                   over number field equal? isppecnfeq(F,P1,P2) is 
			projective point of an elliptic 
curve                   over number field j-invariant 
			ecnfjinv(F,a1,a2,a3,a4,a6) elliptic 
curve                   over number field line through points 
			ecnflp(F,a1,a2,a3,a4,a6,P1,P2) elliptic 
curve                   over number field multiplication-map 
			ecnfmul(F,a1,a2,a3,a4,a6,n,P1) elliptic 
curve                   over number field negative point 
			ecnfneg(F,a1,a2,a3,a4,a6,P) elliptic 
curve                   over number field point at infinity ? 
			isppecnfpai(P) is projective point of an elliptic 
curve                   over number field short normal form line through 
			points ecnfsnflp(F,a,b,P1,P2) elliptic 
curve                   over number field short normal form 
			multiplication-map ecnfsnfmul(F,a,b,n,P1) elliptic 
curve                   over number field short normal form negative point 
			ecnfsnfneg(F,a,b,P) elliptic 
curve                   over number field short normal form sum of points 
			ecnfsnfsum(F,a,b,P1,P2) elliptic 
curve                   over number field standard representation of 
			projective point ecnfsrpp(F,P) elliptic 
curve                   over number field sum of points 
			ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) elliptic 
curve                   over number field to short normal form 
			ecnftosnf(F,a1,a2,a3,a4,a6) elliptic 
curve                   over number field, short normal form ? 
			iselecnfsnf(F,a,b,P) is element of an elliptic 
curve                   over number field, short normal form, discriminant 
			ecnfsnfdisc(F,a,b) elliptic 
curve                   over number field, short normal form, j-invariant 
			ecnfsnfjinv(F,a,b) elliptic 
curve                   over quadratic number field to elliptic curve with 
			integral coefficients ecqnftoeci(D,L) elliptic 
curve                   over quadratic number field, Tate's algorithm 
			ecqnftatealg(D,LC,LTV,P,pi,z,n) elliptic 
curve                   over quadratic number field, actual model, Tate 
			value b2 ecqnfacb2(E) elliptic 
curve                   over quadratic number field, actual model, Tate 
			value b4 ecqnfacb4(E) elliptic 
curve                   over quadratic number field, actual model, Tate 
			value b6 ecqnfacb6(E) elliptic 
curve                   over quadratic number field, actual model, Tate 
			value b8 ecqnfacb8(E) elliptic 
curve                   over quadratic number field, actual model, Tate 
			value c4 ecqnfacc4(E) elliptic 
curve                   over quadratic number field, actual model, Tate 
			value c6 ecqnfacc6(E) elliptic 
curve                   over quadratic number field, actual model, 
			discriminant ecqnfacdisc(E) elliptic 
curve                   over quadratic number field, actual model, 
			factorization of the norm of the discriminant 
			ecqnfacfndisc(E) elliptic 
curve                   over quadratic number field, actual model, norm of 
			the discriminant ecqnfacndisc(E) elliptic 
curve                   over quadratic number field, actual model, prime 
			ideal factorization of the discriminant 
			ecqnfacpifdi(E) elliptic 
curve                   over quadratic number field, conductor ecqnfcond(E) 
			elliptic 
curve                   over quadratic number field, field discriminant 
			ecqnfflddisc(E) (MACRO) elliptic 
curve                   over quadratic number field, field discriminant 
			modulo 4 ecqnfdmod4(E) (MACRO) elliptic 
curve                   over quadratic number field, initialization 
			ecqnfinit(D,a1,a2,a3,a4,a6) elliptic 
curve                   over quadratic number field, j-invariant 
			ecqnfjinv(E) elliptic 
curve                   over rational numbers fgetecr(pf) file get elliptic 
curve                   over rational numbers fgetecrp(pf) file get point 
			on elliptic 
curve                   over rational numbers getecr() get elliptic 
curve                   over rational numbers point getecrp() (MACRO) get 
			elliptic 
curve                   over rational numbers putecr(E) (MACRO) put 
			elliptic 
curve                   over rational numbers reduction list ecrrl(E) 
			elliptic 
curve                   over rational numbers reduction type ecrrt(E,p) 
			elliptic 
curve                   over rational numbers, Fourier expansion of the 
			L-series ecrfelser(E,A,z,result) elliptic 
curve                   over rational numbers, L-series ecrlser(E) elliptic 
curve                   over rational numbers, L-series, first derivative 
			ecrlserfd(E) elliptic 
curve                   over rational numbers, L-series, higher derivative 
			ecrlserhd(E,r) elliptic 
curve                   over rational numbers, L-series, higher derivative, 
			small conductor ecrlserhdsc(E,A,r,result) elliptic 
curve                   over rational numbers, Manin algorithm 
			ecrmaninalg(E) elliptic 
curve                   over rational numbers, Tate's values b2, b4, b6, b8 
			ecrtavalb(a1,a2,a3,a4,a6) elliptic 
curve                   over rational numbers, actual curve fputecrac(E,pf) 
			file put elliptic 
curve                   over rational numbers, actual curve putecrac(E) 
			(MACRO) put elliptic 
curve                   over rational numbers, actual curve to global 
			minimal model ( Laska's algorithm ) 
			ecractoecimin(E) elliptic 
curve                   over rational numbers, actual curve, a1 ecraca1(E) 
			(MACRO) elliptic 
curve                   over rational numbers, actual curve, a2 ecraca2(E) 
			(MACRO) elliptic 
curve                   over rational numbers, actual curve, a3 ecraca3(E) 
			(MACRO) elliptic 
curve                   over rational numbers, actual curve, a4 ecraca4(E) 
			(MACRO) elliptic 
curve                   over rational numbers, actual curve, a6 ecraca6(E) 
			(MACRO) elliptic 
curve                   over rational numbers, actual curve, b2 ecracb2(E) 
			elliptic 
curve                   over rational numbers, actual curve, b4 ecracb4(E) 
			elliptic 
curve                   over rational numbers, actual curve, b6 ecracb6(E) 
			elliptic 
curve                   over rational numbers, actual curve, b8 ecracb8(E) 
			elliptic 
curve                   over rational numbers, actual curve, birational 
			transformation to short normal form ecracbtsnf(E) 
			elliptic 
curve                   over rational numbers, actual curve, c4 ecracc4(E) 
			elliptic 
curve                   over rational numbers, actual curve, c6 ecracc6(E) 
			elliptic 
curve                   over rational numbers, actual curve, discriminant 
			ecracdisc(E) elliptic 
curve                   over rational numbers, actual curve, factorization 
			of discriminant ecracfdisc(E) elliptic 
curve                   over rational numbers, actual curve, generators of 
			torsion group ecracgentor(E) elliptic 
curve                   over rational numbers, actual curve, torsion group 
			ecractorgr(E) elliptic 
curve                   over rational numbers, actual model isponecrac(E,P) 
			is point on elliptic 
curve                   over rational numbers, birational transformation of 
			coefficients ecracbtco(E,BT) elliptic 
curve                   over rational numbers, birational transformation of 
			coefficients ecrbtco(LC,BT) elliptic 
curve                   over rational numbers, birational transformation of 
			list of points ecrbtlistp(LP,BT,modus) elliptic 
curve                   over rational numbers, birational transformation of 
			point ecrbtp(P,BT) elliptic 
curve                   over rational numbers, birational transformation, 
			concatenation of transformations ecrbtconc(BT1,BT2) 
			elliptic 
curve                   over rational numbers, birational transformation, 
			inverse transformation ecrbtinv(BT) elliptic 
curve                   over rational numbers, conductor ecrcond(E) 
			elliptic 
curve                   over rational numbers, exponent of torsion group 
			ecrexptor(E) elliptic 
curve                   over rational numbers, factorization of conductor 
			ecrfcond(E) elliptic 
curve                   over rational numbers, j-invariant ecrjinv(E) 
			elliptic 
curve                   over rational numbers, list of points 
			putecrlistp(P,modus) (MACRO) put elliptic 
curve                   over rational numbers, order of torsion group 
			ecrordtor(E) elliptic 
curve                   over rational numbers, point comparison 
			ecrpcomp(P1,P2) elliptic 
curve                   over rational numbers, point fputecrp(P,pf) file 
			put elliptic 
curve                   over rational numbers, point normalization 
			ecrpnorm(P) elliptic 
curve                   over rational numbers, point putecrp(P) (MACRO) put 
			elliptic 
curve                   over rational numbers, point to projective 
			representation ecrptoproj(P) elliptic 
curve                   over rational numbers, short normal form, real 
			roots of the right side ecrsnfrroots(a,b) elliptic 
curve                   over rational numbers, sign of the functional 
			equation ecrsign(E) elliptic 
curve                   over rational numbers, structure of torsion group 
			ecrstrtor(E) elliptic 
curve                   over the rational numbers initialization 
			ecrinit(a1r,a2r,a3r,a4r,a6r) elliptic 
curve                   over the rational numbers, Weil height 
			ecracweilhe(E,P) elliptic 
curve                   over the rational numbers, actual curve, 
			Mordell-Weil-group, base ecracmwgbase(E) elliptic 
curve                   over the rational numbers, actual curve, 
			multiplication-map ecracmul(E,P,n) elliptic 
curve                   over the rational numbers, actual curve, negative 
			point ecracneg(E,P) elliptic 
curve                   over the rational numbers, actual curve, sum of 
			points ecracsum(E,P,Q) elliptic 
curve                   over the rational numbers, complex period 
			ecrcperiod(E) elliptic 
curve                   over the rational numbers, invariants 
			fputecrinv(E,pf) file put elliptic 
curve                   over the rational numbers, invariants putecrinv(E) 
			(MACRO) put elliptic 
curve                   over the rational numbers, list of points 
			fputecrlistp(P,modus,pf) file put elliptic 
curve                   over the rational numbers, minimal model, double of 
			point ecracdouble(E,P) elliptic 
curve                   over the rational numbers, order of Tate- 
			Shafarevic group ecrordtsg(E) elliptic 
curve                   over the rational numbers, real period 
			ecrrperiod(E) elliptic 
curve                   over the rational numbers, regulator 
			ecrregulator(E) elliptic 
curve                   over the rationals Tate's values c4, c6 
			ecrtavalc(a1,a2,a3,a4,a6) elliptic 
curve                   over the rationals point at infinity ? ispecrpai(P) 
			(MACRO) is point of an elliptic 
curve                   over the rationals, L-series, 'rank'-th derivative 
			ecrlserrkd(E) elliptic 
curve                   over the rationals, L-series, first derivative, 
			special version ecrlserfds(E,A,result) elliptic 
curve                   over the rationals, L-series, higher derivative, 
			large conductor ecrlserhdlc(E,A,s,result) elliptic 
curve                   over the rationals, L-series, special version 
			ecrlsers(E,A,result) elliptic 
curve                   over the rationals, actual curve, birational 
			transformation to minimal model ecracbtmin(E) 
			elliptic 
curve                   over the rationals, coefficients of L- series 
			ecrclser(E,A,n) elliptic 
curve                   over the rationals, factorization of the 
			denominator of the j-invariant ecrfdenjinv(E) 
			elliptic 
curve                   over the rationals, product over all c_p- values 
			ecrprodcp(E) elliptic 
curve                   over the rationals, rank ecrrank(E) elliptic 
curve                   over the rationals, sign of the functional 
			equation, special version ecrsigns(E,A,C) elliptic 
curve                   point product iecpprod(p,E,P,a) integer elliptic 
curve                   point sum iecpsum(p,P,Q,a) integer elliptic 
curve                   primality test iecpt(n,m,lp,a,b,anz) integer 
			elliptic 
curve                   prime divisor search sum 
			elcpdssum(N,x1,y1,x2,y2,px3,py3,a) elliptic 
curve                   pure divisor search elcpds(N,a,z) elliptic 
curve                   putecrac(E) (MACRO) put elliptic curve over 
			rational numbers, actual 
curve                   to global minimal model ( Laska's algorithm ) 
			ecractoecimin(E) elliptic curve over rational 
			numbers, actual 
curve                   with integer coefficients Tate's algorithm 
			ecitatealg(a1,a2,a3,a4,a6,p,n) elliptic 
curve                   with integer coefficients, Tate's values b2, b4, 
			b6, b8 ecitavalb(a1,a2,a3,a4,a6) elliptic 
curve                   with integer coefficients, actual curve, difference 
			of points ecracdif(E,P,Q) elliptic 
curve                   with integer coefficients, minimal model 
			fputecimin(E,pf) file put elliptic 
curve                   with integer coefficients, minimal model 
			isecimintorp(E,P) is torsion point on elliptic 
curve                   with integer coefficients, minimal model 
			isineciminpl(E,P,h,PL) is in list of points on 
			elliptic 
curve                   with integer coefficients, minimal model 
			isponecimin(E,P) is point on elliptic 
curve                   with integer coefficients, minimal model 
			putecimin(E) (MACRO) put elliptic 
curve                   with integer coefficients, minimal model to short 
			normal form ecimintosnf(E) elliptic 
curve                   with integer coefficients, minimal model, 
			Mordell-Weil-group, base eciminmwgbase(E) elliptic 
curve                   with integer coefficients, minimal model, 
			Neron-Tate height eciminnetahe(E,P) elliptic 
curve                   with integer coefficients, minimal model, 
			Neron-Tate pairing eciminnetapa(E,P,Q) elliptic 
curve                   with integer coefficients, minimal model, Tate's 
			algorithm ecimintatealg(E,p,n) elliptic 
curve                   with integer coefficients, minimal model, Tate's 
			values c4, c6 ecitavalc(a1,a2,a3,a4,a6) elliptic 
curve                   with integer coefficients, minimal model, a1 
			ecimina1(E) elliptic 
curve                   with integer coefficients, minimal model, a2 
			ecimina2(E) elliptic 
curve                   with integer coefficients, minimal model, a3 
			ecimina3(E) elliptic 
curve                   with integer coefficients, minimal model, a4 
			ecimina4(E) elliptic 
curve                   with integer coefficients, minimal model, a6 
			ecimina6(E) elliptic 
curve                   with integer coefficients, minimal model, b2 
			eciminb2(E) elliptic 
curve                   with integer coefficients, minimal model, b4 
			eciminb4(E) elliptic 
curve                   with integer coefficients, minimal model, b6 
			eciminb6(E) elliptic 
curve                   with integer coefficients, minimal model, b8 
			eciminb8(E) elliptic 
curve                   with integer coefficients, minimal model, bad 
			reduction type modulo prime eciminbrtmp(E,p,n) 
			elliptic 
curve                   with integer coefficients, minimal model, 
			birational transformation of coefficients 
			eciminbtco(E,BT) elliptic 
curve                   with integer coefficients, minimal model, 
			birational transformation to actual ( rational ) 
			model eciminbtac(E) elliptic 
curve                   with integer coefficients, minimal model, 
			birational transformation to short normal form 
			eciminbtsnf(E) elliptic 
curve                   with integer coefficients, minimal model, c4 
			eciminc4(E) elliptic 
curve                   with integer coefficients, minimal model, c6 
			eciminc6(E) elliptic 
curve                   with integer coefficients, minimal model, 
			difference between Weil height and Neron-Tate 
			height ecimindwhnth(E) elliptic 
curve                   with integer coefficients, minimal model, 
			difference of points ecimindif(E,P,Q) elliptic 
curve                   with integer coefficients, minimal model, 
			difference of points ecisnfdif(E,P,Q) elliptic 
curve                   with integer coefficients, minimal model, 
			discriminant ecimindisc(E) elliptic 
curve                   with integer coefficients, minimal model, division 
			by 2 of a point ecimindivby2(E,P,h,PL,H) elliptic 
curve                   with integer coefficients, minimal model, division 
			of a point by an integer ecimindiv(E,P,n) elliptic 
curve                   with integer coefficients, minimal model, division 
			of a point by an integer, special version 
			ecimindivs(E,P,h,ug,PL,n) elliptic 
curve                   with integer coefficients, minimal model, double of 
			a point ecimindouble(E,P) elliptic 
curve                   with integer coefficients, minimal model, 
			factorization of discriminant eciminfdisc(E) 
			elliptic 
curve                   with integer coefficients, minimal model, 
			generators of torsion group ecimingentor(E) 
			elliptic 
curve                   with integer coefficients, minimal model, local 
			height at the archimedean absolute value 
			eciminlhaav(E,P) elliptic 
curve                   with integer coefficients, minimal model, local 
			heights at all non archimedean absolute values 
			eciminlhnaav(E,P) elliptic 
curve                   with integer coefficients, minimal model, 
			multiplication-map eciminmul(E,P,n) elliptic 
curve                   with integer coefficients, minimal model, 
			multiplicative reduction type modulo prime 
			eciminmrtmp(E,p) elliptic 
curve                   with integer coefficients, minimal model, negative 
			point eciminneg(E,P) elliptic 
curve                   with integer coefficients, minimal model, point 
			comparison modulo torsion eciminpcompmt(E,P1,P2) 
			elliptic 
curve                   with integer coefficients, minimal model, point 
			list union eciminplunion(E,L1,L2,modus) elliptic 
curve                   with integer coefficients, minimal model, point 
			list, insert point eciminplinsp(P,h,PL) elliptic 
curve                   with integer coefficients, minimal model, reduction 
			type eciminredtype(E) elliptic 
curve                   with integer coefficients, minimal model, regulator 
			eciminreg(E,LP,n,modus) elliptic 
curve                   with integer coefficients, minimal model, set 
			NTH_EPS eciminntheps(E,d) elliptic 
curve                   with integer coefficients, minimal model, sum of 
			points eciminsum(E,P,Q) elliptic 
curve                   with integer coefficients, minimal model, torsion 
			group ecimintorgr(E) elliptic 
curve                   with integer coefficients, model in short normal 
			form isponecisnf(E,P) is point on elliptic 
curve                   with integer coefficients, point normalization 
			ecipnorm(P) elliptic 
curve                   with integer coefficients, short normal form 
			fputecisnf(E,*pf) file put elliptic 
curve                   with integer coefficients, short normal form 
			putecisnf(E) (MACRO) put elliptic 
curve                   with integer coefficients, short normal form, 
			Mordell-Weil-group, base ecisnfmwgbase(E) elliptic 
curve                   with integer coefficients, short normal form, a4 
			ecisnfa4(E) elliptic 
curve                   with integer coefficients, short normal form, a6 
			ecisnfa6(E) elliptic 
curve                   with integer coefficients, short normal form, b2 
			ecisnfb2(E) elliptic 
curve                   with integer coefficients, short normal form, b4 
			ecisnfb4(E) elliptic 
curve                   with integer coefficients, short normal form, b6 
			ecisnfb6(E) elliptic 
curve                   with integer coefficients, short normal form, b8 
			ecisnfb8(E) elliptic 
curve                   with integer coefficients, short normal form, 
			birational transformation of coefficients 
			ecisnfbtco(E,BT) elliptic 
curve                   with integer coefficients, short normal form, 
			birational transformation to actual ( rational ) 
			model ecisnfbtac(E) elliptic 
curve                   with integer coefficients, short normal form, 
			birational transformation to minimal model 
			ecisnfbtmin(E) elliptic 
curve                   with integer coefficients, short normal form, c4 
			ecisnfc4(E) elliptic 
curve                   with integer coefficients, short normal form, c6 
			ecisnfc6(E) elliptic 
curve                   with integer coefficients, short normal form, 
			difference between Weil height and Neron-Tate 
			height ecisnfdwhnth(E) elliptic 
curve                   with integer coefficients, short normal form, 
			discriminant ecisnfdisc(E) elliptic 
curve                   with integer coefficients, short normal form, 
			double of point ecisnfdouble(E,P) elliptic 
curve                   with integer coefficients, short normal form, 
			elliptic logarithm of point ecisnfelogp(E,P,n) 
			elliptic 
curve                   with integer coefficients, short normal form, 
			factorization of discriminant ecisnffdisc(E) 
			elliptic 
curve                   with integer coefficients, short normal form, 
			generators of the torsion group ecisnfgentor(E) 
			elliptic 
curve                   with integer coefficients, short normal form, 
			multiplication-map ecisnfmul(E,P,n) elliptic 
curve                   with integer coefficients, short normal form, 
			negative of point ecisnfneg(E,P) elliptic 
curve                   with integer coefficients, short normal form, 
			points of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic 
curve                   with integer coefficients, short normal form, sum 
			of points ecisnfsum(E,P,Q) elliptic 
curve                   with integer coefficients, short normal form, 
			torsion group ecisnftorgr(E) elliptic 
curve                   with integral coefficients ecqnftoeci(D,L) elliptic 
			curve over quadratic number field to elliptic 
curve,                  Mordell-Weil-group, base ecracmwgbase(E) elliptic 
			curve over the rational numbers, actual 
curve,                  a1 ecraca1(E) (MACRO) elliptic curve over rational 
			numbers, actual 
curve,                  a2 ecraca2(E) (MACRO) elliptic curve over rational 
			numbers, actual 
curve,                  a3 ecraca3(E) (MACRO) elliptic curve over rational 
			numbers, actual 
curve,                  a4 ecraca4(E) (MACRO) elliptic curve over rational 
			numbers, actual 
curve,                  a6 ecraca6(E) (MACRO) elliptic curve over rational 
			numbers, actual 
curve,                  b2 ecracb2(E) elliptic curve over rational numbers, 
			actual 
curve,                  b4 ecracb4(E) elliptic curve over rational numbers, 
			actual 
curve,                  b6 ecracb6(E) elliptic curve over rational numbers, 
			actual 
curve,                  b8 ecracb8(E) elliptic curve over rational numbers, 
			actual 
curve,                  birational transformation to minimal model 
			ecracbtmin(E) elliptic curve over the rationals, 
			actual 
curve,                  birational transformation to short normal form 
			ecracbtsnf(E) elliptic curve over rational numbers, 
			actual 
curve,                  c4 ecracc4(E) elliptic curve over rational numbers, 
			actual 
curve,                  c6 ecracc6(E) elliptic curve over rational numbers, 
			actual 
curve,                  difference of points ecracdif(E,P,Q) elliptic curve 
			with integer coefficients, actual 
curve,                  discriminant ecracdisc(E) elliptic curve over 
			rational numbers, actual 
curve,                  factorization of discriminant ecracfdisc(E) 
			elliptic curve over rational numbers, actual 
curve,                  generators of torsion group ecracgentor(E) elliptic 
			curve over rational numbers, actual 
curve,                  multiplication-map ecracmul(E,P,n) elliptic curve 
			over the rational numbers, actual 
curve,                  negative point ecracneg(E,P) elliptic curve over 
			the rational numbers, actual 
curve,                  sum of points ecracsum(E,P,Q) elliptic curve over 
			the rational numbers, actual 
curve,                  torsion group ecractorgr(E) elliptic curve over 
			rational numbers, actual 
cutting                 flcut(A,e,lA) floating point construction by 
cweberf(z)              complex Weber function f 
cweberf1(z)             complex Weber function f1 
cweberf2(z)             complex Weber function f2 
decimal                 fputrd(R,n,pf) file put rational number 
decimal                 putrd(R,n) (MACRO) put rational number 
decomposition           law affmsp1decl(p,F,P) algebraic function field 
			over modular single prime, transcendence degree 1, 
decomposition           law nfipdeclaw(F,P) number field, integer prime 
decomposition           law nfspdeclaw(F,p) number field, single prime 
decomposition           law ouspprmsp1dl(p,F,P,k) order of a univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
defining                polynomial and p-minimal polynomials of the 
			generators ouspiapfgmic(p,P,k) order of an 
			univariate separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal orders 
			of the p-adic divisors of the 
defining                polynomial or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
			modular single prime, transcendence degree 1, 
			P-primality test and factorization of the 
defining                polynomial or the minimal polynomial 
			infepptfact(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and factorization of the 
defining                polynomial or the minimal polynomial with respect 
			to integer primes infepptfip(F,p,Q,ppot,a0,z) 
			integral number field element p-primality test and 
			factorization of the 
defining                polynomial, generators of p-maximal orders of the 
			p-adic divisors of the defining polynomial and 
			p-minimal polynomials of the generators 
			ouspiapfgmic(p,P,k) order of an univariate 
			separable polynomial over the integers 
			approximation of p-adic factorization of the 
definite                binary quadratic forms iprpdbqf(D,h1,h2) integer 
			primitive reduced positive 
degree                  1 ? ismarfmsp1(p,M) (MACRO) is matrix of rational 
			functions over modular single primes, transcendence 
degree                  1 ? isrfmsp1(p,R) is rational function over modular 
			single prime, transcendence 
degree                  1 ? isvecrfmsp1(p,V) (MACRO) is vector of rational 
			functions over modular single primes, transcendence 
degree                  1 cdprfmsp1fup(p,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from univariate polynomial 
			over rational functions over modular single prime, 
			transcendence 
degree                  1 cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, list from common 
			denominator matrix of rational functions over 
			modular single prime, transcendence 
degree                  1 clfcdprfmsp1(P,n) coefficient list from common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence 
degree                  1 fgetmarfmsp1(p,V,pf) (MACRO) file get matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1 fgetrfmsp1(p,V,pf) file get rational function 
			over modular single primes, transcendence 
degree                  1 fgetvrfmsp1(p,VL,pf) (MACRO) file get vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1 fputmarfmsp1(p,M,V,pf) (MACRO) file put matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1 fputrfmsp1(p,R,V,pf) (MACRO) file put rational 
			function over modular single prime, transcendence 
degree                  1 fputvrfmsp1(p,V,VL,pf) (MACRO) file put vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1 getmarfmsp1(p,V) (MACRO) get matrix of rational 
			functions over modular single primes, transcendence 
degree                  1 getrfmsp1(p,V) (MACRO) get rational function over 
			modular single primes, transcendence 
degree                  1 getvecrfmsp1(p,VL) (MACRO) get vector of rational 
			functions over modular single primes, transcendence 
degree                  1 mpmstmrfmsp1(p,M) matrix of polynomials over 
			modular singles to matrix of rational functions 
			over modular single primes, transcendence 
degree                  1 nepousppmsp1(p,F,a) norm of an element of the 
			polynomial order of an univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, transcendence 
degree                  1 pmstorfmsp1(p,P) (MACRO) polynomial over modular 
			singles to rational function over modular single 
			prime, transcendence 
degree                  1 putmarfmsp1(p,M,V) (MACRO) put matrix of rational 
			functions over modular single primes, transcendence 
degree                  1 putrfmsp1(p,R,V) (MACRO) put rational function 
			over modular single prime, transcendence 
degree                  1 putvecrfmsp1(p,V,VL) (MACRO) put vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1 rfmsp1cons(p,P1,P2) rational function over 
			modular single prime construction, transcendence 
degree                  1 rfmsp1dif(p,R1,R2) rational function over modular 
			single prime difference, transcendence 
degree                  1 rfmsp1neg(p,R) rational function over modular 
			single prime negation, transcendence 
degree                  1 rfmsp1prod(p,R1,R2) rational function over 
			modular single prime product, transcendence 
degree                  1 rfmsp1quot(p,R1,R2) rational function over 
			modular single prime quotient, transcendence 
degree                  1 rfmsp1sum(p,R1,R2) rational function over modular 
			single prime sum, transcendence 
degree                  1 sclfuprfmsp1(P,n) special coefficient list from 
			univariate polynomial over rational functions over 
			modular single prime, transcendence 
degree                  1 uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, from common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1 vepepuspmsp1(p,F,a,P,k,v) values of the 
			extensions of the P-adic valuation of an element of 
			the polynomial order of a univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, transcendence 
degree                  1 vpmstvrfmsp1(p,V) vector of polynomials over 
			modular singles to vector of rational functions 
			over modular single primes, transcendence 
degree                  1, Dedekind maximality test ouspprmsp1dm(p,P,F) 
			order of an univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence 
degree                  1, Hensel factorization approximation 
			upprmsp1hfa(p,F,P,L,k) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence 
degree                  1, Hensel lemma initialization upprmsp1hli(p,F,P,L) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence 
degree                  1, Hensel quadratic step upprmsp1hqs(p,F,T,L1,L2,A) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence 
degree                  1, P-primality test and factorization of the 
			defining polynomial or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
			modular single prime, transcendence 
degree                  1, P-star valuation iafmsp1psval(p,P,A) integral 
			algebraic function over modular single prime, 
			transcendence 
degree                  1, algebraic function over modular single prime, 
			transcendence degree 1, evaluation special 
			upprmsp1afes(p,F,P,a) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence 
degree                  1, approximation of P-adic factorization 
			uspprmsp1apf(p,P,F,k) univariate separable 
			polynomial over polynomial ring over modular single 
			prime, transcendence 
degree                  1, basis from generators oprmsp1basfg(p,F,L) order 
			over polynomial ring over modular single prime, 
			transcendence 
degree                  1, basis of a local maximal over-order 
			ouspprmsp1bl(p,F,P,Q,pk) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence 
degree                  1, construction 1 marfmsp1c1(p,n) (MACRO) matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, core algorithm afmsp1coreal(p,F,P,Q,mp) 
			algebraic function over modular single primes, 
			transcendence 
degree                  1, decomposition law affmsp1decl(p,F,P) algebraic 
			function field over modular single prime, 
			transcendence 
degree                  1, decomposition law ouspprmsp1dl(p,F,P,k) order of 
			a univariate separable polynomial over polynomial 
			ring over modular single prime, transcendence 
degree                  1, derivation, main variable prfmsp1deriv(r,p,P) 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, determinant marfmsp1det(p,M) matrix of rational 
			functions over modular single primes transcendence 
degree                  1, difference (rekursiv) prfmsp1dif(r,p,P1,P2) 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, difference marfmsp1dif(p,M,N) (MACRO) matrix of 
			rational functions over modular single primes 
			transcendence 
degree                  1, difference vecrfmsp1dif(p,U,V) (MACRO) vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, discriminant upprmsp1disc(p,F) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence 
degree                  1, element test modprmsp1elt(B,p,a) module over 
			polynomial ring over modular single primes, 
			transcendence 
degree                  1, evaluation special upprmsp1afes(p,F,P,a) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			algebraic function over modular single prime, 
			transcendence 
degree                  1, exponentiation marfmsp1exp(p,M,n) matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, exponentiation special afmsp1expsp(p,F,a,e,M) 
			algebraic function over modular single prime, 
			transcendence 
degree                  1, extended greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over rational functions over modular single prime, 
			transcendence 
degree                  1, from coefficient list cdprfmsp1fcl(L,p) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence 
degree                  1, from common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 uprfmsp1fcdp(p,P) univariate polynomial 
			over rational functions over modular single prime, 
			transcendence 
degree                  1, from special coefficient list uprfmsp1fscl(L) 
			univariate polynomial over rational functions over 
			modular single prime, transcendence 
degree                  1, from univariate polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1fup(p,P) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, hermitian reduction cdmarfmsp1hr(p,M) common 
			denominator matrix of rational functions over 
			modular single prime, transcendence 
degree                  1, identity construction cdmarfmsp1id(n) common 
			denominator matrix of rational functions over 
			modular single prime, transcendence 
degree                  1, increasing the denominator of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over modular single primes, transcendence 
degree                  1, integral basis ouspprmsp1ib(p,F,pL) order of an 
			univariate separable polynomial over the polynomial 
			ring over modular single prime, transcendence 
degree                  1, inverse cdprfmsp1inv(p,F,A) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, inverse marfmsp1inv(p,M) matrix of rational 
			functions over modular single primes, transcendence 
degree                  1, inverse rfmsp1inv(p,R) rational function over 
			modular single primes, transcendence 
degree                  1, linear combination vecrfmsp1lc(p,F1,F2,V1,V2) 
			vector of rational functions over modular single 
			primes, transcendence 
degree                  1, list from common denominator matrix of rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1lfm(M,p) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, minimal polynomial afmsp1minpol(p,F,a) algebraic 
			function over modular single primes, transcendence 
degree                  1, minimal polynomial iafmsp1mpol(p,F,a,Q) integral 
			algebraic function over modular single primes, 
			transcendence 
degree                  1, minimal polynomial modulo power of an univariate 
			prime polynomial over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
degree                  1, module homomorphism cdprfmsp1mh(p,P,M) common 
			denominator polynomial over rational functions over 
			modular single primes, transcendence 
degree                  1, negation (rekursiv) prfmsp1neg(r,p,P) polynomial 
			over rational functions over modular single prime, 
			transcendence 
degree                  1, negation marfmsp1neg(p,M) (MACRO) matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, negation vecrfmsp1neg(p,V) (MACRO) vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, null space basis marfmsp1nsb(p,M) matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, product (rekursiv) prfmsp1prod(r,p,P1,P2) 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, product (rekursiv) prfmsp1rfprd(r,p,P,a) 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, rational 
			function over modular single prime, transcendence 
degree                  1, product marfmsp1prod(p,M,N) (MACRO) matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, product special afmsp1prodsp(p,F,a,b,M) 
			algebraic function over modular single prime, 
			transcendence 
degree                  1, quotient and remainder (rekursiv) 
			prfmsp1qrem(r,p,P1,P2,pR) polynomial over rational 
			functions over modular single prime, transcendence 
degree                  1, rank marfmsp1rk(p,M) matrix of rational 
			functions over modular single primes, transcendence 
degree                  1, rational function over modular single prime, 
			transcendence degree 1, product (rekursiv) 
			prfmsp1rfprd(r,p,P,a) polynomial over rational 
			functions over modular single prime, transcendence 
degree                  1, reduced discriminant upprmsp1redd(p,F) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence 
degree                  1, regulation afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) 
			algebraic function over modular single primes, 
			transcendence 
degree                  1, resultant, Sylvester algorithm 
			pprmsp1ress(r,p,P1,P2) polynomial over polynomial 
			ring over modular single prime, transcendence 
degree                  1, resultant, Sylvester algorithm 
			upprmsp1ress(p,P1,P2) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence 
degree                  1, scalar multiplication marfmsp1smul(p,M,F) matrix 
			of rational functions over modular single primes, 
			transcendence 
degree                  1, scalar multiplication vecrfmsp1sm(p,F,V) vector 
			of rational functions over modular single primes, 
			transcendence 
degree                  1, scalar product vecrfmsp1sp(p,V,W) vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, solution of a system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
			functions over modular single primes, transcendence 
degree                  1, sum (rekursiv) prfmsp1sum(r,p,P1,P2) polynomial 
			over rational functions over modular single prime, 
			transcendence 
degree                  1, sum cdprfmsp1sum(p,P1,P2) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, sum marfmsp1sum(p,M,N) (MACRO) matrix of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, sum vecrfmsp1sum(p,U,V) (MACRO) vector of 
			rational functions over modular single primes, 
			transcendence 
degree                  1, univariate polynomial over modular single prime 
			quotient cdprfmsp1upq(p,F,P) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence 
degree                  1, vector multiplication marfmsp1vmul(p,A,x) 
			(MACRO) matrix of rational functions over modular 
			single primes, transcendence 
degree                  3 characteristic polynomial nf3chpol(F,el) number 
			field of 
degree                  3 equal to number field of degree 3 
			isnf3eqnf3(F,P,pFD,pPD,pQ) is number field of 
degree                  3 isnf3eqnf3(F,P,pFD,pPD,pQ) is number field of 
			degree 3 equal to number field of 
degree                  3 square root nf3sqrt(F,el) number field of 
degree                  4 cubic resolvent upid4cubres(P) univariate 
			polynomial over integers of 
degree                  4 real ? isupid4real(P) is univariate polynomial 
			over integers of 
degree                  diptdg(r,P) distributive polynomial total 
degree                  factorization upgf2ddfact(G,P) univariate 
			polynomial over Galois-field with characteristic 2 
			distinct 
degree                  factorization upgfsddfact(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic distinct 
degree                  factorization upmiddfact(ip,P) univariate 
			polynomial over modular integers distinct 
degree                  factorization upmsddfact(p,F) univariate polynomial 
			distinct 
degree                  ordering dipgfslottdo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic with total 
degree                  ordering dipilototdo(r,P) distributive polynomial 
			over integers in lexicographical order to 
			distributive polynomial over integers with total 
degree                  ordering dipmiplottdo(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular integer primes with total 
degree                  ordering dipmsplottdo(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular single primes with total 
degree                  ordering dipnflototdo(r,F,P) distributive 
			polynomial over number field in lexicographical 
			order to distributive polynomial over number field 
			with total 
degree                  ordering dippilototdo(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers with total 
degree                  ordering diprfrlottdo(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals with total 
degree                  ordering diprlototdo(r,P) distributive polynomial 
			over rationals in lexicographical order to 
			distributive polynomial over rationals with total 
degree                  upgf2sfed(G,H,d) univariate polynomial over 
			Galois-field with characteristic 2, separate factor 
			of equal 
degree                  upgfsrandpd(p,AL,m) univariate polynomial over 
			Galois-field with single characteristic randomize, 
			positive 
degree                  upgfssfed(p,AL,G,d) univariate polynomial over 
			Galois-field with single characteristic, separate 
			factors of equal 
degree                  upmisfed(ip,G,d) univariate polynomial over modular 
			integers separate factor of equal 
degree                  vector (rekursiv) dpdegvec(r,P) dense polynomial 
degree                  vector (rekursiv) pdegvec(r,P) polynomial 
degree,                 main variable pdegree(r,P) (MACRO) polynomial 
degree,                 specified variable (rekursiv) pdegreesv(r,P,n) 
			polynomial 
degrees                 of the residue class fields qnfdegrescf(D,p) 
			quadratic number field 
delete                  1 row and 1 column madel1rc(pM,i,j) matrix 
delete                  lecdel(L,n) list element constructive 
delete                  ledel(pL,n) list element 
delete                  several columns madelsc(pM,I) matrix 
delete                  several rows and columns madelsrc(pM,I,J) (MACRO) 
			matrix 
delete                  several rows madelsr(pM,I) matrix 
denominator             matrix of rational functions over modular single 
			prime, transcendence degree 1 cdprfmsp1lfm(M,p) 
			common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, list from common 
denominator             matrix of rational functions over modular single 
			prime, transcendence degree 1, hermitian reduction 
			cdmarfmsp1hr(p,M) common 
denominator             matrix of rational functions over modular single 
			prime, transcendence degree 1, identity 
			construction cdmarfmsp1id(n) common 
denominator             matrix of rationals cdprlfcdmar(M) common 
			denominator polynomial over the rationals list from 
			common 
denominator             matrix of rationals, hermitian reduction 
			cdmarhermred(M) common 
denominator             matrix of rationals, identity construction 
			cdmarid(n) common 
denominator             of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over modular single primes, transcendence 
			degree 1, increasing the 
denominator             of the j-invariant ecrfdenjinv(E) elliptic curve 
			over the rationals, factorization of the 
denominator             of the p-star value 
			ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
denominator             of the p-star value with respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			clfcdprfmsp1(P,n) coefficient list from common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, from common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1, from 
			coefficient list cdprfmsp1fcl(L,p) common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1, from 
			univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1, inverse 
			cdprfmsp1inv(p,F,A) common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1, list from 
			common denominator matrix of rational functions 
			over modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1, sum 
			cdprfmsp1sum(p,P1,P2) common 
denominator             polynomial over rational functions over modular 
			single prime, transcendence degree 1, univariate 
			polynomial over modular single prime quotient 
			cdprfmsp1upq(p,F,P) common 
denominator             polynomial over rational functions over modular 
			single primes, transcendence degree 1, module 
			homomorphism cdprfmsp1mh(p,P,M) common 
denominator             polynomial over the rationals Z-module homomorphism 
			cdprzmodhom(P,M) common 
denominator             polynomial over the rationals clfcdpr(P,n) 
			coefficient list from common 
denominator             polynomial over the rationals from coefficient list 
			cdprfcl(L) common 
denominator             polynomial over the rationals from univariate 
			polynomial over the rationals cdprfupr(P) common 
denominator             polynomial over the rationals integer quotient 
			cdpriquot(P,I) common 
denominator             polynomial over the rationals inverse cdprinv(F,A) 
			common 
denominator             polynomial over the rationals list from common 
			denominator matrix of rationals cdprlfcdmar(M) 
			common 
denominator             polynomial over the rationals sum cdprsum(P1,P2) 
			common 
denominator             polynomial over the rationals uprfcdpr(PC) 
			univariate polynomial over the rationals from 
			common 
denominator             prnumden(r,P,pA) polynomial over the rationals 
			numerator and 
denominator             rden(R) (MACRO) rational number 
dense                   polynomial (rekursiv) ptodp(r,P) polynomial to 
dense                   polynomial ? (rekursiv) isdpol(r,P) is 
dense                   polynomial degree vector (rekursiv) dpdegvec(r,P) 
dense                   polynomial over Galois-field with characteristic 2 
			remainder, special version udpgf2remsp(G,P1,P2,ilc) 
			univariate 
dense                   polynomial over integers content and primitive part 
			udpicontpp(P,pPP) univariate 
dense                   polynomial over integers difference udpidif(P1,P2) 
			univariate 
dense                   polynomial over integers integer product 
			udpiiprod(P,A) univariate 
dense                   polynomial over integers negation udpineg(P) 
			univariate 
dense                   polynomial over integers product udpiprod(P1,P2) 
			univariate 
dense                   polynomial over integers pseudo remainder 
			udpipsrem(P1,P2) univariate 
dense                   polynomial over integers sum udpisum(P1,P2) 
			univariate 
dense                   polynomial over integers to univariate dense 
			polynomial over modular integers udpitoudpmi(P,M) 
			univariate 
dense                   polynomial over integers to univariate dense 
			polynomial over p-adic field udpitoudppf(P,p,d) 
			univariate 
dense                   polynomial over integers? (rekursiv) isdpi(r,P) is 
dense                   polynomial over modular 2 gf2eltoudpm2(G,a) 
			Galois-field with characteristic 2 element to 
			univariate 
dense                   polynomial over modular 2 in special 
			bit-representation ? isudpm2sb(A) is univariate 
dense                   polynomial over modular 2 sbtoudpm2(a) (MACRO) 
			special bit-representation to univariate 
dense                   polynomial over modular 2 to Galois-field with 
			characteristic 2 element udpm2togf2el(G,P) 
			univariate 
dense                   polynomial over modular 2 to special 
			bit-representation udpm2tosb(P) univariate 
dense                   polynomial over modular integers ? (rekursiv) 
			isdpmi(r,m,P) is 
dense                   polynomial over modular integers Jacobi-symbol 
			udpmijacsym(m,P1,P2) univariate 
dense                   polynomial over modular integers derivation 
			udpmideriv(m,P) univariate 
dense                   polynomial over modular integers difference 
			(rekursiv) dpmidif(r,m,P1,P2) 
dense                   polynomial over modular integers difference 
			udpmidif(m,P1,P2) univariate 
dense                   polynomial over modular integers extended greatest 
			common divisor udpmiegcd(m,P1,P2,pPX,pPY) 
			univariate 
dense                   polynomial over modular integers greatest common 
			divisor udpmigcd(m,P1,P2) univariate 
dense                   polynomial over modular integers half extended 
			greatest common divisor udpmihegcd(m,P1,P2,pP3) 
			univariate 
dense                   polynomial over modular integers monic 
			udpmimonic(m,P) univariate 
dense                   polynomial over modular integers negation 
			(rekursiv) dpmineg(r,m,P) 
dense                   polynomial over modular integers negation 
			udpmineg(m,P) univariate 
dense                   polynomial over modular integers product (rekursiv) 
			dpmiprod(r,M,P1,P2) 
dense                   polynomial over modular integers product 
			udpmiprod(m,P1,P2) univariate 
dense                   polynomial over modular integers quotient and 
			remainder udpmiqrem(m,P1,P2,pP3) univariate 
dense                   polynomial over modular integers quotient 
			udpmiquot(m,P1,P2) (MACRO) univariate 
dense                   polynomial over modular integers remainder 
			udpmirem(ip,P,P2) univariate 
dense                   polynomial over modular integers sum (rekursiv) 
			dpmisum(r,M,P1,P2) 
dense                   polynomial over modular integers sum 
			udpmisum(m,P1,P2) univariate 
dense                   polynomial over modular integers udpitoudpmi(P,M) 
			univariate dense polynomial over integers to 
			univariate 
dense                   polynomial over modular integers, modular integer 
			product udpmimiprod(m,P,a) univariate 
dense                   polynomial over modular single trailing base 
			coefficient udpmstbc(m,P) univariate 
dense                   polynomial over modular singles ? (rekursiv) 
			isdpms(r,m,P) is 
dense                   polynomial over modular singles Jacobi-symbol 
			udpmsjacsym(m,P1,P2) univariate 
dense                   polynomial over modular singles derivation 
			udpmsderiv(m,P) univariate 
dense                   polynomial over modular singles difference 
			(rekursiv) dpmsdif(r,m,P1,P2) 
dense                   polynomial over modular singles difference 
			udpmsdif(m,P1,P2) univariate 
dense                   polynomial over modular singles extended greatest 
			common divisor udpmsegcd(m,P1,P2,pPX,pPY) 
			univariate 
dense                   polynomial over modular singles greatest common 
			divisor udpmsgcd(m,P1,P2) univariate 
dense                   polynomial over modular singles half extended 
			greatest common divisor udpmshegcd(m,P1,P2,pP3) 
			univariate 
dense                   polynomial over modular singles monic 
			udpmsmonic(m,P) univariate 
dense                   polynomial over modular singles negation (rekursiv) 
			dpmsneg(r,m,P) 
dense                   polynomial over modular singles negation 
			udpmsneg(m,P) univariate 
dense                   polynomial over modular singles product (rekursiv) 
			dpmsprod(r,m,P1,P2) 
dense                   polynomial over modular singles product 
			udpmsprod(m,P1,P2) univariate 
dense                   polynomial over modular singles quotient and 
			remainder udpmsqrem(m,P1,P2,pP3) univariate 
dense                   polynomial over modular singles quotient 
			udpmsquot(m,P1,P2) (MACRO) univariate 
dense                   polynomial over modular singles remainder 
			udpmsrem(m,P1,P2) univariate 
dense                   polynomial over modular singles sum (rekursiv) 
			dpmssum(r,m,P1,P2) 
dense                   polynomial over modular singles sum 
			udpmssum(m,P1,P2) univariate 
dense                   polynomial over modular singles, modular single 
			product udpmsmsprod(m,P,a) univariate 
dense                   polynomial over modular singles, summation over 
			Jacobi-symbols udpmssumjs(m,P,n) univariate 
dense                   polynomial over p-adic field ? isdppf(r,p,P) is 
dense                   polynomial over p-adic field difference 
			udppfdif(p,P1,P2) univariate 
dense                   polynomial over p-adic field exponentiation 
			udppfexp(p,P,n) univariate 
dense                   polynomial over p-adic field fitting 
			udppffit(p,P,Pd) univariate 
dense                   polynomial over p-adic field negation udppfneg(p,P) 
			univariate 
dense                   polynomial over p-adic field p-adic field element 
			product udppfpfprod(p,P,a) univariate 
dense                   polynomial over p-adic field prime power product 
			udppfpprod(p,P,i) univariate 
dense                   polynomial over p-adic field product 
			udppfprod(p,P1,P2) univariate 
dense                   polynomial over p-adic field sum udppfsum(p,P1,P2) 
			univariate 
dense                   polynomial over p-adic field udpitoudppf(P,p,d) 
			univariate dense polynomial over integers to 
			univariate 
dense                   polynomial over p-adic field udprtoudppf(P,p,d) 
			univariate dense polynomial over rationals to 
			univariate 
dense                   polynomial over rationals difference udprdif(P1,P2) 
			univariate 
dense                   polynomial over rationals negation udprneg(P) 
			univariate 
dense                   polynomial over rationals nfeltoudpr(a) number 
			field element to univariate 
dense                   polynomial over rationals product udprprod(P1,P2) 
			univariate 
dense                   polynomial over rationals quotient and remainder 
			udprqrem(P1,P2,pP3) univariate 
dense                   polynomial over rationals sum udprsum(P1,P2) 
			univariate 
dense                   polynomial over rationals to number field element 
			udprtonfel(P) univariate 
dense                   polynomial over rationals to univariate dense 
			polynomial over p-adic field udprtoudppf(P,p,d) 
			univariate 
dense                   polynomial over rationals, rational number product 
			udprrprod(P,A) univariate 
dense                   polynomial over rationals? (rekursiv) isdpr(r,P) is 
dense                   polynomial reductum dpred(r,P) 
dense                   polynomial to polynomial (rekursiv) dptop(r,P) 
dense                   polynomial trailing base coefficient udptbc(P) 
			univariate 
dense                   polynomials ? ismadp(r,M) (MACRO) is matrix of 
dense                   polynomials ? isvecdp(r,V) (MACRO) is vector of 
dense                   polynomials maptomadp(r,M) matrix of polynomials to 
			matrix of 
dense                   polynomials over integers ? ismadpi(r,M) (MACRO) is 
			matrix of 
dense                   polynomials over integers ? isvecdpi(r,V) (MACRO) 
			is vector of 
dense                   polynomials over integers to matrix of univariate 
			dense polynomials over modular integers 
			mudpitudpmi(M,m) matrix of univariate 
dense                   polynomials over integers to matrix of univariate 
			dense polynomials over rationals mudpitmudpr(M) 
			matrix of univariate 
dense                   polynomials over integers to vector of univariate 
			dense polynomials over modular integers 
			vudpitudpmi(V,M) vector of univariate 
dense                   polynomials over integers to vector of univariate 
			dense polynomials over rationals vudpitvudpr(V) 
			vector of univariate 
dense                   polynomials over modular integers mudpitudpmi(M,m) 
			matrix of univariate dense polynomials over 
			integers to matrix of univariate 
dense                   polynomials over modular integers vudpitudpmi(V,M) 
			vector of univariate dense polynomials over 
			integers to vector of univariate 
dense                   polynomials over modular singles ? ismadpms(r,m,M) 
			(MACRO) is matrix of 
dense                   polynomials over modular singles ? isvecdpms(r,m,V) 
			(MACRO) is vector of 
dense                   polynomials over rationals ? ismadpr(r,M) (MACRO) 
			is matrix of 
dense                   polynomials over rationals ? isvecdpr(r,V) (MACRO) 
			is vector of 
dense                   polynomials over rationals manftomudpr(F,M) matrix 
			of number field elements to matrix of univariate 
dense                   polynomials over rationals mudpitmudpr(M) matrix of 
			univariate dense polynomials over integers to 
			matrix of univariate 
dense                   polynomials over rationals to matrix of number 
			field elements maudprtomnf(M) matrix of univariate 
dense                   polynomials over rationals to vector of number 
			field elements vudprtovnf(V) vector of univariate 
dense                   polynomials over rationals vnftovudpr(F,V) vector 
			of number field elements to vector of univariate 
dense                   polynomials over rationals vudpitvudpr(V) vector of 
			univariate dense polynomials over integers to 
			vector of univariate 
dense                   polynomials to matrix of polynomials madptomap(r,M) 
			matrix of 
dense                   polynomials to vector of polynomials 
			vecdptovecp(r,V) vector of 
dense                   polynomials vecptovecdp(r,V) vector of polynomials 
			to vector of 
derivation              udpmideriv(m,P) univariate dense polynomial over 
			modular integers 
derivation              udpmsderiv(m,P) univariate dense polynomial over 
			modular singles 
derivation,             main variable (rekursiv) ppfderiv(r,p,P) polynomial 
			over p-adic field 
derivation,             main variable pgf2deriv(r,G,P) polynomial over 
			Galois-field with characteristic 2 
derivation,             main variable pgfsderiv(r,p,AL,P) polynomial over 
			Galois-field with single characteristic 
derivation,             main variable pideriv(r,P) polynomial over integers 
derivation,             main variable pmideriv(r,M,P) polynomial over 
			modular integers 
derivation,             main variable pmsderiv(r,m,P) polynomial over 
			modular singles 
derivation,             main variable pnfderiv(r,F,P) polynomial over 
			number field 
derivation,             main variable prderiv(r,P) polynomial over 
			rationals 
derivation,             main variable prfmsp1deriv(r,p,P) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, 
derivation,             selected variable ppfderivsv(r,p,P,n) polynomial 
			over p-adic field 
derivation,             specified variable (rekursiv) pgf2derivsv(r,G,P,i) 
			polynomial over Galois-field with characteristic 2 
derivation,             specified variable (rekursiv) 
			pgfsderivsv(r,p,AL,P,i) polynomial over 
			Galois-field with single characteristic 
derivation,             specified variable (rekursiv) piderivsv(r,P,n) 
			polynomial over integers 
derivation,             specified variable (rekursiv) pmiderivsv(r,m,P,n) 
			polynomial over modular integers 
derivation,             specified variable (rekursiv) pmsderivsv(r,m,P,n) 
			polynomial over modular singles 
derivation,             specified variable (rekursiv) pnfderivsv(r,F,P,n) 
			polynomial over number field 
derivation,             specified variable (rekursiv) prderivsv(r,P,n) 
			polynomial over rationals 
derivative              ecrlserfd(E) elliptic curve over rational numbers, 
			L-series, first 
derivative              ecrlserhd(E,r) elliptic curve over rational 
			numbers, L-series, higher 
derivative              ecrlserrkd(E) elliptic curve over the rationals, 
			L-series, 'rank'-th 
derivative,             large conductor ecrlserhdlc(E,A,s,result) elliptic 
			curve over the rationals, L-series, higher 
derivative,             small conductor ecrlserhdsc(E,A,r,result) elliptic 
			curve over rational numbers, L-series, higher 
derivative,             special version ecrlserfds(E,A,result) elliptic 
			curve over the rationals, L-series, first 
determinant             mafldet(M) matrix of floatings 
determinant             magfsdet(p,AL,M) matrix of Galois-field with single 
			characteristic elements 
determinant             maidet(M) matrix of integers 
determinant             mamidet(m,M) matrix of modular integers 
determinant             mamsdet(m,M) matrix of modular singles 
determinant             manfdet(F,M) matrix of number field elements 
determinant             manfsdet(F,M) matrix of number field elements, 
			sparse representation, 
determinant             mapgfsdet(r,p,AL,M) matrix of polynomials over 
			Galois-field with single characteristic 
determinant             mapidet(r,M) matrix of polynomials over integers 
determinant             mapmidet(r,m,M) matrix of polynomials over modular 
			integers 
determinant             mapmsdet(r,m,M) matrix of polynomials over modular 
			singles 
determinant             mapnfdet(r,F,M) matrix of polynomials over number 
			field 
determinant             maprdet(r,M) matrix of polynomials over rationals 
determinant             mardet(M) matrix of rationals 
determinant             marfmsp1det(p,M) matrix of rational functions over 
			modular single primes transcendence degree 1, 
determinant             marfrdet(r,M) matrix of rational functions over 
			rationals 
determine               a solution of the diophantine equation x^2+q*y^2=m 
			using the algorithm of cornaccia 
			cornaccia(m,q,x0,pX,pY) 
determined              with the Schoof algorithm ecgf2npmi(G,a6,S,v,pM) 
			elliptic curve over Galois-field with 
			characteristic 2, number of points modulo an 
			integer 
determined              with the Schoof algorithm ecmpsnfnpmi(P,a4,a6,S,pM) 
			elliptic curve over modular primes, short normal 
			form, number of points modulo an integer 
determined              with the Schoof algorithm ecmpsnfnpmsp(P,a4,a6,p,L) 
			elliptic curve over modular primes, short normal 
			form, number of points modulo a single prime 
determined              with the Schoof algorithm, version 1 
			ecgf2npmspv1(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a single prime 
determined              with the Schoof algorithm, version 2 
			ecgf2npmspv2(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a single prime 
diagonal-matrix         maconsdiag(n,el) matrix construction 
difference              (rekursiv) dpmidif(r,m,P1,P2) dense polynomial over 
			modular integers 
difference              (rekursiv) dpmsdif(r,m,P1,P2) dense polynomial over 
			modular singles 
difference              (rekursiv) pgfsdif(r,p,AL,P1,P2) polynomial over 
			Galois-field with single characteristic 
difference              (rekursiv) pidif(r,P1,P2) polynomial over integers 
difference              (rekursiv) pmidif(r,M,P1,P2) polynomial over 
			modular integers 
difference              (rekursiv) pmsdif(r,m,P1,P2) polynomial over 
			modular singles 
difference              (rekursiv) pnfdif(r,F,P1,P2) polynomial over number 
			field 
difference              (rekursiv) prdif(r,P1,P2) polynomial over rationals 
difference              (rekursiv) prfmsp1dif(r,p,P1,P2) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, 
difference              between Weil height and Neron-Tate height 
			ecimindwhnth(E) elliptic curve with integer 
			coefficients, minimal model, 
difference              between Weil height and Neron-Tate height 
			ecisnfdwhnth(E) elliptic curve with integer 
			coefficients, short normal form, 
difference              cdif(v,w) complex 
difference              dipevdif(r,EV1,EV2) distributive polynomial 
			exponent vector 
difference              dipgfsdif(r,p,AL,P1,P2) distributive polynomial 
			over Galois-field with single characteristic 
difference              dipidif(r,P1,P2) distributive polynomial over 
			integers 
difference              dipmipdif(r,p,P1,P2) distributive polynomial over 
			modular integer primes 
difference              dipmspdif(r,p,P1,P2) distributive polynomial over 
			modular single primes 
difference              dipnfdif(r,F,P1,P2) distributive polynomial over 
			number field 
difference              dippidif(r1,r2,P1,P2) distributive polynomial over 
			polynomials over integers 
difference              diprdif(r,P1,P2) distributive polynomial over 
			rationals 
difference              diprfrdif(r1,r2,P1,P2) distributive polynomial over 
			rational functions over the rationals 
difference              fldif(f,g) (MACRO) floating point 
difference              gf2dif(G,a,b) (MACRO) Galois-field with 
			characteristic 2 
difference              gfsdif(p,AL,a,b) (MACRO) Galois-field with single 
			characteristic 
difference              idif(A,B) integer 
difference              iqnfdif(D,a,b) (MACRO) integer, quadratic number 
			field element, 
difference              magfsdif(p,AL,M,N) (MACRO) matrix of Galois-field 
			with single characteristic elements 
difference              maidif(M,N) (MACRO) matrix of integers 
difference              mamidif(m,M,N) (MACRO) matrix of modular integers 
difference              mamsdif(m,M,N) (MACRO) matrix of modular singles 
difference              manfdif(F,M,N) (MACRO) matrix of number field 
			elements 
difference              manfsdif(F,M,N) (MACRO) matrix of number field 
			elements, sparse representation, 
difference              mapgfsdif(r,p,AL,M,N) (MACRO) matrix of polynomials 
			over Galois-field with single characteristic 
difference              mapidif(r,M,N) (MACRO) matrix of polynomials over 
			integers 
difference              mapmidif(r,m,M,N) (MACRO) matrix of polynomials 
			over modular integers 
difference              mapmsdif(r,m,M,N) (MACRO) matrix of polynomials 
			over modular singles 
difference              mapnfdif(r,F,M,N) (MACRO) matrix of polynomials 
			over number field 
difference              maprdif(r,M,N) (MACRO) matrix of polynomials over 
			rationals 
difference              mardif(M,N) (MACRO) matrix of rationals 
difference              marfmsp1dif(p,M,N) (MACRO) matrix of rational 
			functions over modular single primes transcendence 
			degree 1, 
difference              marfrdif(r,M,N) (MACRO) matrix of rational 
			functions over rationals 
difference              midif(M,A,B) modular integer 
difference              msdif(m,a,b) (MACRO) modular single 
difference              nfdif(F,a,b) number field element 
difference              nfsdif(F,a,b) (MACRO) number field, sparse 
			representation, 
difference              of points ecimindif(E,P,Q) elliptic curve with 
			integer coefficients, minimal model, 
difference              of points ecisnfdif(E,P,Q) elliptic curve with 
			integer coefficients, minimal model, 
difference              of points ecracdif(E,P,Q) elliptic curve with 
			integer coefficients, actual curve, 
difference              pfdif(p,a,b) p-adic field element 
difference              pgf2dif(r,G,P1,P2) (MACRO) polynomial over 
			Galois-field with characteristic 2 
difference              ppfdif(r,p,P1,P2) polynomial over p-adic field 
difference              qnfdif(D,a,b) (MACRO) quadratic number field 
			element 
difference              qnfidif(D,a,b) (MACRO) quadratic number field 
			element, integer, 
difference              qnfrdif(D,a,b) (MACRO) quadratic number field 
			element, rational number, 
difference              rdif(R,S) (MACRO) rational number 
difference              rfrdif(r,R1,R2) rational function over the 
			rationals 
difference              rqnfdif(D,a,b) (MACRO) rational number, quadratic 
			number field element, 
difference              sdiff(L1,L2) set 
difference              udpidif(P1,P2) univariate dense polynomial over 
			integers 
difference              udpmidif(m,P1,P2) univariate dense polynomial over 
			modular integers 
difference              udpmsdif(m,P1,P2) univariate dense polynomial over 
			modular singles 
difference              udppfdif(p,P1,P2) univariate dense polynomial over 
			p-adic field 
difference              udprdif(P1,P2) univariate dense polynomial over 
			rationals 
difference              usdiff(L1,L2) unordered set 
difference              ussdiff(L1,L2) unordered set symmetrical 
difference              vecgfsdif(p,AL,U,V) (MACRO) vector of Galois-field 
			with single characteristic elements 
difference              vecidif(U,V) (MACRO) vector of integers 
difference              vecmidif(m,U,V) (MACRO) vector of modular integers 
difference              vecmsdif(m,U,V) (MACRO) vector of modular singles 
difference              vecnfdif(F,U,V) (MACRO) vector of number field 
			elements 
difference              vecnfsdif(F,U,V) (MACRO) vector of number field 
			elements, sparse representation, 
difference              vecpgfsdif(r,p,AL,U,V) (MACRO) vector of 
			polynomials over Galois-field with single 
			characteristic 
difference              vecpidif(r,U,V) (MACRO) vector of polynomials over 
			integers 
difference              vecpmidif(r,m,U,V) (MACRO) vector of polynomials 
			over modular integers 
difference              vecpmsdif(r,m,U,V) (MACRO) vector of polynomials 
			over modular singles 
difference              vecpnfdif(r,F,U,V) (MACRO) vector of polynomials 
			over number field 
difference              vecprdif(r,U,V) (MACRO) vector of polynomials over 
			rationals 
difference              vecrdif(U,V) (MACRO) vector of rationals 
difference              vecrfmsp1dif(p,U,V) (MACRO) vector of rational 
			functions over modular single primes, transcendence 
			degree 1, 
difference              vecrfrdif(r,U,V) (MACRO) vector of rational 
			functions over rationals 
difference,             transcendence degree 1 rfmsp1dif(p,R1,R2) rational 
			function over modular single prime 
digit                   functions HDidigit() Heidelberg arithmetic package: 
dimension               dippidim(r1,r2,s,PL,CONDS,fac,VL1,VL2,pf) 
			distributive polynomial over polynomials over 
			integers 
dimension               fputdipdim(r,dim,S,M,VL,pf) file put distributive 
			polynomial 
dimension               fputdippidim(r1,r2,DIML,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers 
dimension               of a polynomial ideal dipdimpolid(r,G,pS,pM) 
			distributive polynomial 
dimension               putdipdim(r,dim,S,M,VL) (MACRO) put distributive 
			polynomial 
dimension               putdippidim(r1,r2,DIML,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers 
diophantine             equation x^2+q*y^2=m using the algorithm of 
			cornaccia cornaccia(m,q,x0,pX,pY) determine a 
			solution of the 
dipbsort(r,P)           distributive polynomial bubble sort 
dipdimpolid(r,G,pS,pM)  distributive polynomial dimension of a polynomial 
			ideal 
dipevcomp(r,EV1,EV2)    distributive polynomial exponent vector compare 
dipevdif(r,EV1,EV2)     distributive polynomial exponent vector difference 
dipevl(r,P)             distributive polynomial exponent vector of the 
			leading monomial 
dipevlcm(r,EV1,EV2)     distributive polynomial exponent vector least 
			common multiple 
dipevmt(r,EV1,EV2)      distributive polynomial exponent vector multiple 
			test 
dipevsign(r,EV)         distributive polynomial exponent vector signum 
dipevsum(r,EV1,EV2)     distributive polynomial exponent vector sum 
dipfmo(r,BC,EV)         (MACRO) distributive polynomial from monomial 
dipgfsdif(r,p,AL,P1,P2) distributive polynomial over Galois-field with 
			single characteristic difference 
dipgfsgb(r,p,AL,PL)     distributive polynomial over Galois-field with 
			single characteristic Groebner basis 
dipgfsgba(r,p,AL,PL,P)  distributive polynomial over Galois-field with 
			single characteristic Groebner basis augmentation 
dipgfsgbr(r,p,AL,PL)    distributive polynomial over Galois-field with 
			single characteristic Groebner basis recursion 
dipgfsgfprod(r,p,AL,P,a) distributive polynomial over Galois-field with 
			single characteristic, Galois-field with single 
			characteristic element product 
dipgfslotglo(r,p,AL,P)  distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in graduated lexicographical 
			order 
dipgfslotlio(r,p,AL,P)  distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse exponent vector 
dipgfslottdo(r,p,AL,P)  distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic with total degree ordering 
dipgfsmonic(r,p,AL,P)   distributive polynomial over Galois-field with 
			single characteristic monic 
dipgfsneg(r,p,AL,P)     distributive polynomial over Galois-field with 
			single characteristic negation 
dipgfsprod(r,p,AL,P1,P2) distributive polynomial over Galois-field with 
			single characteristic product 
dipgfssp(r,p,AL,P1,P2)  distributive polynomial over Galois-field with 
			single characteristic S-polynomial 
dipgfssum(r,p,AL,P1,P2) distributive polynomial over Galois-field with 
			single characteristic sum 
diphomog(r,P)           distributive polynomial homogenize 
diphomogsv(r,P,n)       distributive polynomial homogenize specified 
			variable 
dipicp(r,P,pPP)         distributive polynomial over integers content and 
			primitive part 
dipidif(r,P1,P2)        distributive polynomial over integers difference 
dipigb(r,PL)            distributive polynomial over integers Groebner 
			basis 
dipigba(r,PL,P)         distributive polynomial over integers Groebner 
			basis augmentation 
dipigbr(r,PL)           distributive polynomial over integers Groebner 
			basis recursion 
dipiiprod(r,P,A)        distributive polynomial over integers, integer 
			product 
dipilotoglo(r,P)        distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over integers in graduated lexicographical order 
dipilotolio(r,P)        distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over integers in lexicographical order with inverse 
			exponent vector 
dipilototdo(r,P)        distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over integers with total degree ordering 
dipineg(r,P)            distributive polynomial over integers negation 
dipiprod(r,P1,P2)       distributive polynomial over integers product 
dipisp(r,P1,P2)         distributive polynomial over integers S-polynomial 
dipisum(r,P1,P2)        distributive polynomial over integers sum 
diplbc(r,P)             (MACRO) distributive polynomial leading base 
			coefficient 
dipmipdif(r,p,P1,P2)    distributive polynomial over modular integer primes 
			difference 
dipmipgb(r,p,PL)        distributive polynomial over modular integer primes 
			Groebner basis 
dipmipgba(r,p,PL,P)     distributive polynomial over modular integer primes 
			Groebner basis augmentation 
dipmipgbr(r,p,PL)       distributive polynomial over modular integer primes 
			Groebner basis recursion 
dipmiplotglo(r,p,P)     distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over modular integer primes in graduated 
			lexicographical order 
dipmiplotlio(r,p,P)     distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over modular integer primes in lexicographical 
			order with inverse exponent vector 
dipmiplottdo(r,p,P)     distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over modular integer primes with total degree 
			ordering 
dipmipmiprod(r,p,P,A)   distributive polynomial over modular integer 
			primes, modular integer primes product 
dipmipmonic(r,p,P)      distributive polynomial over modular integer primes 
			monic 
dipmipneg(r,p,P)        distributive polynomial over modular integer primes 
			negation 
dipmipprod(r,p,P1,P2)   distributive polynomial over modular integer primes 
			product 
dipmipsp(r,p,P1,P2)     distributive polynomial over modular integer primes 
			S-polynomial 
dipmipsum(r,p,P1,P2)    distributive polynomial over modular integer primes 
			sum 
dipmoad(r,P,pLBC,pLEV)  distributive polynomial monomial advance 
dipmspdif(r,p,P1,P2)    distributive polynomial over modular single primes 
			difference 
dipmspgb(r,p,PL)        distributive polynomial over modular single primes 
			Groebner basis 
dipmspgba(r,p,PL,P)     distributive polynomial over modular single primes 
			Groebner basis augmentation 
dipmspgbr(r,p,PL)       distributive polynomial over modular single primes 
			Groebner basis recursion 
dipmsplotglo(r,p,P)     distributive polynomial over modular single primes 
			in lexicographical order to distributive polynomial 
			over modular single primes in graduated 
			lexicographical order 
dipmsplotlio(r,p,P)     distributive polynomial over modular single primes 
			in lexicographical order to distributive polynomial 
			over modular single primes in lexicographical order 
			with inverse exponent vector 
dipmsplottdo(r,p,P)     distributive polynomial over modular single primes 
			in lexicographical order to distributive polynomial 
			over modular single primes with total degree 
			ordering 
dipmspmonic(r,p,P)      distributive polynomial over modular single primes 
			monic 
dipmspmsprod(r,p,P,a)   distributive polynomial over modular single primes, 
			modular single primes product 
dipmspneg(r,p,P)        distributive polynomial over modular single primes 
			negation 
dipmspprod(r,p,P1,P2)   distributive polynomial over modular single primes 
			product 
dipmspsp(r,p,P1,P2)     distributive polynomial over modular single primes 
			S-polynomial 
dipmspsum(r,p,P1,P2)    distributive polynomial over modular single primes 
			sum 
dipnfdif(r,F,P1,P2)     distributive polynomial over number field 
			difference 
dipnfgb(r,F,PL)         distributive polynomial over number field Groebner 
			basis 
dipnfgba(r,F,PL,P)      distributive polynomial over number field Groebner 
			basis augmentation 
dipnfgbr(r,F,PL)        distributive polynomial over number field Groebner 
			basis recursion 
dipnflotoglo(r,F,P)     distributive polynomial over number field in 
			lexicographical order to distributive polynomial 
			over number field in graduated lexicographical 
			order 
dipnflotolio(r,F,P)     distributive polynomial over number field in 
			lexicographical order to distributive polynomial 
			over number field in lexicographical order with 
			inverse exponent vector 
dipnflototdo(r,F,P)     distributive polynomial over number field in 
			lexicographical order to distributive polynomial 
			over number field with total degree ordering 
dipnfmonic(r,F,P)       distributive polynomial over number field monic 
dipnfneg(r,F,P)         distributive polynomial over number field negation 
dipnfnfprod(r,F,P,A)    distributive polynomial over number field, number 
			field element product 
dipnfprod(r,F,P1,P2)    distributive polynomial over number field product 
dipnfsp(r,F,P1,P2)      distributive polynomial over number field 
			S-polynomial 
dipnfsum(r,F,P1,P2)     distributive polynomial over number field sum 
dipnmv(r,P,n)           distributive polynomial new main variable 
dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) distributive polynomial over 
			polynomials over integers comprehensive Groebner 
			basis 
dippicp(r1,r2,P,pPP)    distributive polynomial over polynomials over 
			integers content and primitive part 
dippidif(r1,r2,P1,P2)   distributive polynomial over polynomials over 
			integers difference 
dippidim(r1,r2,s,PL,CONDS,fac,VL1,VL2,pf) distributive polynomial over 
			polynomials over integers dimension 
dippigb(r1,r2,PL)       distributive polynomial over polynomials over 
			integers Groebner basis 
dippigba(r1,r2,PL,P)    distributive polynomial over polynomials over 
			integers Groebner basis augmentation 
dippigbr(r1,r2,PL)      distributive polynomial over polynomials over 
			integers Groebner basis recursion 
dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) distributive polynomial over polynomials 
			over integers Groebner test 
dippilotoglo(r1,r2,P)   distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
			polynomial over polynomials over integers in 
			graduated lexicographical order 
dippilotolio(r1,r2,P)   distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
			polynomial over polynomials over integers in 
			lexicographical order with inverse exponent vector 
dippilototdo(r1,r2,P)   distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
			polynomial over polynomials over integers with 
			total degree ordering 
dippineg(r1,r2,P)       distributive polynomial over polynomials over 
			integers negation 
dippipim(r1,r2,s,PL,PTL,CONDS,OPL) distributive polynomial over polynomials 
			over integers parametric ideal membership test 
dippipiprod(r1,r2,P,A)  distributive polynomial over polynomials over 
			integers, polynomial over integers product 
dippiprod(r1,r2,P1,P2)  distributive polynomial over polynomials over 
			integers product 
dippiqff(r1,r2,s,PL,CONDS,fac) distributive polynomial over polynomials over 
			integers quantifier free formula 
dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) distributive polynomial over 
			polynomials over integers reduced comprehensive 
			Groebner basis 
dippisp(r1,r2,P1,P2)    distributive polynomial over polynomials over 
			integers S-polynomial 
dippisum(r1,r2,P1,P2)   distributive polynomial over polynomials over 
			integers sum 
diprdif(r,P1,P2)        distributive polynomial over rationals difference 
diprfrdif(r1,r2,P1,P2)  distributive polynomial over rational functions 
			over the rationals difference 
diprfrgb(r1,r2,PL)      distributive polynomial over rational functions 
			over the rationals Groebner basis 
diprfrgba(r1,r2,PL,P)   distributive polynomial over rational functions 
			over the rationals Groebner basis augmentation 
diprfrgbr(r1,r2,PL)     distributive polynomial over rational functions 
			over the rationals Groebner basis recursion 
diprfrlotglo(r1,r2,P)   distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals in graduated lexicographical 
			order 
diprfrlotlio(r1,r2,P)   distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order with 
			inverse exponent vector 
diprfrlottdo(r1,r2,P)   distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals with total degree ordering 
diprfrmonic(r1,r2,P)    distributive polynomial over rational functions 
			over the rationals monic 
diprfrneg(r1,r2,P)      distributive polynomial over rational functions 
			over the rationals negation 
diprfrprod(r1,r2,P1,P2) distributive polynomial over rational functions 
			over the rationals product 
diprfrrfprod(r1,r2,P,A) distributive polynomial over rational functions 
			over the rationals rational function over the 
			rationals product 
diprfrsp(r1,r2,P1,P2)   distributive polynomial over rational functions 
			over the rationals S-polynomial 
diprfrsum(r1,r2,P1,P2)  distributive polynomial over rational functions 
			over the rationals sum 
diprfrtorfr(r1,r2,P)    distributive polynomial over rational functions 
			over the rationals to rational function over the 
			rationals 
diprgb(r,PL)            distributive polynomial over rationals Groebner 
			basis 
diprgba(r,PL,P)         distributive polynomial over rationals Groebner 
			basis augmentation 
diprgbr(r,PL)           distributive polynomial over rationals Groebner 
			basis recursion 
diprlotoglo(r,P)        distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over rationals in graduated lexicographical order 
diprlotolio(r,P)        distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over rationals in lexicographical order with 
			inverse exponent vector 
diprlototdo(r,P)        distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over rationals with total degree ordering 
diprmonic(r,P)          distributive polynomial over rationals monic 
diprneg(r,P)            distributive polynomial over rationals negation 
diprprod(r,P1,P2)       distributive polynomial over rationals product 
diprrprod(r,P,A)        distributive polynomial over rationals, rational 
			number product 
diprsp(r,P1,P2)         distributive polynomial over rationals S-polynomial 
diprsum(r,P1,P2)        distributive polynomial over rationals sum 
diptdg(r,P)             distributive polynomial total degree 
diptop(r,P)             distributive polynomial to polynomial (rekursiv) 
discriminant            and content of resultant equation upireddiscc(P,pc) 
			univariate polynomial over the integers reduced 
discriminant            and discriminant of an univariate polynomial over 
			the integers factorization rdiscupifact(rd,c,pL) 
			reduced 
discriminant            class equation sdisccleq(D,L) single 
discriminant            ecgf2disc(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with characteristic 2, 
discriminant            ecimindisc(E) elliptic curve with integer 
			coefficients, minimal model, 
discriminant            eciminfdisc(E) elliptic curve with integer 
			coefficients, minimal model, factorization of 
discriminant            ecisnfdisc(E) elliptic curve with integer 
			coefficients, short normal form, 
discriminant            ecisnffdisc(E) elliptic curve with integer 
			coefficients, short normal form, factorization of 
discriminant            ecmpdisc(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular primes, 
discriminant            ecmpsnfdisc(p,a4,a6) elliptic curve over modular 
			primes, short normal form, 
discriminant            ecnfdisc(F,a1,a2,a3,a4,a6) elliptic curve over 
			number field 
discriminant            ecnfsnfdisc(F,a,b) elliptic curve over number 
			field, short normal form, 
discriminant            ecqnfacdisc(E) elliptic curve over quadratic number 
			field, actual model, 
discriminant            ecqnfacfndisc(E) elliptic curve over quadratic 
			number field, actual model, factorization of the 
			norm of the 
discriminant            ecqnfacndisc(E) elliptic curve over quadratic 
			number field, actual model, norm of the 
discriminant            ecqnfacpifdi(E) elliptic curve over quadratic 
			number field, actual model, prime ideal 
			factorization of the 
discriminant            ecqnfflddisc(E) (MACRO) elliptic curve over 
			quadratic number field, field 
discriminant            ecracdisc(E) elliptic curve over rational numbers, 
			actual curve, 
discriminant            ecracfdisc(E) elliptic curve over rational numbers, 
			actual curve, factorization of 
discriminant            modulo 4 ecqnfdmod4(E) (MACRO) elliptic curve over 
			quadratic number field, field 
discriminant            nffielddiscr(F) number field, field 
discriminant            of an univariate polynomial over the integers 
			factorization rdiscupifact(rd,c,pL) reduced 
			discriminant and 
discriminant            pidiscr(r,P,n) polynomial over integers 
discriminant            pmidiscr(r,M,P,n) polynomial over modular integers 
discriminant            pmsdiscr(r,m,P,n) polynomial over modular singles 
discriminant            qnfdisc(D) quadratic number field 
discriminant            upprmsp1disc(p,F) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, 
discriminant            upprmsp1redd(p,F) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, reduced 
discriminant            via Hankel matrix pmidiscrhank(r,M,P) polynomial 
			over modular integers 
discriminant            via Hankel- matrix pidiscrhank(r,P) polynomial over 
			integers 
distinct                degree factorization upgf2ddfact(G,P) univariate 
			polynomial over Galois-field with characteristic 2 
distinct                degree factorization upgfsddfact(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic 
distinct                degree factorization upmiddfact(ip,P) univariate 
			polynomial over modular integers 
distinct                degree factorization upmsddfact(p,F) univariate 
			polynomial 
distinction             fgetdippicd(r1,r2,VL1,VL2,fac,pf) file get 
			distributive polynomial over polynomials over 
			integers case 
distinction             getdippicd(r1,r2,VL1,VL2,fac) (MACRO) get 
			distributive polynomial over polynomials over 
			integers case 
distributive            polynomial (rekursiv) ptodip(r,P) polynomial to 
distributive            polynomial ? isdipol(r,P) is 
distributive            polynomial bubble sort dipbsort(r,P) 
distributive            polynomial dimension fputdipdim(r,dim,S,M,VL,pf) 
			file put 
distributive            polynomial dimension of a polynomial ideal 
			dipdimpolid(r,G,pS,pM) 
distributive            polynomial dimension putdipdim(r,dim,S,M,VL) 
			(MACRO) put 
distributive            polynomial exponent vector compare 
			dipevcomp(r,EV1,EV2) 
distributive            polynomial exponent vector difference 
			dipevdif(r,EV1,EV2) 
distributive            polynomial exponent vector least common multiple 
			dipevlcm(r,EV1,EV2) 
distributive            polynomial exponent vector multiple test 
			dipevmt(r,EV1,EV2) 
distributive            polynomial exponent vector of the leading monomial 
			dipevl(r,P) 
distributive            polynomial exponent vector signum dipevsign(r,EV) 
distributive            polynomial exponent vector sum dipevsum(r,EV1,EV2) 
distributive            polynomial from monomial dipfmo(r,BC,EV) (MACRO) 
distributive            polynomial homogenize diphomog(r,P) 
distributive            polynomial homogenize specified variable 
			diphomogsv(r,P,n) 
distributive            polynomial leading base coefficient diplbc(r,P) 
			(MACRO) 
distributive            polynomial monomial advance dipmoad(r,P,pLBC,pLEV) 
distributive            polynomial new main variable dipnmv(r,P,n) 
distributive            polynomial over Galois-field with single 
			characteristic Groebner basis augmentation 
			dipgfsgba(r,p,AL,PL,P) 
distributive            polynomial over Galois-field with single 
			characteristic Groebner basis dipgfsgb(r,p,AL,PL) 
distributive            polynomial over Galois-field with single 
			characteristic Groebner basis recursion 
			dipgfsgbr(r,p,AL,PL) 
distributive            polynomial over Galois-field with single 
			characteristic S-polynomial dipgfssp(r,p,AL,P1,P2) 
distributive            polynomial over Galois-field with single 
			characteristic difference dipgfsdif(r,p,AL,P1,P2) 
distributive            polynomial over Galois-field with single 
			characteristic in graduated lexicographical order 
			dipgfslotglo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to 
distributive            polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in graduated lexicographical 
			order dipgfslotglo(r,p,AL,P) 
distributive            polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
distributive            polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) 
distributive            polynomial over Galois-field with single 
			characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
distributive            polynomial over Galois-field with single 
			characteristic list fgetdipgfsl(r,p,AL,VL,Vgfs,pf) 
			file get 
distributive            polynomial over Galois-field with single 
			characteristic list 
			fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put 
distributive            polynomial over Galois-field with single 
			characteristic list getdipgfsl(r,p,AL,VL,Vgfs) 
			(MACRO) get 
distributive            polynomial over Galois-field with single 
			characteristic list putdipgfsl(r,p,AL,PL,VL,Vgfs) 
			(MACRO) put 
distributive            polynomial over Galois-field with single 
			characteristic monic dipgfsmonic(r,p,AL,P) 
distributive            polynomial over Galois-field with single 
			characteristic negation dipgfsneg(r,p,AL,P) 
distributive            polynomial over Galois-field with single 
			characteristic product dipgfsprod(r,p,AL,P1,P2) 
distributive            polynomial over Galois-field with single 
			characteristic sum dipgfssum(r,p,AL,P1,P2) 
distributive            polynomial over Galois-field with single 
			characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to 
distributive            polynomial over Galois-field with single 
			characteristic, Galois-field with single 
			characteristic element product 
			dipgfsgfprod(r,p,AL,P,a) 
distributive            polynomial over integers Groebner basis 
			augmentation dipigba(r,PL,P) 
distributive            polynomial over integers Groebner basis 
			dipigb(r,PL) 
distributive            polynomial over integers Groebner basis recursion 
			dipigbr(r,PL) 
distributive            polynomial over integers S-polynomial 
			dipisp(r,P1,P2) 
distributive            polynomial over integers content and primitive part 
			dipicp(r,P,pPP) 
distributive            polynomial over integers difference 
			dipidif(r,P1,P2) 
distributive            polynomial over integers in graduated 
			lexicographical order dipilotoglo(r,P) distributive 
			polynomial over integers in lexicographical order 
			to 
distributive            polynomial over integers in lexicographical order 
			to distributive polynomial over integers in 
			graduated lexicographical order dipilotoglo(r,P) 
distributive            polynomial over integers in lexicographical order 
			to distributive polynomial over integers in 
			lexicographical order with inverse exponent vector 
			dipilotolio(r,P) 
distributive            polynomial over integers in lexicographical order 
			to distributive polynomial over integers with total 
			degree ordering dipilototdo(r,P) 
distributive            polynomial over integers in lexicographical order 
			with inverse exponent vector dipilotolio(r,P) 
			distributive polynomial over integers in 
			lexicographical order to 
distributive            polynomial over integers list fgetdipil(r,VL,pf) 
			file get 
distributive            polynomial over integers list fputdipil(r,PL,VL,pf) 
			file put 
distributive            polynomial over integers list getdipil(r,VL) 
			(MACRO) get 
distributive            polynomial over integers list putdipil(r,PL,VL) 
			(MACRO) put 
distributive            polynomial over integers negation dipineg(r,P) 
distributive            polynomial over integers one ? isdipione(r,P) is 
distributive            polynomial over integers product dipiprod(r,P1,P2) 
distributive            polynomial over integers sum dipisum(r,P1,P2) 
distributive            polynomial over integers with total degree ordering 
			dipilototdo(r,P) distributive polynomial over 
			integers in lexicographical order to 
distributive            polynomial over integers, integer product 
			dipiiprod(r,P,A) 
distributive            polynomial over modular integer primes Groebner 
			basis augmentation dipmipgba(r,p,PL,P) 
distributive            polynomial over modular integer primes Groebner 
			basis dipmipgb(r,p,PL) 
distributive            polynomial over modular integer primes Groebner 
			basis recursion dipmipgbr(r,p,PL) 
distributive            polynomial over modular integer primes S-polynomial 
			dipmipsp(r,p,P1,P2) 
distributive            polynomial over modular integer primes difference 
			dipmipdif(r,p,P1,P2) 
distributive            polynomial over modular integer primes in graduated 
			lexicographical order dipmiplotglo(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order to 
distributive            polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular integer primes in graduated 
			lexicographical order dipmiplotglo(r,p,P) 
distributive            polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular integer primes in lexicographical 
			order with inverse exponent vector 
			dipmiplotlio(r,p,P) 
distributive            polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular integer primes with total degree 
			ordering dipmiplottdo(r,p,P) 
distributive            polynomial over modular integer primes in 
			lexicographical order with inverse exponent vector 
			dipmiplotlio(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
distributive            polynomial over modular integer primes list 
			fgetdipmipl(r,p,VL,pf) file get 
distributive            polynomial over modular integer primes list 
			fputdipmipl(r,p,PL,VL,pf) file put 
distributive            polynomial over modular integer primes list 
			getdipmipl(r,p,VL) (MACRO) get 
distributive            polynomial over modular integer primes list 
			putdipmipl(r,p,PL,VL) (MACRO) put 
distributive            polynomial over modular integer primes monic 
			dipmipmonic(r,p,P) 
distributive            polynomial over modular integer primes negation 
			dipmipneg(r,p,P) 
distributive            polynomial over modular integer primes product 
			dipmipprod(r,p,P1,P2) 
distributive            polynomial over modular integer primes sum 
			dipmipsum(r,p,P1,P2) 
distributive            polynomial over modular integer primes with total 
			degree ordering dipmiplottdo(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical order to 
distributive            polynomial over modular integer primes, modular 
			integer primes product dipmipmiprod(r,p,P,A) 
distributive            polynomial over modular single primes Groebner 
			basis augmentation dipmspgba(r,p,PL,P) 
distributive            polynomial over modular single primes Groebner 
			basis dipmspgb(r,p,PL) 
distributive            polynomial over modular single primes Groebner 
			basis recursion dipmspgbr(r,p,PL) 
distributive            polynomial over modular single primes S-polynomial 
			dipmspsp(r,p,P1,P2) 
distributive            polynomial over modular single primes difference 
			dipmspdif(r,p,P1,P2) 
distributive            polynomial over modular single primes in graduated 
			lexicographical order dipmsplotglo(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order to 
distributive            polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular single primes in graduated 
			lexicographical order dipmsplotglo(r,p,P) 
distributive            polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular single primes in lexicographical order 
			with inverse exponent vector dipmsplotlio(r,p,P) 
distributive            polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular single primes with total degree 
			ordering dipmsplottdo(r,p,P) 
distributive            polynomial over modular single primes in 
			lexicographical order with inverse exponent vector 
			dipmsplotlio(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
distributive            polynomial over modular single primes list 
			fgetdipmspl(r,p,VL,pf) file get 
distributive            polynomial over modular single primes list 
			fputdipmspl(r,p,PL,VL,pf) file put 
distributive            polynomial over modular single primes list 
			getdipmspl(r,p,VL) (MACRO) get 
distributive            polynomial over modular single primes list 
			putdipmspl(r,p,PL,VL) (MACRO) put 
distributive            polynomial over modular single primes monic 
			dipmspmonic(r,p,P) 
distributive            polynomial over modular single primes negation 
			dipmspneg(r,p,P) 
distributive            polynomial over modular single primes product 
			dipmspprod(r,p,P1,P2) 
distributive            polynomial over modular single primes sum 
			dipmspsum(r,p,P1,P2) 
distributive            polynomial over modular single primes with total 
			degree ordering dipmsplottdo(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to 
distributive            polynomial over modular single primes, modular 
			single primes product dipmspmsprod(r,p,P,a) 
distributive            polynomial over number field Groebner basis 
			augmentation dipnfgba(r,F,PL,P) 
distributive            polynomial over number field Groebner basis 
			dipnfgb(r,F,PL) 
distributive            polynomial over number field Groebner basis 
			recursion dipnfgbr(r,F,PL) 
distributive            polynomial over number field S-polynomial 
			dipnfsp(r,F,P1,P2) 
distributive            polynomial over number field difference 
			dipnfdif(r,F,P1,P2) 
distributive            polynomial over number field in graduated 
			lexicographical order dipnflotoglo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order to 
distributive            polynomial over number field in lexicographical 
			order to distributive polynomial over number field 
			in graduated lexicographical order 
			dipnflotoglo(r,F,P) 
distributive            polynomial over number field in lexicographical 
			order to distributive polynomial over number field 
			in lexicographical order with inverse exponent 
			vector dipnflotolio(r,F,P) 
distributive            polynomial over number field in lexicographical 
			order to distributive polynomial over number field 
			with total degree ordering dipnflototdo(r,F,P) 
distributive            polynomial over number field in lexicographical 
			order with inverse exponent vector 
			dipnflotolio(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
distributive            polynomial over number field list 
			fgetdipnfl(r,F,VL,Vnf,pf) file get 
distributive            polynomial over number field list 
			fputdipnfl(r,F,PL,VL,Vnf,pf) file put 
distributive            polynomial over number field list 
			getdipnfl(r,F,VL,Vnf) (MACRO) get 
distributive            polynomial over number field list 
			putdipnfl(r,F,PL,VL,Vnf) (MACRO) put 
distributive            polynomial over number field monic 
			dipnfmonic(r,F,P) 
distributive            polynomial over number field negation 
			dipnfneg(r,F,P) 
distributive            polynomial over number field product 
			dipnfprod(r,F,P1,P2) 
distributive            polynomial over number field sum 
			dipnfsum(r,F,P1,P2) 
distributive            polynomial over number field with total degree 
			ordering dipnflototdo(r,F,P) distributive 
			polynomial over number field in lexicographical 
			order to 
distributive            polynomial over number field, number field element 
			product dipnfnfprod(r,F,P,A) 
distributive            polynomial over polynomials over integers Groebner 
			basis augmentation dippigba(r1,r2,PL,P) 
distributive            polynomial over polynomials over integers Groebner 
			basis dippigb(r1,r2,PL) 
distributive            polynomial over polynomials over integers Groebner 
			basis recursion dippigbr(r1,r2,PL) 
distributive            polynomial over polynomials over integers Groebner 
			system fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file 
			put 
distributive            polynomial over polynomials over integers Groebner 
			system putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) put 
distributive            polynomial over polynomials over integers Groebner 
			test dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) 
distributive            polynomial over polynomials over integers Groebner 
			test fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) 
			file put 
distributive            polynomial over polynomials over integers Groebner 
			test putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) 
			(MACRO) put 
distributive            polynomial over polynomials over integers 
			S-polynomial dippisp(r1,r2,P1,P2) 
distributive            polynomial over polynomials over integers case 
			distinction fgetdippicd(r1,r2,VL1,VL2,fac,pf) file 
			get 
distributive            polynomial over polynomials over integers case 
			distinction getdippicd(r1,r2,VL1,VL2,fac) (MACRO) 
			get 
distributive            polynomial over polynomials over integers 
			comprehensive Groebner basis 
			dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
distributive            polynomial over polynomials over integers 
			comprehensive Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put 
distributive            polynomial over polynomials over integers 
			comprehensive Groebner basis 
			putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) put 
distributive            polynomial over polynomials over integers content 
			and primitive part dippicp(r1,r2,P,pPP) 
distributive            polynomial over polynomials over integers 
			difference dippidif(r1,r2,P1,P2) 
distributive            polynomial over polynomials over integers dimension 
			dippidim(r1,r2,s,PL,CONDS,fac,VL1,VL2,pf) 
distributive            polynomial over polynomials over integers dimension 
			fputdippidim(r1,r2,DIML,VL1,VL2,pf) file put 
distributive            polynomial over polynomials over integers dimension 
			putdippidim(r1,r2,DIML,VL1,VL2) (MACRO) put 
distributive            polynomial over polynomials over integers in 
			graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to 
distributive            polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers in graduated 
			lexicographical order dippilotoglo(r1,r2,P) 
distributive            polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers in lexicographical 
			order with inverse exponent vector 
			dippilotolio(r1,r2,P) 
distributive            polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers with total degree 
			ordering dippilototdo(r1,r2,P) 
distributive            polynomial over polynomials over integers in 
			lexicographical order with inverse exponent vector 
			dippilotolio(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to 
distributive            polynomial over polynomials over integers list 
			fgetdippil(r1,r2,VL1,VL2,pf) file get 
distributive            polynomial over polynomials over integers list 
			fputdippil(r1,r2,PL,VL1,VL2,pf) file put 
distributive            polynomial over polynomials over integers list 
			getdippil(r1,r2,VL1,VL2) (MACRO) get 
distributive            polynomial over polynomials over integers list 
			putdippil(r1,r2,PL,VL1,VL2) (MACRO) put 
distributive            polynomial over polynomials over integers negation 
			dippineg(r1,r2,P) 
distributive            polynomial over polynomials over integers one ? 
			isdippione(r1,r2,P) is 
distributive            polynomial over polynomials over integers 
			parametric ideal membership test 
			dippipim(r1,r2,s,PL,PTL,CONDS,OPL) 
distributive            polynomial over polynomials over integers 
			parametric ideal membership test 
			fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put 
distributive            polynomial over polynomials over integers 
			parametric ideal membership test 
			putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put 
distributive            polynomial over polynomials over integers product 
			dippiprod(r1,r2,P1,P2) 
distributive            polynomial over polynomials over integers 
			quantifier free formula 
			dippiqff(r1,r2,s,PL,CONDS,fac) 
distributive            polynomial over polynomials over integers 
			quantifier free formula 
			fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file put 
distributive            polynomial over polynomials over integers 
			quantifier free formula 
			putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put 
distributive            polynomial over polynomials over integers reduced 
			comprehensive Groebner basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
distributive            polynomial over polynomials over integers sum 
			dippisum(r1,r2,P1,P2) 
distributive            polynomial over polynomials over integers with 
			total degree ordering dippilototdo(r1,r2,P) 
			distributive polynomial over polynomials over 
			integers in lexicographical order to 
distributive            polynomial over polynomials over integers, 
			polynomial over integers product 
			dippipiprod(r1,r2,P,A) 
distributive            polynomial over rational functions over the 
			rationals Groebner basis augmentation 
			diprfrgba(r1,r2,PL,P) 
distributive            polynomial over rational functions over the 
			rationals Groebner basis diprfrgb(r1,r2,PL) 
distributive            polynomial over rational functions over the 
			rationals Groebner basis recursion 
			diprfrgbr(r1,r2,PL) 
distributive            polynomial over rational functions over the 
			rationals S-polynomial diprfrsp(r1,r2,P1,P2) 
distributive            polynomial over rational functions over the 
			rationals difference diprfrdif(r1,r2,P1,P2) 
distributive            polynomial over rational functions over the 
			rationals in graduated lexicographical order 
			diprfrlotglo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to 
distributive            polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals in graduated lexicographical order 
			diprfrlotglo(r1,r2,P) 
distributive            polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order with inverse 
			exponent vector diprfrlotlio(r1,r2,P) 
distributive            polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals with total degree ordering 
			diprfrlottdo(r1,r2,P) 
distributive            polynomial over rational functions over the 
			rationals in lexicographical order with inverse 
			exponent vector diprfrlotlio(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to 
distributive            polynomial over rational functions over the 
			rationals list fgetdiprfrl(r1,r2,VL1,VL2,pf) file 
			get 
distributive            polynomial over rational functions over the 
			rationals list fputdiprfrl(r1,r2,PL,VL1,VL2,pf) 
			file put 
distributive            polynomial over rational functions over the 
			rationals list getdiprfrl(r1,r2,VL1,VL2) (MACRO) 
			get 
distributive            polynomial over rational functions over the 
			rationals list putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) 
			put 
distributive            polynomial over rational functions over the 
			rationals monic diprfrmonic(r1,r2,P) 
distributive            polynomial over rational functions over the 
			rationals negation diprfrneg(r1,r2,P) 
distributive            polynomial over rational functions over the 
			rationals one ? isdiprfrone(r1,r2,P) is 
distributive            polynomial over rational functions over the 
			rationals product diprfrprod(r1,r2,P1,P2) 
distributive            polynomial over rational functions over the 
			rationals rational function over the rationals 
			product diprfrrfprod(r1,r2,P,A) 
distributive            polynomial over rational functions over the 
			rationals rfrtodiprfr(r1,r2,F) rational function 
			over the rationals to 
distributive            polynomial over rational functions over the 
			rationals sum diprfrsum(r1,r2,P1,P2) 
distributive            polynomial over rational functions over the 
			rationals to rational function over the rationals 
			diprfrtorfr(r1,r2,P) 
distributive            polynomial over rational functions over the 
			rationals with total degree ordering 
			diprfrlottdo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to 
distributive            polynomial over rationals Groebner basis 
			augmentation diprgba(r,PL,P) 
distributive            polynomial over rationals Groebner basis 
			diprgb(r,PL) 
distributive            polynomial over rationals Groebner basis recursion 
			diprgbr(r,PL) 
distributive            polynomial over rationals S-polynomial 
			diprsp(r,P1,P2) 
distributive            polynomial over rationals difference 
			diprdif(r,P1,P2) 
distributive            polynomial over rationals in graduated 
			lexicographical order diprlotoglo(r,P) distributive 
			polynomial over rationals in lexicographical order 
			to 
distributive            polynomial over rationals in lexicographical order 
			to distributive polynomial over rationals in 
			graduated lexicographical order diprlotoglo(r,P) 
distributive            polynomial over rationals in lexicographical order 
			to distributive polynomial over rationals in 
			lexicographical order with inverse exponent vector 
			diprlotolio(r,P) 
distributive            polynomial over rationals in lexicographical order 
			to distributive polynomial over rationals with 
			total degree ordering diprlototdo(r,P) 
distributive            polynomial over rationals in lexicographical order 
			with inverse exponent vector diprlotolio(r,P) 
			distributive polynomial over rationals in 
			lexicographical order to 
distributive            polynomial over rationals list fgetdiprl(r,VL,pf) 
			file get 
distributive            polynomial over rationals list 
			fputdiprl(r,PL,VL,pf) file put 
distributive            polynomial over rationals list getdiprl(r,VL) 
			(MACRO) get 
distributive            polynomial over rationals list putdiprl(r,PL,VL) 
			(MACRO) put 
distributive            polynomial over rationals monic diprmonic(r,P) 
distributive            polynomial over rationals negation diprneg(r,P) 
distributive            polynomial over rationals one ? isdiprone(r,P) is 
distributive            polynomial over rationals product diprprod(r,P1,P2) 
distributive            polynomial over rationals sum diprsum(r,P1,P2) 
distributive            polynomial over rationals with total degree 
			ordering diprlototdo(r,P) distributive polynomial 
			over rationals in lexicographical order to 
distributive            polynomial over rationals, rational number product 
			diprrprod(r,P,A) 
distributive            polynomial to polynomial (rekursiv) diptop(r,P) 
distributive            polynomial total degree diptdg(r,P) 
divisibility            imp2d(A) integer maximal power of 2 
division                HDidiv() Heidelberg arithmetic package: integer 
division                PAFdiv() Papanikolaou floating point package: 
division                by 2 of a point ecimindivby2(E,P,h,PL,H) elliptic 
			curve with integer coefficients, minimal model, 
division                of a point by an integer ecimindiv(E,P,n) elliptic 
			curve with integer coefficients, minimal model, 
division                of a point by an integer, special version 
			ecimindivs(E,P,h,ug,PL,n) elliptic curve with 
			integer coefficients, minimal model, 
division                polynomials ecgf2cdivp(G,a6,m) elliptic curve over 
			Galois-field with characteristic 2, construction of 
division                polynomials ecmpsnfcdivp(P,a4,a6,n) elliptic curve 
			over modular primes, short normal form, 
			construction of 
division                with reference to SIMATH divs(A,B) (MACRO) 
divisor                 (rekursiv) upgfsgsd(p,AL,P) univariate polynomial 
			over Galois-field with single characteristic 
			greatest squarefree 
divisor                 (rekursiv) upmigsd(ip,P) univariate polynomial over 
			modular integers greatest squarefree 
divisor                 (rekursiv) upmsgsd(m,P) univariate polynomial over 
			modular singles greatest squarefree 
divisor                 HDigcd() Heidelberg arithmetic package: greatest 
			common 
divisor                 and cofactors (rekursiv) 
			pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
			integers greatest common 
divisor                 and cofactors (rekursiv) 
			pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
			singles greatest common 
divisor                 and cofactors igcdcf(A,B,pU,pV) integer greatest 
			common 
divisor                 and cofactors pigcdcf(r,P1,P2,pQ1,pQ2) polynomial 
			over integers greatest common 
divisor                 and cofactors upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate 
			polynomial over number field greatest common 
divisor                 class number qffmsdcn(m,P) quadratic function field 
			over modular singles 
divisor                 class number subroutine 1 qffmsdcns1(m,P) quadratic 
			function field over modular singles 
divisor                 class number subroutine 2 qffmsdcns2(m,P) quadratic 
			function field over modular singles 
divisor                 class number subroutine 3 qffmsdcns3(m,P) quadratic 
			function field over modular singles 
divisor                 form and cofactors maiedfcf(M,pA,pB) matrix of 
			integers elementary 
divisor                 form and cofactors maupmipedfcf(p,M,pA,pB) matrix 
			of univariate polynomials over modular integer 
			primes elementary 
divisor                 form and cofactors maupmspedfcf(p,M,pA,pB) matrix 
			of univariate polynomials over modular single 
			primes elementary 
divisor                 form and cofactors maupredfcf(M,pA,pB) matrix of 
			univariate polynomials over rationals elementary 
divisor                 iegcd(A,B,pU,pV) integer extended greatest common 
divisor                 igcd(A,B) integer greatest common 
divisor                 ihegcd(A,B,pV) integer half extended greatest 
			common 
divisor                 search ( lists only ) rhopds_lo(N,b,z) rho- method 
			by Pollard 
divisor                 search (rekursiv) irds(n,G,p) integer random 
divisor                 search dpipds(a,N) double precision integer prime 
divisor                 search elcfds(N,b,e) elliptic curve fast 
divisor                 search elcpds(N,a,z) elliptic curve pure 
divisor                 search ilpds(N,A,B,pP,pN1) integer large prime 
divisor                 search impds(N,A,B,pP,pQ) integer medium prime 
divisor                 search imspds(N,a,b) integer medium single prime 
divisor                 search rhofrpds(N,b,z) rho- method ( fast reduction 
			) by Pollard 
divisor                 search rhopds(N,b,z) rho- method by Pollard 
divisor                 search sum elcpdssum(N,x1,y1,x2,y2,px3,py3,a) 
			elliptic curve prime 
divisor                 segcd(a,b,pu,pv) single-precision extended greatest 
			common 
divisor                 sgcd(a,b) single-precision greatest common 
divisor                 udpmiegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over modular integers extended greatest 
			common 
divisor                 udpmigcd(m,P1,P2) univariate dense polynomial over 
			modular integers greatest common 
divisor                 udpmihegcd(m,P1,P2,pP3) univariate dense polynomial 
			over modular integers half extended greatest common 
divisor                 udpmsegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over modular singles extended greatest 
			common 
divisor                 udpmsgcd(m,P1,P2) univariate dense polynomial over 
			modular singles greatest common 
divisor                 udpmshegcd(m,P1,P2,pP3) univariate dense polynomial 
			over modular singles half extended greatest common 
divisor                 upgf2gcd(G,P1,P2) univariate polynomial over 
			Galois-field with characteristic 2 greatest common 
divisor                 upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate polynomial 
			over Galois-field with single characteristic 
			extended greatest common 
divisor                 upgfsgcd(p,AL,P1,P2) univariate polynomial over 
			Galois-field with single characteristic greatest 
			common 
divisor                 upgfshegcd(p,AL,P1,P2,pP3) univariate polynomial 
			over Galois-field with single characteristic half 
			extended greatest common 
divisor                 upmiegcd(P,P1,P2,pP3,pP4) univariate polynomial 
			over modular integers extended greatest common 
divisor                 upmigcd(ip,P1,P2) univariate polynomial over 
			modular integers greatest common 
divisor                 upmihegcd(P,P1,P2,pP3) univariate polynomial over 
			modular integers half extended greatest common 
divisor                 upmsegcd(m,P1,P2,pP3,pP4) univariate polynomial 
			over modular singles extended greatest common 
divisor                 upmsgcd(m,P1,P2) univariate polynomial over modular 
			singles greatest common 
divisor                 upmshegcd(m,P1,P2,pP3) univariate polynomial over 
			modular singles half extended greatest common 
divisor                 upnfgcd(F,P1,P2) univariate polynomial over number 
			field greatest common 
divisor                 uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, extended greatest common 
divisor,                lists only igcd_lo(A,B) integer greatest common 
divisors                ( lists only ) ispd_lo(N,pM) integer small prime 
divisors                of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable polynomial over 
			the integers approximation of p-adic factorization 
			of the defining polynomial, generators of p-maximal 
			orders of the p-adic 
divisors                search ispd(N,pM) integer small prime 
divs(A,B)               (MACRO) division with reference to SIMATH 
double                  of a point ecimindouble(E,P) elliptic curve with 
			integer coefficients, minimal model, 
double                  of point ecisnfdouble(E,P) elliptic curve with 
			integer coefficients, short normal form, 
double                  of point ecracdouble(E,P) elliptic curve over the 
			rational numbers, minimal model, 
double                  precision integer prime divisor search dpipds(a,N) 
dpdegvec(r,P)           dense polynomial degree vector (rekursiv) 
dpipds(a,N)             double precision integer prime divisor search 
dpmidif(r,m,P1,P2)      dense polynomial over modular integers difference 
			(rekursiv) 
dpmineg(r,m,P)          dense polynomial over modular integers negation 
			(rekursiv) 
dpmiprod(r,M,P1,P2)     dense polynomial over modular integers product 
			(rekursiv) 
dpmisum(r,M,P1,P2)      dense polynomial over modular integers sum 
			(rekursiv) 
dpmsdif(r,m,P1,P2)      dense polynomial over modular singles difference 
			(rekursiv) 
dpmsneg(r,m,P)          dense polynomial over modular singles negation 
			(rekursiv) 
dpmsprod(r,m,P1,P2)     dense polynomial over modular singles product 
			(rekursiv) 
dpmssum(r,m,P1,P2)      dense polynomial over modular singles sum 
			(rekursiv) 
dpred(r,P)              dense polynomial reductum 
dptop(r,P)              dense polynomial to polynomial (rekursiv) 
ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve over Galois-field with 
			characteristic 2, birational transformation of 
			coefficients 
ecgf2cdivp(G,a6,m)      elliptic curve over Galois-field with 
			characteristic 2, construction of division 
			polynomials 
ecgf2cssa(G,a6,s,pl,ts) elliptic curve over Galois field with 
			characteristic 2, combined Schoof- Shanks- 
			algorithm 
ecgf2disc(G,a1,a2,a3,a4,a6) elliptic curve over Galois-field with 
			characteristic 2, discriminant 
ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) elliptic curve over Galois-field with 
			characteristic 2, finding a multiple of the order 
			of a point with the Pollard Lambda method 
ecgf2fp(G,a1,a2,a3,a4,a6) elliptic curve over Galois-field with 
			characteristic 2, find point 
ecgf2jinv(G,a1,a2,a3,a4,a6) elliptic curve over Galois-field with 
			characteristic 2, j-invariant 
ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve over Galois-field with 
			characteristic 2, line through points 
ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve over Galois-field with 
			characteristic 2, multiple of the order of a point 
			to exact order of the point 
ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) elliptic curve over Galois-field 
			with characteristic 2, modified Shanks' algorithm, 
			first part 
ecgf2mul(G,a1,a2,a3,a4,a6,k,P1) elliptic curve Galois-field with 
			characteristic 2, multiplication-map 
ecgf2neg(G,a1,a2,a3,a4,a6,P) elliptic curve over Galois-field with 
			characteristic 2, negative point 
ecgf2npca(G,a6)         elliptic curve over Galois-field with 
			characteristic 2, counting algorithm 
ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic curve over Galois field with 
			characteristic 2, number of points after field 
			extension 
ecgf2npmi(G,a6,S,v,pM)  elliptic curve over Galois-field with 
			characteristic 2, number of points modulo an 
			integer determined with the Schoof algorithm 
ecgf2npmp2(G,a6,c,L)    elliptic curve over Galois-field with 
			characteristic 2, number of points modulo a power 
			of 2 
ecgf2npmspv1(G,a6,p,L)  elliptic curve over Galois-field with 
			characteristic 2, number of points modulo a single 
			prime determined with the Schoof algorithm, version 
			1 
ecgf2npmspv2(G,a6,p,L)  elliptic curve over Galois-field with 
			characteristic 2, number of points modulo a single 
			prime determined with the Schoof algorithm, version 
			2 
ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve over Galois-field with 
			characteristic 2, special form, multiplication-map, 
			special version 
ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic curve over Galois-field with 
			characteristic 2, special form, sum of points, 
			special version 
ecgf2srpp(G,P)          elliptic curve over Galois-field with 
			characteristic 2, standard representation of 
			projective point 
ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve over Galois-field with 
			characteristic 2, sum of points 
ecgf2tavb6(G,a1,a2,a3,a4,a6) elliptic curve over Galois-field with 
			characteristic 2, Tate's values b2, b4, b6 
ecgf2tavb8(G,a1,a2,a3,a4,a6) elliptic curve over Galois-field with 
			characteristic 2, Tate's values b2, b4, b6, b8 
ecgf2tavc6(G,a1,a2,a3,a4,a6) elliptic curve over Galois-field with 
			characteristic 2, Tate's values c4, c6 
ecimina1(E)             elliptic curve with integer coefficients, minimal 
			model, a1 
ecimina2(E)             elliptic curve with integer coefficients, minimal 
			model, a2 
ecimina3(E)             elliptic curve with integer coefficients, minimal 
			model, a3 
ecimina4(E)             elliptic curve with integer coefficients, minimal 
			model, a4 
ecimina6(E)             elliptic curve with integer coefficients, minimal 
			model, a6 
eciminb2(E)             elliptic curve with integer coefficients, minimal 
			model, b2 
eciminb4(E)             elliptic curve with integer coefficients, minimal 
			model, b4 
eciminb6(E)             elliptic curve with integer coefficients, minimal 
			model, b6 
eciminb8(E)             elliptic curve with integer coefficients, minimal 
			model, b8 
eciminbrtmp(E,p,n)      elliptic curve with integer coefficients, minimal 
			model, bad reduction type modulo prime 
eciminbtac(E)           elliptic curve with integer coefficients, minimal 
			model, birational transformation to actual ( 
			rational ) model 
eciminbtco(E,BT)        elliptic curve with integer coefficients, minimal 
			model, birational transformation of coefficients 
eciminbtsnf(E)          elliptic curve with integer coefficients, minimal 
			model, birational transformation to short normal 
			form 
eciminc4(E)             elliptic curve with integer coefficients, minimal 
			model, c4 
eciminc6(E)             elliptic curve with integer coefficients, minimal 
			model, c6 
ecimindif(E,P,Q)        elliptic curve with integer coefficients, minimal 
			model, difference of points 
ecimindisc(E)           elliptic curve with integer coefficients, minimal 
			model, discriminant 
ecimindiv(E,P,n)        elliptic curve with integer coefficients, minimal 
			model, division of a point by an integer 
ecimindivby2(E,P,h,PL,H) elliptic curve with integer coefficients, minimal 
			model, division by 2 of a point 
ecimindivs(E,P,h,ug,PL,n) elliptic curve with integer coefficients, minimal 
			model, division of a point by an integer, special 
			version 
ecimindouble(E,P)       elliptic curve with integer coefficients, minimal 
			model, double of a point 
ecimindwhnth(E)         elliptic curve with integer coefficients, minimal 
			model, difference between Weil height and 
			Neron-Tate height 
eciminfdisc(E)          elliptic curve with integer coefficients, minimal 
			model, factorization of discriminant 
ecimingentor(E)         elliptic curve with integer coefficients, minimal 
			model, generators of torsion group 
eciminlhaav(E,P)        elliptic curve with integer coefficients, minimal 
			model, local height at the archimedean absolute 
			value 
eciminlhnaav(E,P)       elliptic curve with integer coefficients, minimal 
			model, local heights at all non archimedean 
			absolute values 
eciminmrtmp(E,p)        elliptic curve with integer coefficients, minimal 
			model, multiplicative reduction type modulo prime 
eciminmul(E,P,n)        elliptic curve with integer coefficients, minimal 
			model, multiplication-map 
eciminmwgbase(E)        elliptic curve with integer coefficients, minimal 
			model, Mordell-Weil-group, base 
eciminneg(E,P)          elliptic curve with integer coefficients, minimal 
			model, negative point 
eciminnetahe(E,P)       elliptic curve with integer coefficients, minimal 
			model, Neron-Tate height 
eciminnetapa(E,P,Q)     elliptic curve with integer coefficients, minimal 
			model, Neron-Tate pairing 
eciminntheps(E,d)       elliptic curve with integer coefficients, minimal 
			model, set NTH_EPS 
eciminpcompmt(E,P1,P2)  elliptic curve with integer coefficients, minimal 
			model, point comparison modulo torsion 
eciminplinsp(P,h,PL)    elliptic curve with integer coefficients, minimal 
			model, point list, insert point 
eciminplunion(E,L1,L2,modus) elliptic curve with integer coefficients, 
			minimal model, point list union 
eciminredtype(E)        elliptic curve with integer coefficients, minimal 
			model, reduction type 
eciminreg(E,LP,n,modus) elliptic curve with integer coefficients, minimal 
			model, regulator 
eciminsum(E,P,Q)        elliptic curve with integer coefficients, minimal 
			model, sum of points 
ecimintatealg(E,p,n)    elliptic curve with integer coefficients, minimal 
			model, Tate's algorithm 
ecimintorgr(E)          elliptic curve with integer coefficients, minimal 
			model, torsion group 
ecimintosnf(E)          elliptic curve with integer coefficients, minimal 
			model to short normal form 
ecipnorm(P)             elliptic curve with integer coefficients, point 
			normalization 
ecisnfa4(E)             elliptic curve with integer coefficients, short 
			normal form, a4 
ecisnfa6(E)             elliptic curve with integer coefficients, short 
			normal form, a6 
ecisnfb2(E)             elliptic curve with integer coefficients, short 
			normal form, b2 
ecisnfb4(E)             elliptic curve with integer coefficients, short 
			normal form, b4 
ecisnfb6(E)             elliptic curve with integer coefficients, short 
			normal form, b6 
ecisnfb8(E)             elliptic curve with integer coefficients, short 
			normal form, b8 
ecisnfbtac(E)           elliptic curve with integer coefficients, short 
			normal form, birational transformation to actual ( 
			rational ) model 
ecisnfbtco(E,BT)        elliptic curve with integer coefficients, short 
			normal form, birational transformation of 
			coefficients 
ecisnfbtmin(E)          elliptic curve with integer coefficients, short 
			normal form, birational transformation to minimal 
			model 
ecisnfc4(E)             elliptic curve with integer coefficients, short 
			normal form, c4 
ecisnfc6(E)             elliptic curve with integer coefficients, short 
			normal form, c6 
ecisnfdif(E,P,Q)        elliptic curve with integer coefficients, minimal 
			model, difference of points 
ecisnfdisc(E)           elliptic curve with integer coefficients, short 
			normal form, discriminant 
ecisnfdouble(E,P)       elliptic curve with integer coefficients, short 
			normal form, double of point 
ecisnfdwhnth(E)         elliptic curve with integer coefficients, short 
			normal form, difference between Weil height and 
			Neron-Tate height 
ecisnfelogp(E,P,n)      elliptic curve with integer coefficients, short 
			normal form, elliptic logarithm of point 
ecisnffdisc(E)          elliptic curve with integer coefficients, short 
			normal form, factorization of discriminant 
ecisnfgentor(E)         elliptic curve with integer coefficients, short 
			normal form, generators of the torsion group 
ecisnfmul(E,P,n)        elliptic curve with integer coefficients, short 
			normal form, multiplication-map 
ecisnfmwgbase(E)        elliptic curve with integer coefficients, short 
			normal form, Mordell-Weil-group, base 
ecisnfneg(E,P)          elliptic curve with integer coefficients, short 
			normal form, negative of point 
ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve with integer 
			coefficients, short normal form, points of bounded 
			Weil height 
ecisnfsum(E,P,Q)        elliptic curve with integer coefficients, short 
			normal form, sum of points 
ecisnftorgr(E)          elliptic curve with integer coefficients, short 
			normal form, torsion group 
ecitatealg(a1,a2,a3,a4,a6,p,n) elliptic curve with integer coefficients 
			Tate's algorithm 
ecitavalb(a1,a2,a3,a4,a6) elliptic curve with integer coefficients, Tate's 
			values b2, b4, b6, b8 
ecitavalc(a1,a2,a3,a4,a6) elliptic curve with integer coefficients, minimal 
			model, Tate's values c4, c6 
ecmipsnfnpsv(p,a4,a6)   elliptic curve over modular integer primes short 
			normal form number of points special version 
ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve over modular primes, 
			birational transformation of coefficients 
ecmpdisc(p,a1,a2,a3,a4,a6) elliptic curve over modular primes, discriminant 
ecmpfp(p,a1,a2,a3,a4,a6) elliptic curve over modular primes, find point 
ecmpjinv(p,a1,a2,a3,a4,a6) elliptic curve over modular primes, j-invariant 
ecmplp(p,a1,a2,a3,a4,a6,P1,P2) elliptic curve over modular primes, line 
			through points 
ecmpmul(p,a1,a2,a3,a4,a6,n,P1) elliptic curve over modular primes 
			multiplication-map 
ecmpneg(p,a1,a2,a3,a4,a6,P) elliptic curve over modular primes negative 
			point 
ecmpsnfcdivp(P,a4,a6,n) elliptic curve over modular primes, short normal 
			form, construction of division polynomials 
ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic curve over modular primes, short 
			normal form, combined Schoof- Shanks- algorithm 
ecmpsnfdisc(p,a4,a6)    elliptic curve over modular primes, short normal 
			form, discriminant 
ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over modular primes, short normal 
			form, finding a multiple of the order of a point 
			with the Pollard Lambda method 
ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over modular primes, short normal 
			form, finding a multiple of the order of a point 
			with the Pollard Rho method 
ecmpsnffp(p,a4,a6)      elliptic curve over modular primes, short normal 
			form, find point 
ecmpsnfjinv(p,a4,a6)    elliptic curve over modular primes, short normal 
			form, j-invariant 
ecmpsnflp(p,a4,a6,P1,P2) elliptic curve over modular primes, short normal 
			form, line through points 
ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over modular primes, short normal 
			form, multiple of the order of a point to exact 
			order of the point 
ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve over modular primes, short 
			normal form, modified Shanks' algorithm, first part 
ecmpsnfmul(p,a4,a6,n,P1) elliptic curve over modular primes, short normal 
			form, multiplication-map 
ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve over modular primes, short 
			normal form, multiplication-map, special version 
ecmpsnfneg(p,a4,a6,P)   elliptic curve over modular primes, short normal 
			form, negative point 
ecmpsnfnpm2(P,a4,a6)    elliptic curve over modular primes, short normal 
			form, number of points modulo 2 
ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve over modular primes, short normal 
			form, number of points modulo an integer determined 
			with the Schoof algorithm 
ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over modular primes, short normal 
			form, number of points modulo a single prime 
			determined with the Schoof algorithm 
ecmpsnfsum(p,a4,a6,P1,P2) elliptic curve over modular primes, short normal 
			form, sum of points 
ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve over modular primes, short 
			normal form, sum of points, special version 
ecmpsrpp(p,P)           elliptic curve over modular primes, standard 
			representation of projective point 
ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) elliptic curve over modular primes, sum of 
			points 
ecmptavb6(p,a1,a2,a3,a4,a6) elliptic curve over modular primes Tate's values 
			b2, b4, b6 
ecmptavb8(p,a1,a2,a3,a4,a6) elliptic curve over modular primes Tate's values 
			b2, b4, b6, b8 
ecmptavc6(p,a1,a2,a3,a4,a6) elliptic curve over modular primes Tate's values 
			c4, c6 
ecmptosnf(p,a1,a2,a3,a4,a6) elliptic curve over modular primes to short 
			normal form 
ecmspnp(p,a1,a2,a3,a4,a6) elliptic curve over modular single prime, number 
			of points 
ecmspsnfnp(p,a4,a6)     elliptic curve over modular single primes, short 
			normal form, number of points 
ecmspsnfsha(p,a4,a6)    (MACRO) elliptic curve over modular single primes, 
			short normal form, Shanks' algorithm 
ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve over number field 
			birational transformation of coefficients 
ecnfdisc(F,a1,a2,a3,a4,a6) elliptic curve over number field discriminant 
ecnfjinv(F,a1,a2,a3,a4,a6) elliptic curve over number field j-invariant 
ecnflp(F,a1,a2,a3,a4,a6,P1,P2) elliptic curve over number field line through 
			points 
ecnfmul(F,a1,a2,a3,a4,a6,n,P1) elliptic curve over number field 
			multiplication-map 
ecnfneg(F,a1,a2,a3,a4,a6,P) elliptic curve over number field negative point 
ecnfsnfdisc(F,a,b)      elliptic curve over number field, short normal 
			form, discriminant 
ecnfsnfjinv(F,a,b)      elliptic curve over number field, short normal 
			form, j-invariant 
ecnfsnflp(F,a,b,P1,P2)  elliptic curve over number field short normal form 
			line through points 
ecnfsnfmul(F,a,b,n,P1)  elliptic curve over number field short normal form 
			multiplication-map 
ecnfsnfneg(F,a,b,P)     elliptic curve over number field short normal form 
			negative point 
ecnfsnfsum(F,a,b,P1,P2) elliptic curve over number field short normal form 
			sum of points 
ecnfsrpp(F,P)           elliptic curve over number field standard 
			representation of projective point 
ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) elliptic curve over number field sum of 
			points 
ecnftavb6(F,a1,a2,a3,a4,a6) elliptic curve over number field Tate's values 
			b2, b4, b6 
ecnftavb8(F,a1,a2,a3,a4,a6) elliptic curve over number field Tate's values 
			b2, b4, b6, b8 
ecnftavc6(F,a1,a2,a3,a4,a6) elliptic curve over number field Tate's values 
			c4, c6 
ecnftosnf(F,a1,a2,a3,a4,a6) elliptic curve over number field to short normal 
			form 
ecqnfacb2(E)            elliptic curve over quadratic number field, actual 
			model, Tate value b2 
ecqnfacb4(E)            elliptic curve over quadratic number field, actual 
			model, Tate value b4 
ecqnfacb6(E)            elliptic curve over quadratic number field, actual 
			model, Tate value b6 
ecqnfacb8(E)            elliptic curve over quadratic number field, actual 
			model, Tate value b8 
ecqnfacc4(E)            elliptic curve over quadratic number field, actual 
			model, Tate value c4 
ecqnfacc6(E)            elliptic curve over quadratic number field, actual 
			model, Tate value c6 
ecqnfacdisc(E)          elliptic curve over quadratic number field, actual 
			model, discriminant 
ecqnfacfndisc(E)        elliptic curve over quadratic number field, actual 
			model, factorization of the norm of the 
			discriminant 
ecqnfacndisc(E)         elliptic curve over quadratic number field, actual 
			model, norm of the discriminant 
ecqnfacpifdi(E)         elliptic curve over quadratic number field, actual 
			model, prime ideal factorization of the 
			discriminant 
ecqnfcond(E)            elliptic curve over quadratic number field, 
			conductor 
ecqnfdmod4(E)           (MACRO) elliptic curve over quadratic number field, 
			field discriminant modulo 4 
ecqnfflddisc(E)         (MACRO) elliptic curve over quadratic number field, 
			field discriminant 
ecqnfinit(D,a1,a2,a3,a4,a6) elliptic curve over quadratic number field, 
			initialization 
ecqnfjinv(E)            elliptic curve over quadratic number field, 
			j-invariant 
ecqnftatealg(D,LC,LTV,P,pi,z,n) elliptic curve over quadratic number field, 
			Tate's algorithm 
ecqnftoeci(D,L)         elliptic curve over quadratic number field to 
			elliptic curve with integral coefficients 
ecraca1(E)              (MACRO) elliptic curve over rational numbers, 
			actual curve, a1 
ecraca2(E)              (MACRO) elliptic curve over rational numbers, 
			actual curve, a2 
ecraca3(E)              (MACRO) elliptic curve over rational numbers, 
			actual curve, a3 
ecraca4(E)              (MACRO) elliptic curve over rational numbers, 
			actual curve, a4 
ecraca6(E)              (MACRO) elliptic curve over rational numbers, 
			actual curve, a6 
ecracb2(E)              elliptic curve over rational numbers, actual curve, 
			b2 
ecracb4(E)              elliptic curve over rational numbers, actual curve, 
			b4 
ecracb6(E)              elliptic curve over rational numbers, actual curve, 
			b6 
ecracb8(E)              elliptic curve over rational numbers, actual curve, 
			b8 
ecracbtco(E,BT)         elliptic curve over rational numbers, birational 
			transformation of coefficients 
ecracbtmin(E)           elliptic curve over the rationals, actual curve, 
			birational transformation to minimal model 
ecracbtsnf(E)           elliptic curve over rational numbers, actual curve, 
			birational transformation to short normal form 
ecracc4(E)              elliptic curve over rational numbers, actual curve, 
			c4 
ecracc6(E)              elliptic curve over rational numbers, actual curve, 
			c6 
ecracdif(E,P,Q)         elliptic curve with integer coefficients, actual 
			curve, difference of points 
ecracdisc(E)            elliptic curve over rational numbers, actual curve, 
			discriminant 
ecracdouble(E,P)        elliptic curve over the rational numbers, minimal 
			model, double of point 
ecracfdisc(E)           elliptic curve over rational numbers, actual curve, 
			factorization of discriminant 
ecracgentor(E)          elliptic curve over rational numbers, actual curve, 
			generators of torsion group 
ecracmul(E,P,n)         elliptic curve over the rational numbers, actual 
			curve, multiplication-map 
ecracmwgbase(E)         elliptic curve over the rational numbers, actual 
			curve, Mordell-Weil-group, base 
ecracneg(E,P)           elliptic curve over the rational numbers, actual 
			curve, negative point 
ecracsum(E,P,Q)         elliptic curve over the rational numbers, actual 
			curve, sum of points 
ecractoecimin(E)        elliptic curve over rational numbers, actual curve 
			to global minimal model ( Laska's algorithm ) 
ecractorgr(E)           elliptic curve over rational numbers, actual curve, 
			torsion group 
ecracweilhe(E,P)        elliptic curve over the rational numbers, Weil 
			height 
ecrbtco(LC,BT)          elliptic curve over rational numbers, birational 
			transformation of coefficients 
ecrbtconc(BT1,BT2)      elliptic curve over rational numbers, birational 
			transformation, concatenation of transformations 
ecrbtinv(BT)            elliptic curve over rational numbers, birational 
			transformation, inverse transformation 
ecrbtlistp(LP,BT,modus) elliptic curve over rational numbers, birational 
			transformation of list of points 
ecrbtp(P,BT)            elliptic curve over rational numbers, birational 
			transformation of point 
ecrclser(E,A,n)         elliptic curve over the rationals, coefficients of 
			L- series 
ecrcond(E)              elliptic curve over rational numbers, conductor 
ecrcperiod(E)           elliptic curve over the rational numbers, complex 
			period 
ecrexptor(E)            elliptic curve over rational numbers, exponent of 
			torsion group 
ecrfcond(E)             elliptic curve over rational numbers, factorization 
			of conductor 
ecrfdenjinv(E)          elliptic curve over the rationals, factorization of 
			the denominator of the j-invariant 
ecrfelser(E,A,z,result) elliptic curve over rational numbers, Fourier 
			expansion of the L-series 
ecrinit(a1r,a2r,a3r,a4r,a6r) elliptic curve over the rational numbers 
			initialization 
ecrjinv(E)              elliptic curve over rational numbers, j-invariant 
ecrlser(E)              elliptic curve over rational numbers, L-series 
ecrlserfd(E)            elliptic curve over rational numbers, L-series, 
			first derivative 
ecrlserfds(E,A,result)  elliptic curve over the rationals, L-series, first 
			derivative, special version 
ecrlserhd(E,r)          elliptic curve over rational numbers, L-series, 
			higher derivative 
ecrlserhdlc(E,A,s,result) elliptic curve over the rationals, L-series, 
			higher derivative, large conductor 
ecrlserhdsc(E,A,r,result) elliptic curve over rational numbers, L-series, 
			higher derivative, small conductor 
ecrlserrkd(E)           elliptic curve over the rationals, L-series, 
			'rank'-th derivative 
ecrlsers(E,A,result)    elliptic curve over the rationals, L-series, 
			special version 
ecrmaninalg(E)          elliptic curve over rational numbers, Manin 
			algorithm 
ecrordtor(E)            elliptic curve over rational numbers, order of 
			torsion group 
ecrordtsg(E)            elliptic curve over the rational numbers, order of 
			Tate- Shafarevic group 
ecrpcomp(P1,P2)         elliptic curve over rational numbers, point 
			comparison 
ecrpnorm(P)             elliptic curve over rational numbers, point 
			normalization 
ecrprodcp(E)            elliptic curve over the rationals, product over all 
			c_p- values 
ecrptoproj(P)           elliptic curve over rational numbers, point to 
			projective representation 
ecrrank(E)              elliptic curve over the rationals, rank 
ecrregulator(E)         elliptic curve over the rational numbers, regulator 
ecrrl(E)                elliptic curve over rational numbers reduction list 
ecrrperiod(E)           elliptic curve over the rational numbers, real 
			period 
ecrrt(E,p)              elliptic curve over rational numbers reduction type 
ecrsign(E)              elliptic curve over rational numbers, sign of the 
			functional equation 
ecrsigns(E,A,C)         elliptic curve over the rationals, sign of the 
			functional equation, special version 
ecrsnfrroots(a,b)       elliptic curve over rational numbers, short normal 
			form, real roots of the right side 
ecrstrtor(E)            elliptic curve over rational numbers, structure of 
			torsion group 
ecrtavalb(a1,a2,a3,a4,a6) elliptic curve over rational numbers, Tate's 
			values b2, b4, b6, b8 
ecrtavalc(a1,a2,a3,a4,a6) elliptic curve over the rationals Tate's values 
			c4, c6 
eigenvalues             and irreducible factors of the characteristic 
			polynomial magfsevifcp(p,AL,M,pL) matrix over 
			Galois-field with single characteristic 
eigenvalues             and irreducible factors of the characteristic 
			polynomial maievifcp(M,pL) matrix of integers 
eigenvalues             and irreducible factors of the characteristic 
			polynomial mamievifcp(p,M,pL) matrix of modular 
			integers 
eigenvalues             and irreducible factors of the characteristic 
			polynomial mamsevifcp(p,M,pL) matrix of modular 
			singles 
eigenvalues             and irreducible factors of the characteristic 
			polynomial marevifcp(M,*pL) matrix of rationals 
eigenvalues             maiev(M) (MACRO) matrix of integers 
eigenvalues             mamiev(p,M) (MACRO) matrix of modular integers 
eigenvalues             mamsev(p,M) (MACRO) matrix of modular singles 
eigenvalues             marev(M) (MACRO) matrix of rationals 
elcfds(N,b,e)           elliptic curve fast divisor search 
elcpds(N,a,z)           elliptic curve pure divisor search 
elcpdssum(N,x1,y1,x2,y2,px3,py3,a) elliptic curve prime divisor search sum 
element                 ? isgf2el(G,a) (MACRO) is Galois-field with 
			characteristic 2 
element                 ? isgfsel(p,AL,a) is Galois-field with single 
			characteristic 
element                 ? islelt(L,a) is list 
element                 comparison qnfelcomp(D,A,B) quadratic number field 
element                 constructive delete lecdel(L,n) list 
element                 constructive insert lecins(L,k,a) list 
element                 delete ledel(pL,n) list 
element                 difference nfdif(F,a,b) number field 
element                 difference pfdif(p,a,b) p-adic field 
element                 difference qnfdif(D,a,b) (MACRO) quadratic number 
			field 
element                 evaluation first variable special version 
			(rekursiv) pigf2evalfvs(r,G,P) polynomial over 
			integers Galois-field with characteristic 2 
element                 evaluation first variable special version 
			(rekursiv) pigfsevalfvs(r,p,AL,P) polynomial over 
			integers Galois-field with single characteristic 
element                 evaluation first variable special version 
			mapigfsevfvs(r,p,AL,M) matrix over polynomials over 
			integers Galois-field with single characteristic 
element                 evaluation first variable special version 
			mapinfevlfvs(r,F,M) matrix of polynomials over 
			integers number field 
element                 evaluation first variable special version 
			maprnfevlfvs(r,F,M) matrix of polynomials over 
			rationals number field 
element                 evaluation first variable special version 
			pinfevalfvs(r,F,P) polynomial over integers number 
			field 
element                 evaluation first variable special version 
			prnfevalfvs(r,F,P) polynomial over rationals number 
			field 
element                 evaluation first variable special version 
			vecpigfsefvs(r,p,AL,V) vector over polynomials over 
			integers Galois-field with single characteristic 
element                 evaluation first variable special version 
			vpinfevalfvs(r,F,V) vector of polynomials over 
			integers number field 
element                 evaluation first variable special version 
			vprnfevalfvs(r,F,V) vector of polynomials over 
			rationals number field 
element                 evaluation special upinfeevals(F,P,a) univariate 
			polynomial over the integers number field 
element                 evaluation upinfeval(P,F,a) univariate polynomial 
			over integers number field 
element                 evaluation uprnfeval(P,F,a) univariate polynomial 
			over rationals number field 
element                 exponentiation nfexp(F,a,n) number field 
element                 exponentiation pfexp(p,a,n) p-adic field 
element                 exponentiation qnfexp(D,a,e) quadratic number field 
element                 exponentiation special nfeexpspec(F,a,e,M) number 
			field 
element                 factor exponent list fputqnffel(D,L,pf) file put 
			quadratic number field 
element                 factor exponent list putqnffel(D,L) (MACRO) put 
			quadratic number field 
element                 fgetgf2el(G,V,pf) file get Galois-field with 
			characteristic 2 
element                 fgetgfsel(p,AL,V,pf) file get Galois-field with 
			single characteristic 
element                 fgetnfel(F,V,pf) file get number field 
element                 fgetpfel(p,pf) file get p-adic field 
element                 fgetqnfel(D,pf) file get quadratic number field 
element                 fgetspfel(p,pf) file get special p-adic field 
element                 fputgf2el(G,a,V,pf) file put Galois-field with 
			characteristic 2 
element                 fputgfsel(p,AL,a,V,pf) file put Galois-field with 
			single characteristic 
element                 fputnfel(F,a,V,pf) file put number field 
element                 fputonfel(F,a,V,pf) file put original number field 
element                 fputpfel(p,a,pf) file put p-adic field 
element                 fputqnfel(D,a,pf) file put quadratic number field 
element                 fputspfel(p,a,pf) file put special p-adic field 
element                 getgf2el(G,V) (MACRO) get Galois-field with 
			characteristic 2 
element                 getgfsel(p,AL,V) (MACRO) get Galois-field with 
			single characteristic 
element                 getnfel(F,V) (MACRO) get number field 
element                 getpfel(p) (MACRO) get p-adic field 
element                 getqnfel(D) (MACRO) get quadratic number field 
element                 getspfel(p) (MACRO) get special p-adic field 
element                 gf2eltogfsel(G,a) (MACRO) Galois-field with 
			characteristic 2 element to Galois-field with 
			single characteristic 
element                 gfseltogf2el(G,a) Galois-field with single 
			characteristic element to Galois-field with 
			characteristic 2 
element                 insert leins(L,k,a) list 
element                 insert, 2nd position leins2(a,L) list 
element                 integer product nfeliprod(F,a,i) number field 
element                 integer product pfeliprod(p,a,i) p-adic field 
element                 integer? isqnfint(D,a) (MACRO) is quadratic number 
			field 
element                 integral element? isqnfiel(D,a) is quadratic number 
			field 
element                 inverse element qnfinv(D,a) quadratic number field 
element                 inverse pfinv(p,a) p-adic field 
element                 itonf(A) (MACRO) integer to number field 
element                 itopfel(p,d,A) integer to p-adic field 
element                 itoqnf(D,a) (MACRO) integer to quadratic number 
			field 
element                 lelt(L,k) list 
element                 maselel(M,m,n) (MACRO) matrix select 
element                 masetel(M,m,n,el) (MACRO) matrix set 
element                 minimal polynomial modulo p-power 
			infeminpmpp(F,a,p,e,Q) integral number field 
element                 minimal polynomial modulo p-power with respect to 
			integer primes infempmppip(F,a,p,e,Q) integral 
			number field 
element                 minimal representation qnfminrep(D,a) quadratic 
			number field 
element                 modulo integer nfelmodi(F,a,M) number field 
element                 negation nfneg(F,a) number field 
element                 negation pfneg(p,a) p-adic field 
element                 negation qnfneg(D,a,b) quadratic number field 
element                 norm nfnorm(F,a) number field 
element                 normalized representation nfelnormal(L) number 
			field 
element                 of an elliptic curve over Galois-field with 
			characteristic 2 ? iselecgf2(G,a1,a2,a3,a4,a6,P) is 
element                 of an elliptic curve over modular primes ? 
			iselecmp(p,a1,a2,a3,a4,a6,P) is 
element                 of an elliptic curve over modular primes, short 
			normal form ? iselecmpsnf(p,a,b,P) is 
element                 of an elliptic curve over number field ? 
			iselecnf(F,a1,a2,a3,a4,a6,P) is 
element                 of an elliptic curve over number field, short 
			normal form ? iselecnfsnf(F,a,b,P) is 
element                 of an ideal class qffmsiselic(m,D,L,Q,P) quadratic 
			function field over modular singles is 
element                 of the polynomial order of a univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the extensions 
			of the P-adic valuation of an 
element                 of the polynomial order of an univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, transcendence degree 1 
			nepousppmsp1(p,F,a) norm of an 
element                 of the polynomial ring of an univariate separable 
			polynomial over the integers normelpruspi(P,a) norm 
			of an 
element                 of the polynomial ring of an univariate separable 
			polynomial over the integers 
			vepvelpruspi(F,a,p,k,v) values of the extensions of 
			the p-adic valuation of an 
element                 one ? isgfsone(p,AL,a) is Galois-field with single 
			characteristic 
element                 one isnfone(F,A) is number field 
element                 one? isqnfone(D,a) (MACRO) is quadratic number 
			field 
element                 p-primality test and factorization of the defining 
			polynomial or the minimal polynomial 
			infepptfact(F,p,Q,ppot,a0,z) integral number field 
element                 p-primality test and factorization of the defining 
			polynomial or the minimal polynomial with respect 
			to integer primes infepptfip(F,p,Q,ppot,a0,z) 
			integral number field 
element                 p-star valuation infepstarval(p,A) integral number 
			field 
element                 p-star valuation with respect to integer primes 
			infepstarvip(P,A) integral number field 
element                 permutations generator lepermg(L) list 
element                 power of prime ideal homomorphism zero? 
			isqnfppihom0(D,P,k,pi,z,a) is quadratic number 
			field 
element                 prime ideal factorization qnfpifact(D,a) quadratic 
			number field 
element                 prime ideal factorization, special version 
			qnfielpifacts(D,a,L) quadratic number field 
			integral 
element                 prime ideal order qnfpiord(D,P,pi,z,a) quadratic 
			number field 
element                 prime power product pfpprod(p,a,i) p-adic field 
element                 product (rekursiv) pgf2gf2prod(r,G,P,a) polynomial 
			over Galois-field with characteristic 2, 
			Galois-field with characteristic 2 
element                 product (rekursiv) pgfsgfsprod(r,p,AL,P,a) 
			polynomial over Galois-field with single 
			characteristic, Galois-field with single 
			characteristic 
element                 product (rekursiv) pnfnfprod(r,F,P,a) polynomial 
			over number field, number field 
element                 product dipgfsgfprod(r,p,AL,P,a) distributive 
			polynomial over Galois-field with single 
			characteristic, Galois-field with single 
			characteristic 
element                 product dipnfnfprod(r,F,P,A) distributive 
			polynomial over number field, number field 
element                 product nfprod(F,a,b) number field 
element                 product pfprod(p,a,b) p-adic field 
element                 product ppfpfprod(r,p,P,b) polynomial over p-adic 
			field p-adic field 
element                 product qnfprod(D,a,b) quadratic number field 
element                 product special nfeprodspec(F,a,b,M) number field 
element                 product udppfpfprod(p,P,a) univariate dense 
			polynomial over p-adic field p-adic field 
element                 putgf2el(G,a,V) (MACRO) put Galois-field with 
			characteristic 2 
element                 putgfsel(p,AL,a,V) (MACRO) put Galois-field with 
			single characteristic 
element                 putnfel(F,a,V) (MACRO) put number field 
element                 putonfel(F,a,V) (MACRO) put original number field 
element                 putpfel(p,a) (MACRO) put p-adic field 
element                 putqnfel(D,a) (MACRO) put quadratic number field 
element                 putspfel(p,a) (MACRO) put special p-adic field 
element                 qnfconj(D,a) quadratic number field conjugate 
element                 qnfinv(D,a) quadratic number field element inverse 
element                 qnfnorm(D,a) quadratic number field norm of an 
element                 qnftrace(D,a) quadratic number field trace of an 
element                 quotient (rekursiv) pgfsgfsquot(r,p,AL,P,a) 
			polynomial over Galois-field with single 
			characteristic, Galois-field with single 
			characteristic 
element                 quotient (rekursiv) pnfnfquot(r,F,P,a) polynomial 
			over number field, number field 
element                 quotient qnfquot(D,a,b) (MACRO) quadratic number 
			field 
element                 randomize gf2elrand(G) Galois-field with 
			characteristic 2 
element                 randomize gfselrand(p,AL) Galois-field with single 
			characteristic, 
element                 rational isqnfrat(D,a) (MACRO) is quadratic number 
			field 
element                 rational number product nfelrprod(F,a,R) number 
			field 
element                 rational number product pfelrprod(p,a,R) p-adic 
			field 
element                 regulation with respect to integer primes 
			ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field 
element                 regulation, version1 
			ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field 
element                 regulation, version2 
			ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field 
element                 rotation lerot(L,k,l) list 
element                 rtonf(R) rational number to number field 
element                 rtopfel(p,d,R) rational to p-adic field 
element                 rtoqnf(D,A) (MACRO) rational number to quadratic 
			number field 
element                 set leset(L,k,a) list 
element                 special minimal polynomial, Collins algorithm, 
			version1 nfespecmpc1(F,a) number field 
element                 special minimal polynomial, Collins algorithm, 
			version2 nfespecmpc2(F,a) number field 
element                 square qnfsquare(D,a) quadratic number field 
element                 sum nfsum(F,a,b) number field 
element                 sum pfsum(p,a,b) p-adic field 
element                 sum qnfsum(D,a,b) quadratic number field 
element                 test modielemtest(B,a) module over the integers 
element                 test modprmsp1elt(B,p,a) module over polynomial 
			ring over modular single primes, transcendence 
			degree 1, 
element                 to Galois-field with characteristic 2 element 
			gfseltogf2el(G,a) Galois-field with single 
			characteristic 
element                 to Galois-field with single characteristic element 
			gf2eltogfsel(G,a) (MACRO) Galois-field with 
			characteristic 2 
element                 to matrix line nfeltomaln(n,a) number field 
element                 to univariate dense polynomial over modular 2 
			gf2eltoudpm2(G,a) Galois-field with characteristic 
			2 
element                 to univariate dense polynomial over rationals 
			nfeltoudpr(a) number field 
element                 trace nftrace(F,a) number field 
element                 udpm2togf2el(G,P) univariate dense polynomial over 
			modular 2 to Galois-field with characteristic 2 
element                 udprtonfel(P) univariate dense polynomial over 
			rationals to number field 
element                 uprtonfel(F,P) univariate polynomial over rationals 
			to number field 
element,                core algorithm ippnfecoreal(F,p,Q,mp) integral 
			p-primary number field 
element,                core algorithm with respect to integer primes 
			ippnfecalip(F,P,Q,mp) integral P-primary number 
			field 
element,                difference iqnfdif(D,a,b) (MACRO) integer, 
			quadratic number field 
element,                difference rqnfdif(D,a,b) (MACRO) rational number, 
			quadratic number field 
element,                increasing the denominator of the p-star value 
			ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field 
element,                increasing the denominator of the p-star value with 
			respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field 
element,                integer, difference qnfidif(D,a,b) (MACRO) 
			quadratic number field 
element,                integer, product qnfiprod(D,a,b) quadratic number 
			field 
element,                integer, quotient qnfiquot(D,a,b) quadratic number 
			field 
element,                integer, sum qnfisum(D,a,b) quadratic number field 
element,                prime ideal order qnfielpiord(D,P,pi,z,a) quadratic 
			number field, integral 
element,                quotient iqnfquot(D,a,b) integer, quadratic number 
			field 
element,                quotient rqnfquot(D,a,b) rational number, quadratic 
			number field 
element,                rational number, difference qnfrdif(D,a,b) (MACRO) 
			quadratic number field 
element,                rational number, product qnfrprod(D,a,b) quadratic 
			number field 
element,                rational number, quotient qnfrquot(D,a,b) (MACRO) 
			quadratic number field 
element,                rational number, sum qnfrsum(D,a,b) quadratic 
			number field 
element,                real case, qffmspidgenr(m,D,Q,P,G,pB) quadratic 
			function field over modular singles, principal 
			ideal generating 
element,                sparse representation ? isnfels(F,a) is number 
			field 
element,                sparse representation fgetnfels(F,V,pf) file get 
			number field 
element,                sparse representation fputnfels(F,a,V,pf) file put 
			number field 
element,                sparse representation getnfels(F,V) (MACRO) get 
			number field 
element,                sparse representation itonfs(A) integer to number 
			field 
element,                sparse representation putnfels(F,a,V) (MACRO) put 
			number field 
element,                sparse representation rtonfs(R) rational number to 
			number field 
element,                sparse representation, evaluation upinfseval(P,F,a) 
			univariate polynomial over integers number field 
element,                sparse representation, evaluation uprnfseval(P,F,a) 
			univariate polynomial over rationals number field 
element?                isnfel(F,a) is number field 
element?                ispfel(p,a) is p-adic field 
element?                isqnfiel(D,a) is quadratic number field element 
			integral 
elementary              divisor form and cofactors maiedfcf(M,pA,pB) matrix 
			of integers 
elementary              divisor form and cofactors maupmipedfcf(p,M,pA,pB) 
			matrix of univariate polynomials over modular 
			integer primes 
elementary              divisor form and cofactors maupmspedfcf(p,M,pA,pB) 
			matrix of univariate polynomials over modular 
			single primes 
elementary              divisor form and cofactors maupredfcf(M,pA,pB) 
			matrix of univariate polynomials over rationals 
elements                ? islistgf2(G,L) is list of Galois-field with 
			characteristic 2 
elements                ? islistgfs(p,AL,L) is list of Galois-field with 
			single characteristic 
elements                ? ismagfs(p,AL,M) (MACRO) is matrix of Galois-field 
			with single characteristic 
elements                ? ismanf(F,M) (MACRO) is matrix of number field 
elements                ? isvecgfs(p,AL,A) (MACRO) is vector of 
			Galois-field with single characteristic 
elements                ? isvecnf(F,V) (MACRO) is vector of number field 
elements                characteristic polynomial magfschpol(p,AL,M) 
			(MACRO) matrix of Galois-field with single 
			characteristic 
elements                characteristic polynomial manfchpol(F,M) (MACRO) 
			matrix of number field 
elements                construction 1 magfscons1(p,AL,n) (MACRO) matrix of 
			Galois-field with single characteristic 
elements                construction 1 manfcons1(F,n) (MACRO) matrix of 
			number field 
elements                determinant magfsdet(p,AL,M) matrix of Galois-field 
			with single characteristic 
elements                determinant manfdet(F,M) matrix of number field 
elements                difference magfsdif(p,AL,M,N) (MACRO) matrix of 
			Galois-field with single characteristic 
elements                difference manfdif(F,M,N) (MACRO) matrix of number 
			field 
elements                difference vecgfsdif(p,AL,U,V) (MACRO) vector of 
			Galois-field with single characteristic 
elements                difference vecnfdif(F,U,V) (MACRO) vector of number 
			field 
elements                exponentiation magfsexp(p,AL,M,n) matrix of 
			Galois-field with single characteristic 
elements                exponentiation manfexp(F,M,n) matrix of number 
			field 
elements                fgetmagfs(p,AL,V,pf) (MACRO) file get matrix of 
			Galois-field with single characteristic 
elements                fgetmanf(F,VL,pf) (MACRO) file get matrix of number 
			field 
elements                fgetvecgfs(p,AL,VL,pf) (MACRO) file get vector of 
			Galois-field with single characteristic 
elements                fgetvecnf(F,VL,pf) (MACRO) file get vector of 
			number field 
elements                fputmagfs(p,AL,M,V,pf) (MACRO) file put matrix of 
			Galois-field with single characteristic 
elements                fputmanf(F,M,VL,pf) (MACRO) file put matrix of 
			number field 
elements                fputvecgfs(p,AL,V,VL,pf) (MACRO) file put vector of 
			Galois-field with single characteristic 
elements                fputvecnf(F,V,VL,pf) (MACRO) file put vector of 
			number field 
elements                getmagfs(p,AL,V) (MACRO) get matrix of Galois-field 
			with single characteristic 
elements                getmanf(F,VL) (MACRO) get matrix of number field 
elements                getvecgfs(p,AL,VL) (MACRO) get vector of 
			Galois-field with single characteristic 
elements                getvecnf(F,VL) (MACRO) get vector of number field 
elements                inverse magfsinv(p,AL,M) matrix of Galois-field 
			with single characteristic 
elements                inverse manfinv(F,M) matrix of number field 
elements                ismaeqel(M,el) is matrix of equal 
elements                linear combination vecgfslc(p,AL,s1,s2,L1,L2) 
			vector of Galois-field with single characteristic 
elements                linear combination vecnflc(F,s1,s2,L1,L2) vector of 
			number field 
elements                maitomanf(M) matrix of integers to matrix of number 
			field 
elements                martomanf(M) matrix of rationals to matrix of 
			number field 
elements                maudprtomnf(M) matrix of univariate dense 
			polynomials over rationals to matrix of number 
			field 
elements                negation magfsneg(p,AL,M) (MACRO) matrix of 
			Galois-field with single characteristic 
elements                negation manfneg(F,M) (MACRO) matrix of number 
			field 
elements                negation vecgfsneg(p,AL,V) (MACRO) vector of 
			Galois-field with single characteristic 
elements                negation vecnfneg(F,V) (MACRO) vector of number 
			field 
elements                null space basis manfnsb(F,M) matrix of number 
			field 
elements                product magfsprod(p,AL,M,N) (MACRO) matrix of 
			Galois-field with single characteristic 
elements                product manfprod(F,M,N) (MACRO) matrix of number 
			field 
elements                putmagfs(p,AL,M,V) (MACRO) put matrix of 
			Galois-field with single characteristic 
elements                putmanf(F,M,VL) (MACRO) put matrix of number field 
elements                putvecgfs(p,AL,V,VL) (MACRO) put vector of 
			Galois-field with single characteristic 
elements                putvecnf(F,V,VL) (MACRO) put vector of number field 
elements                rank magfsrk(p,AL,M) matrix of Galois-field with 
			single characteristic 
elements                rank manfrk(F,M) matrix of number field 
elements                scalar multiplication magfssmul(p,AL,M,el) matrix 
			of Galois-field with single characteristic 
elements                scalar multiplication manfsmul(F,M,el) matrix of 
			number field 
elements                scalar multiplication vecgfssmul(p,AL,V,el) vector 
			of Galois-field with single characteristic 
elements                scalar multiplication vecnfsmul(F,V,el) vector of 
			number field 
elements                scalar product vecgf2sprod(G,V,W) vector of 
			Galois-field with characteristic 2 
elements                scalar product vecgfssprod(p,AL,V,W) vector of 
			Galois-field with single characteristic 
elements                scalar product vecnfsprod(F,V,W) vector of number 
			field 
elements                solution of a system of linear equations 
			magfsssle(p,AL,A,b,pX,pN) matrix of Galois-field 
			with single characteristic 
elements                solution of a system of linear equations 
			manfssle(F,A,b,pX,pN) matrix of number field 
elements                sum magfssum(p,AL,M,N) (MACRO) matrix of 
			Galois-field with single characteristic 
elements                sum manfsum(F,M,N) (MACRO) matrix of number field 
elements                sum vecgfssum(p,AL,U,V) (MACRO) vector of 
			Galois-field with single characteristic 
elements                sum vecnfsum(F,U,V) (MACRO) vector of number field 
elements                to matrix of univariate dense polynomials over 
			rationals manftomudpr(F,M) matrix of number field 
elements                to vector of univariate dense polynomials over 
			rationals vnftovudpr(F,V) vector of number field 
elements                vecitovecnf(V) vector of integers to vector of 
			number field 
elements                vecrtovecnf(V) vector of rationals to vector of 
			number field 
elements                vector multiplication magfsvecmul(p,AL,A,x) (MACRO) 
			matrix of Galois-field with single characteristic 
elements                vector multiplication manfvecmul(F,A,x) (MACRO) 
			matrix of number field 
elements                vudprtovnf(V) vector of univariate dense 
			polynomials over rationals to vector of number 
			field 
elements,               null space basis magfsnsb(p,AL,M) matrix of 
			Galois-field with single characteristic 
elements,               sparse representation ? ismanfs(F,M) (MACRO) is 
			matrix of number field 
elements,               sparse representation ? isvecnfs(F,V) (MACRO) is 
			vector of number field 
elements,               sparse representation fgetmanfs(F,VL,pf) (MACRO) 
			file get matrix of number field 
elements,               sparse representation fgetvecnfs(F,VL,pf) (MACRO) 
			file get vector of number field 
elements,               sparse representation fputmanfs(F,M,VL,pf) (MACRO) 
			file put matrix of number field 
elements,               sparse representation fputvecnfs(F,V,VL,pf) (MACRO) 
			file put vector of number field 
elements,               sparse representation getmanfs(F,VL) (MACRO) get 
			matrix of number field 
elements,               sparse representation getvecnfs(F,VL) (MACRO) get 
			vector of number field 
elements,               sparse representation maitomanfs(M) matrix of 
			integers to matrix of number field 
elements,               sparse representation martomanfs(M) matrix of 
			rationals to matrix of number field 
elements,               sparse representation putmanfs(F,M,VL) (MACRO) put 
			matrix of number field 
elements,               sparse representation putvecnfs(F,V,VL) (MACRO) put 
			vector of number field 
elements,               sparse representation vecitovnfs(V) vector of 
			integers to vector of number field 
elements,               sparse representation vecrtovnfs(V) vector of 
			rationals to vector of number field 
elements,               sparse representation, construction 1 
			manfscons1(F,n) (MACRO) matrix of number field 
elements,               sparse representation, determinant manfsdet(F,M) 
			matrix of number field 
elements,               sparse representation, difference manfsdif(F,M,N) 
			(MACRO) matrix of number field 
elements,               sparse representation, difference vecnfsdif(F,U,V) 
			(MACRO) vector of number field 
elements,               sparse representation, exponentiation 
			manfsexp(F,M,n) matrix of number field 
elements,               sparse representation, inverse manfsinv(F,M) matrix 
			of number field 
elements,               sparse representation, linear combination 
			vecnfslc(F,s1,s2,L1,L2) vector of number field 
elements,               sparse representation, negation manfsneg(F,M) 
			(MACRO) matrix of number field 
elements,               sparse representation, negation vecnfsneg(F,V) 
			(MACRO) vector of number field 
elements,               sparse representation, null space basis 
			manfsnsb(F,M) matrix of number field 
elements,               sparse representation, product manfsprod(F,M,N) 
			(MACRO) matrix of number field 
elements,               sparse representation, rank manfsrk(F,M) matrix of 
			number field 
elements,               sparse representation, scalar multiplication 
			manfssmul(F,M,el) matrix of number field 
elements,               sparse representation, scalar multiplication 
			vecnfssmul(F,V,el) vector of number field 
elements,               sparse representation, scalar product 
			vecnfssprod(F,V,W) vector of number field 
elements,               sparse representation, solution of a system of 
			linear equations manfsssle(F,A,b,pX,pN) matrix of 
			number field 
elements,               sparse representation, sum manfssum(F,M,N) (MACRO) 
			matrix of number field 
elements,               sparse representation, sum vecnfssum(F,U,V) (MACRO) 
			vector of number field 
elements,               sparse representation, vector multiplication 
			manfsvecmul(F,A,x) (MACRO) matrix of number field 
elliptic                curve Galois-field with characteristic 2, 
			multiplication-map ecgf2mul(G,a1,a2,a3,a4,a6,k,P1) 
elliptic                curve fast divisor search elcfds(N,b,e) 
elliptic                curve find point iecfindp(p,a,b) integer 
elliptic                curve fputecr(E,pf) file put 
elliptic                curve j-invariant to equation iecjtoeq(p,j) integer 
elliptic                curve j-invariant to equation special version 
			iecjtoeqsv(p,j,pi) integer 
elliptic                curve of given number of points, j-invariant 
			iecgnpj(p,m,h1,h2,D) integer 
elliptic                curve over Galois field with characteristic 2, 
			combined Schoof- Shanks- algorithm 
			ecgf2cssa(G,a6,s,pl,ts) 
elliptic                curve over Galois field with characteristic 2, 
			number of points after field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) 
elliptic                curve over Galois-field with characteristic 2 ? 
			iselecgf2(G,a1,a2,a3,a4,a6,P) is element of an 
elliptic                curve over Galois-field with characteristic 2 equal 
			? isppecgf2eq(p,P1,P2) is projective point of an 
elliptic                curve over Galois-field with characteristic 2 point 
			at infinity ? isppecgf2pai(G,P) is projective point 
			of an 
elliptic                curve over Galois-field with characteristic 2, 
			Tate's values b2, b4, b6 
			ecgf2tavb6(G,a1,a2,a3,a4,a6) 
elliptic                curve over Galois-field with characteristic 2, 
			Tate's values b2, b4, b6, b8 
			ecgf2tavb8(G,a1,a2,a3,a4,a6) 
elliptic                curve over Galois-field with characteristic 2, 
			Tate's values c4, c6 ecgf2tavc6(G,a1,a2,a3,a4,a6) 
elliptic                curve over Galois-field with characteristic 2, 
			birational transformation of coefficients 
			ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) 
elliptic                curve over Galois-field with characteristic 2, 
			construction of division polynomials 
			ecgf2cdivp(G,a6,m) 
elliptic                curve over Galois-field with characteristic 2, 
			counting algorithm ecgf2npca(G,a6) 
elliptic                curve over Galois-field with characteristic 2, 
			discriminant ecgf2disc(G,a1,a2,a3,a4,a6) 
elliptic                curve over Galois-field with characteristic 2, find 
			point ecgf2fp(G,a1,a2,a3,a4,a6) 
elliptic                curve over Galois-field with characteristic 2, 
			finding a multiple of the order of a point with the 
			Pollard Lambda method 
			ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) 
elliptic                curve over Galois-field with characteristic 2, 
			j-invariant ecgf2jinv(G,a1,a2,a3,a4,a6) 
elliptic                curve over Galois-field with characteristic 2, line 
			through points ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) 
elliptic                curve over Galois-field with characteristic 2, 
			modified Shanks' algorithm, first part 
			ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) 
elliptic                curve over Galois-field with characteristic 2, 
			multiple of the order of a point to exact order of 
			the point ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) 
elliptic                curve over Galois-field with characteristic 2, 
			negative point ecgf2neg(G,a1,a2,a3,a4,a6,P) 
elliptic                curve over Galois-field with characteristic 2, 
			number of points modulo a power of 2 
			ecgf2npmp2(G,a6,c,L) 
elliptic                curve over Galois-field with characteristic 2, 
			number of points modulo a single prime determined 
			with the Schoof algorithm, version 1 
			ecgf2npmspv1(G,a6,p,L) 
elliptic                curve over Galois-field with characteristic 2, 
			number of points modulo a single prime determined 
			with the Schoof algorithm, version 2 
			ecgf2npmspv2(G,a6,p,L) 
elliptic                curve over Galois-field with characteristic 2, 
			number of points modulo an integer determined with 
			the Schoof algorithm ecgf2npmi(G,a6,S,v,pM) 
elliptic                curve over Galois-field with characteristic 2, 
			special form, multiplication-map, special version 
			ecgf2sfmuls(p,a6,x1,y1,n) 
elliptic                curve over Galois-field with characteristic 2, 
			special form, sum of points, special version 
			ecgf2sfsums(G,a6,x1,y1,x2,y2) 
elliptic                curve over Galois-field with characteristic 2, 
			standard representation of projective point 
			ecgf2srpp(G,P) 
elliptic                curve over Galois-field with characteristic 2, sum 
			of points ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) 
elliptic                curve over modular integer primes short normal form 
			number of points special version 
			ecmipsnfnpsv(p,a4,a6) 
elliptic                curve over modular primes ? 
			iselecmp(p,a1,a2,a3,a4,a6,P) is element of an 
elliptic                curve over modular primes Tate's values b2, b4, b6 
			ecmptavb6(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes Tate's values b2, b4, b6, 
			b8 ecmptavb8(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes Tate's values c4, c6 
			ecmptavc6(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes equal ? 
			isppecmpeq(p,P1,P2) is projective point of an 
elliptic                curve over modular primes multiplication-map 
			ecmpmul(p,a1,a2,a3,a4,a6,n,P1) 
elliptic                curve over modular primes negative point 
			ecmpneg(p,a1,a2,a3,a4,a6,P) 
elliptic                curve over modular primes point at infinity ? 
			isppecmppai(p,P) is projective point of an 
elliptic                curve over modular primes to short normal form 
			ecmptosnf(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes, birational 
			transformation of coefficients 
			ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) 
elliptic                curve over modular primes, discriminant 
			ecmpdisc(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes, find point 
			ecmpfp(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes, j-invariant 
			ecmpjinv(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular primes, line through points 
			ecmplp(p,a1,a2,a3,a4,a6,P1,P2) 
elliptic                curve over modular primes, short normal form ? 
			iselecmpsnf(p,a,b,P) is element of an 
elliptic                curve over modular primes, short normal form, 
			combined Schoof- Shanks- algorithm 
			ecmpsnfcssa(p,a4,a6,s,pl,ts) 
elliptic                curve over modular primes, short normal form, 
			construction of division polynomials 
			ecmpsnfcdivp(P,a4,a6,n) 
elliptic                curve over modular primes, short normal form, 
			discriminant ecmpsnfdisc(p,a4,a6) 
elliptic                curve over modular primes, short normal form, find 
			point ecmpsnffp(p,a4,a6) 
elliptic                curve over modular primes, short normal form, 
			finding a multiple of the order of a point with the 
			Pollard Lambda method ecmpsnffmopl(p,a4,a6,P,L,N) 
elliptic                curve over modular primes, short normal form, 
			finding a multiple of the order of a point with the 
			Pollard Rho method ecmpsnffmopr(p,a4,a6,P,k) 
elliptic                curve over modular primes, short normal form, 
			j-invariant ecmpsnfjinv(p,a4,a6) 
elliptic                curve over modular primes, short normal form, line 
			through points ecmpsnflp(p,a4,a6,P1,P2) 
elliptic                curve over modular primes, short normal form, 
			modified Shanks' algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) 
elliptic                curve over modular primes, short normal form, 
			multiple of the order of a point to exact order of 
			the point ecmpsnfmopto(p,a4,a6,P,mul) 
elliptic                curve over modular primes, short normal form, 
			multiplication-map ecmpsnfmul(p,a4,a6,n,P1) 
elliptic                curve over modular primes, short normal form, 
			multiplication-map, special version 
			ecmpsnfmuls(p,a4,a6,x1,y1,n) 
elliptic                curve over modular primes, short normal form, 
			negative point ecmpsnfneg(p,a4,a6,P) 
elliptic                curve over modular primes, short normal form, 
			number of points modulo 2 ecmpsnfnpm2(P,a4,a6) 
elliptic                curve over modular primes, short normal form, 
			number of points modulo a single prime determined 
			with the Schoof algorithm ecmpsnfnpmsp(P,a4,a6,p,L) 
elliptic                curve over modular primes, short normal form, 
			number of points modulo an integer determined with 
			the Schoof algorithm ecmpsnfnpmi(P,a4,a6,S,pM) 
elliptic                curve over modular primes, short normal form, sum 
			of points ecmpsnfsum(p,a4,a6,P1,P2) 
elliptic                curve over modular primes, short normal form, sum 
			of points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) 
elliptic                curve over modular primes, standard representation 
			of projective point ecmpsrpp(p,P) 
elliptic                curve over modular primes, sum of points 
			ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) 
elliptic                curve over modular single prime, number of points 
			ecmspnp(p,a1,a2,a3,a4,a6) 
elliptic                curve over modular single primes, short normal 
			form, Shanks' algorithm ecmspsnfsha(p,a4,a6) 
			(MACRO) 
elliptic                curve over modular single primes, short normal 
			form, number of points ecmspsnfnp(p,a4,a6) 
elliptic                curve over number field ? 
			iselecnf(F,a1,a2,a3,a4,a6,P) is element of an 
elliptic                curve over number field Tate's values b2, b4, b6 
			ecnftavb6(F,a1,a2,a3,a4,a6) 
elliptic                curve over number field Tate's values b2, b4, b6, 
			b8 ecnftavb8(F,a1,a2,a3,a4,a6) 
elliptic                curve over number field Tate's values c4, c6 
			ecnftavc6(F,a1,a2,a3,a4,a6) 
elliptic                curve over number field birational transformation 
			of coefficients ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) 
elliptic                curve over number field discriminant 
			ecnfdisc(F,a1,a2,a3,a4,a6) 
elliptic                curve over number field equal? isppecnfeq(F,P1,P2) 
			is projective point of an 
elliptic                curve over number field j-invariant 
			ecnfjinv(F,a1,a2,a3,a4,a6) 
elliptic                curve over number field line through points 
			ecnflp(F,a1,a2,a3,a4,a6,P1,P2) 
elliptic                curve over number field multiplication-map 
			ecnfmul(F,a1,a2,a3,a4,a6,n,P1) 
elliptic                curve over number field negative point 
			ecnfneg(F,a1,a2,a3,a4,a6,P) 
elliptic                curve over number field point at infinity ? 
			isppecnfpai(P) is projective point of an 
elliptic                curve over number field short normal form line 
			through points ecnfsnflp(F,a,b,P1,P2) 
elliptic                curve over number field short normal form 
			multiplication-map ecnfsnfmul(F,a,b,n,P1) 
elliptic                curve over number field short normal form negative 
			point ecnfsnfneg(F,a,b,P) 
elliptic                curve over number field short normal form sum of 
			points ecnfsnfsum(F,a,b,P1,P2) 
elliptic                curve over number field standard representation of 
			projective point ecnfsrpp(F,P) 
elliptic                curve over number field sum of points 
			ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) 
elliptic                curve over number field to short normal form 
			ecnftosnf(F,a1,a2,a3,a4,a6) 
elliptic                curve over number field, short normal form ? 
			iselecnfsnf(F,a,b,P) is element of an 
elliptic                curve over number field, short normal form, 
			discriminant ecnfsnfdisc(F,a,b) 
elliptic                curve over number field, short normal form, 
			j-invariant ecnfsnfjinv(F,a,b) 
elliptic                curve over quadratic number field to elliptic curve 
			with integral coefficients ecqnftoeci(D,L) 
elliptic                curve over quadratic number field, Tate's algorithm 
			ecqnftatealg(D,LC,LTV,P,pi,z,n) 
elliptic                curve over quadratic number field, actual model, 
			Tate value b2 ecqnfacb2(E) 
elliptic                curve over quadratic number field, actual model, 
			Tate value b4 ecqnfacb4(E) 
elliptic                curve over quadratic number field, actual model, 
			Tate value b6 ecqnfacb6(E) 
elliptic                curve over quadratic number field, actual model, 
			Tate value b8 ecqnfacb8(E) 
elliptic                curve over quadratic number field, actual model, 
			Tate value c4 ecqnfacc4(E) 
elliptic                curve over quadratic number field, actual model, 
			Tate value c6 ecqnfacc6(E) 
elliptic                curve over quadratic number field, actual model, 
			discriminant ecqnfacdisc(E) 
elliptic                curve over quadratic number field, actual model, 
			factorization of the norm of the discriminant 
			ecqnfacfndisc(E) 
elliptic                curve over quadratic number field, actual model, 
			norm of the discriminant ecqnfacndisc(E) 
elliptic                curve over quadratic number field, actual model, 
			prime ideal factorization of the discriminant 
			ecqnfacpifdi(E) 
elliptic                curve over quadratic number field, conductor 
			ecqnfcond(E) 
elliptic                curve over quadratic number field, field 
			discriminant ecqnfflddisc(E) (MACRO) 
elliptic                curve over quadratic number field, field 
			discriminant modulo 4 ecqnfdmod4(E) (MACRO) 
elliptic                curve over quadratic number field, initialization 
			ecqnfinit(D,a1,a2,a3,a4,a6) 
elliptic                curve over quadratic number field, j-invariant 
			ecqnfjinv(E) 
elliptic                curve over rational numbers fgetecr(pf) file get 
elliptic                curve over rational numbers fgetecrp(pf) file get 
			point on 
elliptic                curve over rational numbers getecr() get 
elliptic                curve over rational numbers point getecrp() (MACRO) 
			get 
elliptic                curve over rational numbers putecr(E) (MACRO) put 
elliptic                curve over rational numbers reduction list ecrrl(E) 
elliptic                curve over rational numbers reduction type 
			ecrrt(E,p) 
elliptic                curve over rational numbers, Fourier expansion of 
			the L-series ecrfelser(E,A,z,result) 
elliptic                curve over rational numbers, L-series ecrlser(E) 
elliptic                curve over rational numbers, L-series, first 
			derivative ecrlserfd(E) 
elliptic                curve over rational numbers, L-series, higher 
			derivative ecrlserhd(E,r) 
elliptic                curve over rational numbers, L-series, higher 
			derivative, small conductor 
			ecrlserhdsc(E,A,r,result) 
elliptic                curve over rational numbers, Manin algorithm 
			ecrmaninalg(E) 
elliptic                curve over rational numbers, Tate's values b2, b4, 
			b6, b8 ecrtavalb(a1,a2,a3,a4,a6) 
elliptic                curve over rational numbers, actual curve 
			fputecrac(E,pf) file put 
elliptic                curve over rational numbers, actual curve 
			putecrac(E) (MACRO) put 
elliptic                curve over rational numbers, actual curve to global 
			minimal model ( Laska's algorithm ) 
			ecractoecimin(E) 
elliptic                curve over rational numbers, actual curve, a1 
			ecraca1(E) (MACRO) 
elliptic                curve over rational numbers, actual curve, a2 
			ecraca2(E) (MACRO) 
elliptic                curve over rational numbers, actual curve, a3 
			ecraca3(E) (MACRO) 
elliptic                curve over rational numbers, actual curve, a4 
			ecraca4(E) (MACRO) 
elliptic                curve over rational numbers, actual curve, a6 
			ecraca6(E) (MACRO) 
elliptic                curve over rational numbers, actual curve, b2 
			ecracb2(E) 
elliptic                curve over rational numbers, actual curve, b4 
			ecracb4(E) 
elliptic                curve over rational numbers, actual curve, b6 
			ecracb6(E) 
elliptic                curve over rational numbers, actual curve, b8 
			ecracb8(E) 
elliptic                curve over rational numbers, actual curve, 
			birational transformation to short normal form 
			ecracbtsnf(E) 
elliptic                curve over rational numbers, actual curve, c4 
			ecracc4(E) 
elliptic                curve over rational numbers, actual curve, c6 
			ecracc6(E) 
elliptic                curve over rational numbers, actual curve, 
			discriminant ecracdisc(E) 
elliptic                curve over rational numbers, actual curve, 
			factorization of discriminant ecracfdisc(E) 
elliptic                curve over rational numbers, actual curve, 
			generators of torsion group ecracgentor(E) 
elliptic                curve over rational numbers, actual curve, torsion 
			group ecractorgr(E) 
elliptic                curve over rational numbers, actual model 
			isponecrac(E,P) is point on 
elliptic                curve over rational numbers, birational 
			transformation of coefficients ecracbtco(E,BT) 
elliptic                curve over rational numbers, birational 
			transformation of coefficients ecrbtco(LC,BT) 
elliptic                curve over rational numbers, birational 
			transformation of list of points 
			ecrbtlistp(LP,BT,modus) 
elliptic                curve over rational numbers, birational 
			transformation of point ecrbtp(P,BT) 
elliptic                curve over rational numbers, birational 
			transformation, concatenation of transformations 
			ecrbtconc(BT1,BT2) 
elliptic                curve over rational numbers, birational 
			transformation, inverse transformation ecrbtinv(BT) 
elliptic                curve over rational numbers, conductor ecrcond(E) 
elliptic                curve over rational numbers, exponent of torsion 
			group ecrexptor(E) 
elliptic                curve over rational numbers, factorization of 
			conductor ecrfcond(E) 
elliptic                curve over rational numbers, j-invariant ecrjinv(E) 
elliptic                curve over rational numbers, list of points 
			putecrlistp(P,modus) (MACRO) put 
elliptic                curve over rational numbers, order of torsion group 
			ecrordtor(E) 
elliptic                curve over rational numbers, point comparison 
			ecrpcomp(P1,P2) 
elliptic                curve over rational numbers, point fputecrp(P,pf) 
			file put 
elliptic                curve over rational numbers, point normalization 
			ecrpnorm(P) 
elliptic                curve over rational numbers, point putecrp(P) 
			(MACRO) put 
elliptic                curve over rational numbers, point to projective 
			representation ecrptoproj(P) 
elliptic                curve over rational numbers, short normal form, 
			real roots of the right side ecrsnfrroots(a,b) 
elliptic                curve over rational numbers, sign of the functional 
			equation ecrsign(E) 
elliptic                curve over rational numbers, structure of torsion 
			group ecrstrtor(E) 
elliptic                curve over the rational numbers initialization 
			ecrinit(a1r,a2r,a3r,a4r,a6r) 
elliptic                curve over the rational numbers, Weil height 
			ecracweilhe(E,P) 
elliptic                curve over the rational numbers, actual curve, 
			Mordell-Weil-group, base ecracmwgbase(E) 
elliptic                curve over the rational numbers, actual curve, 
			multiplication-map ecracmul(E,P,n) 
elliptic                curve over the rational numbers, actual curve, 
			negative point ecracneg(E,P) 
elliptic                curve over the rational numbers, actual curve, sum 
			of points ecracsum(E,P,Q) 
elliptic                curve over the rational numbers, complex period 
			ecrcperiod(E) 
elliptic                curve over the rational numbers, invariants 
			fputecrinv(E,pf) file put 
elliptic                curve over the rational numbers, invariants 
			putecrinv(E) (MACRO) put 
elliptic                curve over the rational numbers, list of points 
			fputecrlistp(P,modus,pf) file put 
elliptic                curve over the rational numbers, minimal model, 
			double of point ecracdouble(E,P) 
elliptic                curve over the rational numbers, order of Tate- 
			Shafarevic group ecrordtsg(E) 
elliptic                curve over the rational numbers, real period 
			ecrrperiod(E) 
elliptic                curve over the rational numbers, regulator 
			ecrregulator(E) 
elliptic                curve over the rationals Tate's values c4, c6 
			ecrtavalc(a1,a2,a3,a4,a6) 
elliptic                curve over the rationals point at infinity ? 
			ispecrpai(P) (MACRO) is point of an 
elliptic                curve over the rationals, L-series, 'rank'-th 
			derivative ecrlserrkd(E) 
elliptic                curve over the rationals, L-series, first 
			derivative, special version ecrlserfds(E,A,result) 
elliptic                curve over the rationals, L-series, higher 
			derivative, large conductor 
			ecrlserhdlc(E,A,s,result) 
elliptic                curve over the rationals, L-series, special version 
			ecrlsers(E,A,result) 
elliptic                curve over the rationals, actual curve, birational 
			transformation to minimal model ecracbtmin(E) 
elliptic                curve over the rationals, coefficients of L- series 
			ecrclser(E,A,n) 
elliptic                curve over the rationals, factorization of the 
			denominator of the j-invariant ecrfdenjinv(E) 
elliptic                curve over the rationals, product over all c_p- 
			values ecrprodcp(E) 
elliptic                curve over the rationals, rank ecrrank(E) 
elliptic                curve over the rationals, sign of the functional 
			equation, special version ecrsigns(E,A,C) 
elliptic                curve point product iecpprod(p,E,P,a) integer 
elliptic                curve point sum iecpsum(p,P,Q,a) integer 
elliptic                curve primality test iecpt(n,m,lp,a,b,anz) integer 
elliptic                curve prime divisor search sum 
			elcpdssum(N,x1,y1,x2,y2,px3,py3,a) 
elliptic                curve pure divisor search elcpds(N,a,z) 
elliptic                curve with integer coefficients Tate's algorithm 
			ecitatealg(a1,a2,a3,a4,a6,p,n) 
elliptic                curve with integer coefficients, Tate's values b2, 
			b4, b6, b8 ecitavalb(a1,a2,a3,a4,a6) 
elliptic                curve with integer coefficients, actual curve, 
			difference of points ecracdif(E,P,Q) 
elliptic                curve with integer coefficients, minimal model 
			fputecimin(E,pf) file put 
elliptic                curve with integer coefficients, minimal model 
			isecimintorp(E,P) is torsion point on 
elliptic                curve with integer coefficients, minimal model 
			isineciminpl(E,P,h,PL) is in list of points on 
elliptic                curve with integer coefficients, minimal model 
			isponecimin(E,P) is point on 
elliptic                curve with integer coefficients, minimal model 
			putecimin(E) (MACRO) put 
elliptic                curve with integer coefficients, minimal model to 
			short normal form ecimintosnf(E) 
elliptic                curve with integer coefficients, minimal model, 
			Mordell-Weil-group, base eciminmwgbase(E) 
elliptic                curve with integer coefficients, minimal model, 
			Neron-Tate height eciminnetahe(E,P) 
elliptic                curve with integer coefficients, minimal model, 
			Neron-Tate pairing eciminnetapa(E,P,Q) 
elliptic                curve with integer coefficients, minimal model, 
			Tate's algorithm ecimintatealg(E,p,n) 
elliptic                curve with integer coefficients, minimal model, 
			Tate's values c4, c6 ecitavalc(a1,a2,a3,a4,a6) 
elliptic                curve with integer coefficients, minimal model, a1 
			ecimina1(E) 
elliptic                curve with integer coefficients, minimal model, a2 
			ecimina2(E) 
elliptic                curve with integer coefficients, minimal model, a3 
			ecimina3(E) 
elliptic                curve with integer coefficients, minimal model, a4 
			ecimina4(E) 
elliptic                curve with integer coefficients, minimal model, a6 
			ecimina6(E) 
elliptic                curve with integer coefficients, minimal model, b2 
			eciminb2(E) 
elliptic                curve with integer coefficients, minimal model, b4 
			eciminb4(E) 
elliptic                curve with integer coefficients, minimal model, b6 
			eciminb6(E) 
elliptic                curve with integer coefficients, minimal model, b8 
			eciminb8(E) 
elliptic                curve with integer coefficients, minimal model, bad 
			reduction type modulo prime eciminbrtmp(E,p,n) 
elliptic                curve with integer coefficients, minimal model, 
			birational transformation of coefficients 
			eciminbtco(E,BT) 
elliptic                curve with integer coefficients, minimal model, 
			birational transformation to actual ( rational ) 
			model eciminbtac(E) 
elliptic                curve with integer coefficients, minimal model, 
			birational transformation to short normal form 
			eciminbtsnf(E) 
elliptic                curve with integer coefficients, minimal model, c4 
			eciminc4(E) 
elliptic                curve with integer coefficients, minimal model, c6 
			eciminc6(E) 
elliptic                curve with integer coefficients, minimal model, 
			difference between Weil height and Neron-Tate 
			height ecimindwhnth(E) 
elliptic                curve with integer coefficients, minimal model, 
			difference of points ecimindif(E,P,Q) 
elliptic                curve with integer coefficients, minimal model, 
			difference of points ecisnfdif(E,P,Q) 
elliptic                curve with integer coefficients, minimal model, 
			discriminant ecimindisc(E) 
elliptic                curve with integer coefficients, minimal model, 
			division by 2 of a point ecimindivby2(E,P,h,PL,H) 
elliptic                curve with integer coefficients, minimal model, 
			division of a point by an integer ecimindiv(E,P,n) 
elliptic                curve with integer coefficients, minimal model, 
			division of a point by an integer, special version 
			ecimindivs(E,P,h,ug,PL,n) 
elliptic                curve with integer coefficients, minimal model, 
			double of a point ecimindouble(E,P) 
elliptic                curve with integer coefficients, minimal model, 
			factorization of discriminant eciminfdisc(E) 
elliptic                curve with integer coefficients, minimal model, 
			generators of torsion group ecimingentor(E) 
elliptic                curve with integer coefficients, minimal model, 
			local height at the archimedean absolute value 
			eciminlhaav(E,P) 
elliptic                curve with integer coefficients, minimal model, 
			local heights at all non archimedean absolute 
			values eciminlhnaav(E,P) 
elliptic                curve with integer coefficients, minimal model, 
			multiplication-map eciminmul(E,P,n) 
elliptic                curve with integer coefficients, minimal model, 
			multiplicative reduction type modulo prime 
			eciminmrtmp(E,p) 
elliptic                curve with integer coefficients, minimal model, 
			negative point eciminneg(E,P) 
elliptic                curve with integer coefficients, minimal model, 
			point comparison modulo torsion 
			eciminpcompmt(E,P1,P2) 
elliptic                curve with integer coefficients, minimal model, 
			point list union eciminplunion(E,L1,L2,modus) 
elliptic                curve with integer coefficients, minimal model, 
			point list, insert point eciminplinsp(P,h,PL) 
elliptic                curve with integer coefficients, minimal model, 
			reduction type eciminredtype(E) 
elliptic                curve with integer coefficients, minimal model, 
			regulator eciminreg(E,LP,n,modus) 
elliptic                curve with integer coefficients, minimal model, set 
			NTH_EPS eciminntheps(E,d) 
elliptic                curve with integer coefficients, minimal model, sum 
			of points eciminsum(E,P,Q) 
elliptic                curve with integer coefficients, minimal model, 
			torsion group ecimintorgr(E) 
elliptic                curve with integer coefficients, model in short 
			normal form isponecisnf(E,P) is point on 
elliptic                curve with integer coefficients, point 
			normalization ecipnorm(P) 
elliptic                curve with integer coefficients, short normal form 
			fputecisnf(E,*pf) file put 
elliptic                curve with integer coefficients, short normal form 
			putecisnf(E) (MACRO) put 
elliptic                curve with integer coefficients, short normal form, 
			Mordell-Weil-group, base ecisnfmwgbase(E) 
elliptic                curve with integer coefficients, short normal form, 
			a4 ecisnfa4(E) 
elliptic                curve with integer coefficients, short normal form, 
			a6 ecisnfa6(E) 
elliptic                curve with integer coefficients, short normal form, 
			b2 ecisnfb2(E) 
elliptic                curve with integer coefficients, short normal form, 
			b4 ecisnfb4(E) 
elliptic                curve with integer coefficients, short normal form, 
			b6 ecisnfb6(E) 
elliptic                curve with integer coefficients, short normal form, 
			b8 ecisnfb8(E) 
elliptic                curve with integer coefficients, short normal form, 
			birational transformation of coefficients 
			ecisnfbtco(E,BT) 
elliptic                curve with integer coefficients, short normal form, 
			birational transformation to actual ( rational ) 
			model ecisnfbtac(E) 
elliptic                curve with integer coefficients, short normal form, 
			birational transformation to minimal model 
			ecisnfbtmin(E) 
elliptic                curve with integer coefficients, short normal form, 
			c4 ecisnfc4(E) 
elliptic                curve with integer coefficients, short normal form, 
			c6 ecisnfc6(E) 
elliptic                curve with integer coefficients, short normal form, 
			difference between Weil height and Neron-Tate 
			height ecisnfdwhnth(E) 
elliptic                curve with integer coefficients, short normal form, 
			discriminant ecisnfdisc(E) 
elliptic                curve with integer coefficients, short normal form, 
			double of point ecisnfdouble(E,P) 
elliptic                curve with integer coefficients, short normal form, 
			elliptic logarithm of point ecisnfelogp(E,P,n) 
elliptic                curve with integer coefficients, short normal form, 
			factorization of discriminant ecisnffdisc(E) 
elliptic                curve with integer coefficients, short normal form, 
			generators of the torsion group ecisnfgentor(E) 
elliptic                curve with integer coefficients, short normal form, 
			multiplication-map ecisnfmul(E,P,n) 
elliptic                curve with integer coefficients, short normal form, 
			negative of point ecisnfneg(E,P) 
elliptic                curve with integer coefficients, short normal form, 
			points of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) 
elliptic                curve with integer coefficients, short normal form, 
			sum of points ecisnfsum(E,P,Q) 
elliptic                curve with integer coefficients, short normal form, 
			torsion group ecisnftorgr(E) 
elliptic                curve with integral coefficients ecqnftoeci(D,L) 
			elliptic curve over quadratic number field to 
elliptic                logarithm of point ecisnfelogp(E,P,n) elliptic 
			curve with integer coefficients, short normal form, 
embedding               in field extension (rekursiv) pgf2efe(r,GmtoGn,P) 
			polynomial over Galois-field with characteristic 2 
embedding               in field extension (rekursiv) pgfsefe(r,p,ALm,P,g) 
			polynomial over Galois-field with single 
			characteristic 
embedding               in field extension gf2efe(GmtoGn,gm) Galois-field 
			with characteristic 2 
embedding               in field extension gfsefe(p,ALm,a,g) Galois-field 
			with single characteristic 
embedding               in field extension magfsefe(p,ALm,M,g) matrix over 
			Galois-field with single characteristic 
embedding               in field extension mapgfsefe(r,p,ALm,M,g) matrix 
			over polynomials over Galois-field with single 
			characteristic 
embedding               in field extension vecgfsefe(p,ALm,V,g) vector over 
			Galois-field with single characteristic 
embedding               in field extension vecpgfsefe(r,p,ALm,V,g) vector 
			over polynomials over Galois-field with single 
			characteristic 
embedding               of subfield gf2ies(Gm,Gn,n) Galois field with 
			characteristic 2 isomorphic 
embedding               of subfield gfsalgenies(p,m,n,ALn) Galois-field 
			with single characteristic arithmetic list 
			generator isomorphic 
entries                 ) maihermltne(A) (MACRO) matrix of integers Hermite 
			normal form ( lower triangular form with negative 
entries                 ) maihermltpe(A) (MACRO) matrix of integers Hermite 
			normal form ( lower triangular form with positive 
entries                 liprodoe(L) list of integers product over all 
equal                   (rekursiv) oequal(a,b) object 
equal                   ? isppecgf2eq(p,P1,P2) is projective point of an 
			elliptic curve over Galois-field with 
			characteristic 2 
equal                   ? isppecmpeq(p,P1,P2) is projective point of an 
			elliptic curve over modular primes 
equal                   degree upgf2sfed(G,H,d) univariate polynomial over 
			Galois-field with characteristic 2, separate factor 
			of 
equal                   degree upgfssfed(p,AL,G,d) univariate polynomial 
			over Galois-field with single characteristic, 
			separate factors of 
equal                   degree upmisfed(ip,G,d) univariate polynomial over 
			modular integers separate factor of 
equal                   elements ismaeqel(M,el) is matrix of 
equal                   ideal special qffmsiseqids(m,D,Q1,P1,Q2,P2) 
			quadratic function field over modular singles is 
equal                   one ? ispione(r,P) is polynomial over integers 
equal                   to number field of degree 3 
			isnf3eqnf3(F,P,pFD,pPD,pQ) is number field of 
			degree 3 
equal?                  isppecnfeq(F,P1,P2) is projective point of an 
			elliptic curve over number field 
equation                bpmisubcubeq(p,P,R) bivariate polynomial over 
			modular integers substitution with respect to a 
			cubic 
equation                ecrsign(E) elliptic curve over rational numbers, 
			sign of the functional 
equation                iecjtoeq(p,j) integer elliptic curve j-invariant to 
equation                pmimidse(r,M,S,P1,P2,F1,F2,H,pV) polynomial over 
			modular integers modular ideal solution of 
equation                sdisccleq(D,L) single discriminant class 
equation                special version iecjtoeqsv(p,j,pi) integer elliptic 
			curve j-invariant to 
equation                upireddiscc(P,pc) univariate polynomial over the 
			integers reduced discriminant and content of 
			resultant 
equation                upiresulc(P1,P2,pB) univariate polynomial over the 
			integers resultant and cofactor of resultant 
equation                upmiresulc(m,P1,P2,pC) univariate polynomial over 
			modular integers resultant and cofactor of 
			resultant 
equation                upmsresulc(m,P1,P2,pC) univariate polynomial over 
			modular singles resultant and cofactor of resultant 
equation                x^2+q*y^2=m using the algorithm of cornaccia 
			cornaccia(m,q,x0,pX,pY) determine a solution of the 
			diophantine 
equation,               special version ecrsigns(E,A,C) elliptic curve over 
			the rationals, sign of the functional 
equations               magfsssle(p,AL,A,b,pX,pN) matrix of Galois-field 
			with single characteristic elements solution of a 
			system of linear 
equations               mamsssle(p,A,b,pX,pN) matrix of modular singles 
			solution of a system of linear 
equations               manfssle(F,A,b,pX,pN) matrix of number field 
			elements solution of a system of linear 
equations               manfsssle(F,A,b,pX,pN) matrix of number field 
			elements, sparse representation, solution of a 
			system of linear 
equations               marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, solution of a system of linear 
equations               marfrssle(r,A,b,pX,pN) matrix of rational functions 
			over rationals solution of a system of linear 
equations               marssle(A,b,pX,pN) matrix of rationals solution of 
			a system of linear 
errmsgio(name,errno)    error message, I/O-operations 
error                   floverflow(a) floating point overflow 
error                   handling flerr() (MACRO) floating point overflow 
error                   message, I/O-operations errmsgio(name,errno) 
eta                     function special cdedeetas(q,ln_q) complex Dedekind 
eulerian                phi-value iphi(N) integer 
evaluation              first variable special version (rekursiv) 
			pigf2evalfvs(r,G,P) polynomial over integers 
			Galois-field with characteristic 2 element 
evaluation              first variable special version (rekursiv) 
			pigfsevalfvs(r,p,AL,P) polynomial over integers 
			Galois-field with single characteristic element 
evaluation              first variable special version 
			mapigfsevfvs(r,p,AL,M) matrix over polynomials over 
			integers Galois-field with single characteristic 
			element 
evaluation              first variable special version mapinfevlfvs(r,F,M) 
			matrix of polynomials over integers number field 
			element 
evaluation              first variable special version maprnfevlfvs(r,F,M) 
			matrix of polynomials over rationals number field 
			element 
evaluation              first variable special version pinfevalfvs(r,F,P) 
			polynomial over integers number field element 
evaluation              first variable special version prnfevalfvs(r,F,P) 
			polynomial over rationals number field element 
evaluation              first variable special version 
			vecpigfsefvs(r,p,AL,V) vector over polynomials over 
			integers Galois-field with single characteristic 
			element 
evaluation              first variable special version vpinfevalfvs(r,F,V) 
			vector of polynomials over integers number field 
			element 
evaluation              first variable special version vprnfevalfvs(r,F,V) 
			vector of polynomials over rationals number field 
			element 
evaluation              points picevalp(r,P,sA) polynomial over integers 
			choice of 
evaluation              special upinfeevals(F,P,a) univariate polynomial 
			over the integers number field element 
evaluation              special upprmsp1afes(p,F,P,a) univariate polynomial 
			over polynomial ring over modular single prime, 
			transcendence degree 1, algebraic function over 
			modular single prime, transcendence degree 1, 
evaluation              upgf2eval(G,P,a) polynomial over Galois-field with 
			characteristic 2 
evaluation              upinfeval(P,F,a) univariate polynomial over 
			integers number field element 
evaluation              upinfseval(P,F,a) univariate polynomial over 
			integers number field element, sparse 
			representation, 
evaluation              upnfeval(F,P,A) univariate polynomial over a number 
			field 
evaluation              uprnfeval(P,F,a) univariate polynomial over 
			rationals number field element 
evaluation              uprnfseval(P,F,a) univariate polynomial over 
			rationals number field element, sparse 
			representation, 
evaluation,             main variable pgf2eval(r,G,P,a) polynomial over 
			Galois-field with characteristic 2 
evaluation,             main variable pgfseval(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic 
evaluation,             main variable pieval(r,P,A) polynomial over 
			integers 
evaluation,             main variable pmieval(r,M,P,A) polynomial over 
			modular integers 
evaluation,             main variable pmseval(r,m,P,a) polynomial over 
			modular singles 
evaluation,             main variable pnfeval(r,F,P,a) polynomial over 
			number field 
evaluation,             main variable ppfeval(r,p,P,A) polynomial over 
			p-adic field 
evaluation,             main variable preval(r,P,A) polynomial over 
			rationals 
evaluation,             selected variable ppfevalsv(r,p,P,n,A) polynomial 
			over p-adic field 
evaluation,             specified variable (rekursiv) 
			pgfsevalsv(r,p,AL,P,d,a) polynomial over 
			Galois-field with single characteristic 
evaluation,             specified variable (rekursiv) pievalsv(r,P,n,A) 
			polynomial over integers 
evaluation,             specified variable (rekursiv) pmievalsv(r,m,P,n,a) 
			polynomial over modular integers 
evaluation,             specified variable (rekursiv) pmsevalsv(r,m,P,n,a) 
			polynomial over modular singles 
evaluation,             specified variable (rekursiv) pnfevalsv(r,F,P,n,a) 
			polynomial over number field 
evaluation,             specified variable (rekursiv) prevalsv(r,P,n,A) 
			polynomial over rationals 
even                    ieven(A) integer 
even                    seven(a) (MACRO) single-precision 
exact                   order of the point ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) 
			elliptic curve over Galois-field with 
			characteristic 2, multiple of the order of a point 
			to 
exact                   order of the point ecmpsnfmopto(p,a4,a6,P,mul) 
			elliptic curve over modular primes, short normal 
			form, multiple of the order of a point to 
expansion               ifactcfe(n,Large_P,K,mode) integer factorization 
			continued fraction 
expansion               of the L-series ecrfelser(E,A,z,result) elliptic 
			curve over rational numbers, Fourier 
exponent                flexpo(f) (MACRO) floating point 
exponent                list fputifel(L,pf) file put integer factor 
exponent                list fputqnffel(D,L,pf) file put quadratic number 
			field element factor 
exponent                list ifel(LP) integer factor 
exponent                list product ifelprod(a,b) integer factor 
exponent                list putifel(L) (MACRO) put integer factor 
exponent                list putqnffel(D,L) (MACRO) put quadratic number 
			field element factor 
exponent                list sfel(n) single factor 
exponent                of torsion group ecrexptor(E) elliptic curve over 
			rational numbers, 
exponent                vector compare dipevcomp(r,EV1,EV2) distributive 
			polynomial 
exponent                vector difference dipevdif(r,EV1,EV2) distributive 
			polynomial 
exponent                vector dipgfslotlio(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse 
exponent                vector dipilotolio(r,P) distributive polynomial 
			over integers in lexicographical order to 
			distributive polynomial over integers in 
			lexicographical order with inverse 
exponent                vector dipmiplotlio(r,p,P) distributive polynomial 
			over modular integer primes in lexicographical 
			order to distributive polynomial over modular 
			integer primes in lexicographical order with 
			inverse 
exponent                vector dipmsplotlio(r,p,P) distributive polynomial 
			over modular single primes in lexicographical order 
			to distributive polynomial over modular single 
			primes in lexicographical order with inverse 
exponent                vector dipnflotolio(r,F,P) distributive polynomial 
			over number field in lexicographical order to 
			distributive polynomial over number field in 
			lexicographical order with inverse 
exponent                vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers in lexicographical 
			order with inverse 
exponent                vector diprfrlotlio(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order with inverse 
exponent                vector diprlotolio(r,P) distributive polynomial 
			over rationals in lexicographical order to 
			distributive polynomial over rationals in 
			lexicographical order with inverse 
exponent                vector least common multiple dipevlcm(r,EV1,EV2) 
			distributive polynomial 
exponent                vector multiple test dipevmt(r,EV1,EV2) 
			distributive polynomial 
exponent                vector of the leading monomial dipevl(r,P) 
			distributive polynomial 
exponent                vector signum dipevsign(r,EV) distributive 
			polynomial 
exponent                vector sum dipevsum(r,EV1,EV2) distributive 
			polynomial 
exponential             function cexp(z) complex 
exponential             function flexp(f) floating point 
exponential             function special version cexpsv(z,n) complex 
exponentiation          ( lists only ) miexp_lo(M,A,E) modular integer 
exponentiation          csexp(v,n) complex single 
exponentiation          flsexp(f,n) floating point single 
exponentiation          gf2exp(G,a,m) Galois-field with characteristic 2 
exponentiation          gfsexp(p,AL,a,m) Galois-field with single 
			characteristic 
exponentiation          iexp(A,n) integer 
exponentiation          magfsexp(p,AL,M,n) matrix of Galois-field with 
			single characteristic elements 
exponentiation          maiexp(M,n) matrix of integers 
exponentiation          mamiexp(m,M,n) matrix of modular integers 
exponentiation          mamsexp(m,M,n) matrix of modular singles 
exponentiation          manfexp(F,M,n) matrix of number field elements 
exponentiation          manfsexp(F,M,n) matrix of number field elements, 
			sparse representation, 
exponentiation          mapgfsexp(r,p,AL,M,n) matrix of polynomials over 
			Galois-field with single characteristic 
exponentiation          mapiexp(r,M,n) matrix of polynomials over integers 
exponentiation          mapmiexp(r,m,M,n) matrix of polynomials over 
			modular integers 
exponentiation          mapmsexp(r,m,M,n) matrix of polynomials over 
			modular singles 
exponentiation          mapnfexp(r,F,M,n) matrix of polynomials over number 
			field 
exponentiation          maprexp(r,M,n) matrix of polynomials over rationals 
exponentiation          marexp(M,n) matrix of rationals 
exponentiation          marfmsp1exp(p,M,n) matrix of rational functions 
			over modular single primes, transcendence degree 1, 
exponentiation          marfrexp(r,M,n) matrix of rational functions over 
			rationals 
exponentiation          miexp(M,A,E) modular integer 
exponentiation          msexp(m,a,n) modular single 
exponentiation          nfexp(F,a,n) number field element 
exponentiation          pfexp(p,a,n) p-adic field element 
exponentiation          pgf2exp(r,G,P,n) polynomial over Galois-field with 
			characteristic 2 
exponentiation          pgfsexp(r,p,AL,P,m) polynomial over Galois-field 
			with single characteristic 
exponentiation          piexp(r,P,n) polynomial over integers 
exponentiation          pmiexp(r,m,P,n) polynomial over modular integers 
exponentiation          pmsexp(r,m,P,n) polynomial over modular singles 
exponentiation          pnfexp(r,F,P,n) polynomial over number field 
exponentiation          ppfexp(r,p,P,n) polynomial over p-adic field 
exponentiation          prexp(r,P,n) polynomial over rationals 
exponentiation          qnfexp(D,a,e) quadratic number field element 
exponentiation          qnfidexp(D,A,e) quadratic number field ideal 
exponentiation          rexp(R,n) rational number 
exponentiation          sexp(a,n) (MACRO) single-precision 
exponentiation          special afmsp1expsp(p,F,a,e,M) algebraic function 
			over modular single prime, transcendence degree 1, 
exponentiation          special nfeexpspec(F,a,e,M) number field element 
exponentiation          udppfexp(p,P,n) univariate dense polynomial over 
			p-adic field 
exponentiation          upmimpexp(ip,K,E,P) univariate polynomial over 
			modular integers modular polynomial 
exponentiation,         polynomial remainder pgf2expprem(r,G,F,E,M) 
			polynomial over Galois-field with characteristic 2, 
exponentiation,         polynomial remainder pgfsexpprem(r,p,AL,F,E,M) 
			polynomial over Galois-field with single 
			characteristic, 
exponentiation,         polynomial, remainder upgfsmieprem(p,AL,a,t,P) 
			univariate polynomial over Galois-field, monomial, 
			integer 
exponentiation,         special version upgf2modexps(G,F,m,P,pM) univariate 
			polynomial over Galois-field with characteristic 2, 
			modular 
extended                greatest common divisor iegcd(A,B,pU,pV) integer 
extended                greatest common divisor ihegcd(A,B,pV) integer half 
extended                greatest common divisor segcd(a,b,pu,pv) 
			single-precision 
extended                greatest common divisor udpmiegcd(m,P1,P2,pPX,pPY) 
			univariate dense polynomial over modular integers 
extended                greatest common divisor udpmihegcd(m,P1,P2,pP3) 
			univariate dense polynomial over modular integers 
			half 
extended                greatest common divisor udpmsegcd(m,P1,P2,pPX,pPY) 
			univariate dense polynomial over modular singles 
extended                greatest common divisor udpmshegcd(m,P1,P2,pP3) 
			univariate dense polynomial over modular singles 
			half 
extended                greatest common divisor 
			upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate polynomial 
			over Galois-field with single characteristic 
extended                greatest common divisor upgfshegcd(p,AL,P1,P2,pP3) 
			univariate polynomial over Galois-field with single 
			characteristic half 
extended                greatest common divisor upmiegcd(P,P1,P2,pP3,pP4) 
			univariate polynomial over modular integers 
extended                greatest common divisor upmihegcd(P,P1,P2,pP3) 
			univariate polynomial over modular integers half 
extended                greatest common divisor upmsegcd(m,P1,P2,pP3,pP4) 
			univariate polynomial over modular singles 
extended                greatest common divisor upmshegcd(m,P1,P2,pP3) 
			univariate polynomial over modular singles half 
extended                greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, 
extension               (rekursiv) pgf2efe(r,GmtoGn,P) polynomial over 
			Galois-field with characteristic 2 embedding in 
			field 
extension               (rekursiv) pgfsefe(r,p,ALm,P,g) polynomial over 
			Galois-field with single characteristic embedding 
			in field 
extension               ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
			curve over Galois field with characteristic 2, 
			number of points after field 
extension               gf2efe(GmtoGn,gm) Galois-field with characteristic 
			2 embedding in field 
extension               gfsefe(p,ALm,a,g) Galois-field with single 
			characteristic embedding in field 
extension               magfsefe(p,ALm,M,g) matrix over Galois-field with 
			single characteristic embedding in field 
extension               mapgfsefe(r,p,ALm,M,g) matrix over polynomials over 
			Galois-field with single characteristic embedding 
			in field 
extension               pvext(r,P,V,VN) polynomial variable list 
extension               vecgfsefe(p,ALm,V,g) vector over Galois-field with 
			single characteristic embedding in field 
extension               vecpgfsefe(r,p,ALm,V,g) vector over polynomials 
			over Galois-field with single characteristic 
			embedding in field 
extensions              of the P-adic valuation of an element of the 
			polynomial order of a univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the 
extensions              of the p-adic valuation of an element of the 
			polynomial ring of an univariate separable 
			polynomial over the integers 
			vepvelpruspi(F,a,p,k,v) values of the 
extent                  (rekursiv) oextent(a) object 
f                       cweberf(z) complex Weber function 
f1                      cweberf1(z) complex Weber function 
f2                      cweberf2(z) complex Weber function 
factor                  coefficient bound pifcb(L) polynomial over integers 
factor                  coefficient bound pilmfcb(r,P) polynomial over 
			integers Landau- Mignotte- 
factor                  exponent list fputifel(L,pf) file put integer 
factor                  exponent list fputqnffel(D,L,pf) file put quadratic 
			number field element 
factor                  exponent list ifel(LP) integer 
factor                  exponent list product ifelprod(a,b) integer 
factor                  exponent list putifel(L) (MACRO) put integer 
factor                  exponent list putqnffel(D,L) (MACRO) put quadratic 
			number field element 
factor                  exponent list sfel(n) single 
factor                  ifactlf(n,G,p,quot) integer factorization large 
factor                  list fputfactl(L,pf) file put 
factor                  list putfactl(L) (MACRO) put 
factor                  of equal degree upgf2sfed(G,H,d) univariate 
			polynomial over Galois-field with characteristic 2, 
			separate 
factor                  of equal degree upmisfed(ip,G,d) univariate 
			polynomial over modular integers separate 
factorial               ifactl(a) integer 
factorization           (rekursiv) ifact([-brk,][-imp,][-elc,][-rho,]N) 
			integer 
factorization           (rekursiv) pifact(r,P) polynomial over integers 
factorization           (rekursiv) upgf2sfact(G,P) univariate polynomial 
			over Galois-field with characteristic 2 squarefree 
factorization           (rekursiv) upgfssfact(p,AL,P) univariate polynomial 
			over Galois-field with single characteristic 
			squarefree 
factorization           (rekursiv) upmisfact(ip,P) univariate polynomial 
			over modular integers squarefree 
factorization           (rekursiv) upmssfact(m,P) univariate polynomial 
			over modular singles squarefree 
factorization           approximation pihlfa(r,p,L,M,S,P) polynomial over 
			integers, Hensel lemma 
factorization           approximation upihlfa(p,P,L,k) univariate 
			polynomial over the integers, Hensel lemma 
factorization           approximation upprmsp1hfa(p,F,P,L,k) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Hensel 
factorization           approximation with respect to integer prime 
			upihlfaip(p,P,L,k) univariate polynomial over 
			integers, Hensel lemma 
factorization           continued fraction expansion 
			ifactcfe(n,Large_P,K,mode) integer 
factorization           into pseudoprimes (rekursiv) ifactpp(N) integer 
factorization           large factor ifactlf(n,G,p,quot) integer 
factorization           of conductor ecrfcond(E) elliptic curve over 
			rational numbers, 
factorization           of discriminant eciminfdisc(E) elliptic curve with 
			integer coefficients, minimal model, 
factorization           of discriminant ecisnffdisc(E) elliptic curve with 
			integer coefficients, short normal form, 
factorization           of discriminant ecracfdisc(E) elliptic curve over 
			rational numbers, actual curve, 
factorization           of the defining polynomial or the minimal 
			polynomial afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic 
			function over modular single prime, transcendence 
			degree 1, P-primality test and 
factorization           of the defining polynomial or the minimal 
			polynomial infepptfact(F,p,Q,ppot,a0,z) integral 
			number field element p-primality test and 
factorization           of the defining polynomial or the minimal 
			polynomial with respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and 
factorization           of the defining polynomial, generators of p-maximal 
			orders of the p-adic divisors of the defining 
			polynomial and p-minimal polynomials of the 
			generators ouspiapfgmic(p,P,k) order of an 
			univariate separable polynomial over the integers 
			approximation of p-adic 
factorization           of the denominator of the j-invariant 
			ecrfdenjinv(E) elliptic curve over the rationals, 
factorization           of the discriminant ecqnfacpifdi(E) elliptic curve 
			over quadratic number field, actual model, prime 
			ideal 
factorization           of the norm of the discriminant ecqnfacfndisc(E) 
			elliptic curve over quadratic number field, actual 
			model, 
factorization           pisfact(r,P) polynomial over integers squarefree 
factorization           qnfpifact(D,a) quadratic number field element prime 
			ideal 
factorization           rdiscupifact(rd,c,pL) reduced discriminant and 
			discriminant of an univariate polynomial over the 
			integers 
factorization           sfact(n) single 
factorization           special upgfscfacts(p,AL,P) univariate polynomial 
			over Galois-field with single characteristic 
			complete 
factorization           special upmicfacts(P,F) univariate polynomial over 
			modular integers, complete 
factorization           special upmscfacts(p,A) univariate polynomial over 
			modular single prime, complete 
factorization           spifact(r,P) squarefree polynomial over integers 
factorization           upgf2bofact(G,P) univariate polynomial over 
			Galois-field with characteristic 2, Ben-Or 
factorization           upgf2ddfact(G,P) univariate polynomial over 
			Galois-field with characteristic 2 distinct degree 
factorization           upgfsbfact(p,AL,P,d) univariate polynomial over 
			Galois-field with single characteristic Berlekamp 
factorization           upgfsbofact(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic, Ben-Or 
factorization           upgfscfact(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic complete 
factorization           upgfsddfact(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic distinct 
			degree 
factorization           upgfsrelpfac(p,AL,P,Fak,pA2) univariate polynomial 
			over Galois-field with single characteristic 
			relative prime 
factorization           upifact(P) univariate polynomial over integers 
factorization           upmibofact(ip,P) univariate polynomial over modular 
			integers Ben-Or 
factorization           upmicfact(ip,P) univariate polynomial over modular 
			integers complete 
factorization           upmiddfact(ip,P) univariate polynomial over modular 
			integers distinct degree 
factorization           upmirelpfact(P,F,Fak,pA2) univariate polynomial 
			over modular integers relative prime 
factorization           upmscfact(p,A) univariate polynomial over modular 
			singles complete 
factorization           upmsddfact(p,F) univariate polynomial distinct 
			degree 
factorization           upmsrelpfact(p,P,Fak,pA2) univariate polynomial 
			over modular singles relative prime 
factorization           upnfsfact(F,P) univariate polynomial over number 
			field squarefree 
factorization           uprfact(P) univariate polynomial over rationals 
factorization           uspiapf(p,P,k) univariate separable polynomial over 
			the integers, approximation of p-adic 
factorization           uspifact(P) univariate squarefree polynomial over 
			integers 
factorization           uspprmsp1apf(p,P,F,k) univariate separable 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, approximation of 
			P-adic 
factorization,          Berlekamp algorithm upmibfact(ip,P,d) univariate 
			polynomial over modular integers 
factorization,          Berlekamp algorithm upmsbfact(p,A,d) univariate 
			polynomial over modular singles 
factorization,          N < 2^60 ifact60(N) integer 
factorization,          Zassenhaus method upgfsbfzm(p,AL,s,P,G) univariate 
			polynomial over Galois-field with single 
			characteristic Berlekamp 
factorization,          Zassenhaus method upmibfzm(ip,s,P,G) univariate 
			polynomial over modular integers, Berlekamp 
factorization,          Zassenhaus method upmsbfzm(m,s,P,G) univariate 
			polynomial over modular singles, Berlekamp 
factorization,          last step upgfsbfls(p,AL,P,B,d) univariate 
			polynomial over Galois-field with single 
			characteristic Berlekamp 
factorization,          last step upmibfls(ip,P,B,d) univariate polynomial 
			over modular integers Berlekamp 
factorization,          last step upmsbfls(m,P,B,d) univariate polynomial 
			over modular singles Berlekamp 
factorization,          old version (rekursiv) ifact_o(N) integer 
factorization,          special upgf2bofacts(G,P) univariate polynomial 
			over Galois-field with characteristic 2 Ben-Or 
factorization,          special upgfsbofacts(p,AL,P) univariate polynomial 
			over Galois-field with single characteristic, 
			Ben-Or 
factorization,          special upmibofacts(ip,P) univariate polynomial 
			over modular integers Ben-Or 
factorization,          special version qnfielpifacts(D,a,L) quadratic 
			number field integral element prime ideal 
factors                 of equal degree upgfssfed(p,AL,G,d) univariate 
			polynomial over Galois-field with single 
			characteristic, separate 
factors                 of the characteristic polynomial 
			magfsevifcp(p,AL,M,pL) matrix over Galois-field 
			with single characteristic eigenvalues and 
			irreducible 
factors                 of the characteristic polynomial maievifcp(M,pL) 
			matrix of integers eigenvalues and irreducible 
factors                 of the characteristic polynomial mamievifcp(p,M,pL) 
			matrix of modular integers eigenvalues and 
			irreducible 
factors                 of the characteristic polynomial mamsevifcp(p,M,pL) 
			matrix of modular singles eigenvalues and 
			irreducible 
factors                 of the characteristic polynomial marevifcp(M,*pL) 
			matrix of rationals eigenvalues and irreducible 
factors                 sfactors(n) single 
factors                 upgfsnif(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic number of 
			irreducible 
factors                 upminif(m,P) univariate polynomial over modular 
			integers, number of irreducible 
factors                 upmsnif(m,P) univariate polynomial over modular 
			singles, number of irreducible 
fast                    divisor search elcfds(N,b,e) elliptic curve 
fast                    reduction ) by Pollard divisor search 
			rhofrpds(N,b,z) rho- method ( 
fgeta(pf)               file get atom 
fgetc(pf)               (MACRO) file get character 
fgetcb(pf)              file get character, skipping blanks 
fgetcs(pf)              file get character, skipping space 
fgetdipgfsl(r,p,AL,VL,Vgfs,pf) file get distributive polynomial over 
			Galois-field with single characteristic list 
fgetdipil(r,VL,pf)      file get distributive polynomial over integers list 
fgetdipmipl(r,p,VL,pf)  file get distributive polynomial over modular 
			integer primes list 
fgetdipmspl(r,p,VL,pf)  file get distributive polynomial over modular 
			single primes list 
fgetdipnfl(r,F,VL,Vnf,pf) file get distributive polynomial over number field 
			list 
fgetdippicd(r1,r2,VL1,VL2,fac,pf) file get distributive polynomial over 
			polynomials over integers case distinction 
fgetdippil(r1,r2,VL1,VL2,pf) file get distributive polynomial over 
			polynomials over integers list 
fgetdiprfrl(r1,r2,VL1,VL2,pf) file get distributive polynomial over rational 
			functions over the rationals list 
fgetdiprl(r,VL,pf)      file get distributive polynomial over rationals 
			list 
fgetecr(pf)             file get elliptic curve over rational numbers 
fgetecrp(pf)            file get point on elliptic curve over rational 
			numbers 
fgetfl(pf)              file get floating point 
fgetgf2el(G,V,pf)       file get Galois-field with characteristic 2 element 
fgetgfsel(p,AL,V,pf)    file get Galois-field with single characteristic 
			element 
fgeti(pf)               file get integer 
fgetl(pf)               file get list (rekursiv) 
fgetli(pf)              file get list of integers 
fgetlr(pf)              file get list of rational numbers 
fgetma(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) file get matrix 
fgetmagfs(p,AL,V,pf)    (MACRO) file get matrix of Galois-field with single 
			characteristic elements 
fgetmai(pf)             (MACRO) file get matrix of integers 
fgetmami(m,pf)          (MACRO) file get matrix of modular integers 
fgetmams(m,pf)          (MACRO) file get matrix of modular singles 
fgetmanf(F,VL,pf)       (MACRO) file get matrix of number field elements 
fgetmanfs(F,VL,pf)      (MACRO) file get matrix of number field elements, 
			sparse representation 
fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get matrix of polynomials over 
			Galois-field with single characteristic 
fgetmapi(r,V,pf)        (MACRO) file get matrix of polynomials over 
			integers 
fgetmapmi(r,m,V,pf)     (MACRO) file get matrix of polynomials over modular 
			integers 
fgetmapms(r,m,V,pf)     (MACRO) file get matrix of polynomials over modular 
			singles 
fgetmapnf(r,F,V,Vnf,pf) (MACRO) file get matrix of polynomials over number 
			field 
fgetmapr(r,V,pf)        (MACRO) file get matrix of polynomials over 
			rationals 
fgetmar(pf)             (MACRO) file get matrix of rationals 
fgetmarfmsp1(p,V,pf)    (MACRO) file get matrix of rational functions over 
			modular single primes, transcendence degree 1 
fgetmarfr(r,V,pf)       (MACRO) file get matrix of rational functions over 
			rationals 
fgetmaspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) file get matrix special 
fgetmi(M,pf)            file get modular integer 
fgetms(m,pf)            file get modular single 
fgetnfel(F,V,pf)        file get number field element 
fgetnfels(F,V,pf)       file get number field element, sparse 
			representation 
fgeto(pf)               file get object 
fgetpfel(p,pf)          file get p-adic field element 
fgetpgf2(r,G,V,Vgf2,pf) file get polynomial over Galois-field with 
			characteristic 2 
fgetpgfs(r,p,AL,V,Vgfs,pf) file get polynomial over Galois-field with single 
			characteristic 
fgetpi(r,V,pf)          file get polynomial over integers 
fgetpmi(r,M,V,pf)       file get polynomial over modular integers 
fgetpms(r,m,V,pf)       file get polynomial over modular singles 
fgetpnf(r,F,V,Vnf,pf)   file get polynomial over number field 
fgetppf(r,p,V,pf)       file get polynomial over p-adic field 
fgetpr(r,V,pf)          file get polynomial over rationals 
fgetqnfel(D,pf)         file get quadratic number field element 
fgetr(pf)               file get rational number 
fgetrfmsp1(p,V,pf)      file get rational function over modular single 
			primes, transcendence degree 1 
fgetrfr(r,V,pf)         file get rational function over rationals 
fgets(s,n,pf)           (MACRO) file get string 
fgetsi(pf)              file get single 
fgetspfel(p,pf)         file get special p-adic field element 
fgetvec(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) file get vector 
fgetvecgfs(p,AL,VL,pf)  (MACRO) file get vector of Galois-field with single 
			characteristic elements 
fgetveci(pf)            (MACRO) file get vector of integers 
fgetvecmi(m,pf)         (MACRO) file get vector of modular integers 
fgetvecms(m,pf)         (MACRO) file get vector of modular singles 
fgetvecnf(F,VL,pf)      (MACRO) file get vector of number field elements 
fgetvecnfs(F,VL,pf)     (MACRO) file get vector of number field elements, 
			sparse representation 
fgetvecpi(r,VL,pf)      (MACRO) file get vector of polynomials over 
			integers 
fgetvecpmi(r,m,VL,pf)   (MACRO) file get vector of polynomials over modular 
			integers 
fgetvecpms(r,m,VL,pf)   (MACRO) file get vector of polynomials over modular 
			singles 
fgetvecpnf(r,F,VL,VLnf,pf) (MACRO) file get vector of polynomials over 
			number field 
fgetvecpr(r,VL,pf)      (MACRO) file get vector of polynomials over 
			rationals 
fgetvecr(pf)            (MACRO) file get vector of rationals 
fgetvecrfr(r,VL,pf)     (MACRO) file get vector of rational functions over 
			rationals 
fgetvecspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) file get vector special 
fgetvl(pf)              file get variable list 
fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get vector of polynomials over 
			Galois-field with single characteristic 
fgetvrfmsp1(p,VL,pf)    (MACRO) file get vector of rational functions over 
			modular single primes, transcendence degree 1 
field                   (rekursiv) pitopnf(r,P) polynomial over the 
			integers to polynomial over a number 
field                   (rekursiv) prtopnf(r,P) polynomial over rationals 
			to polynomial over number 
field                   ? isdppf(r,p,P) is dense polynomial over p-adic 
field                   ? iselecnf(F,a1,a2,a3,a4,a6,P) is element of an 
			elliptic curve over number 
field                   Dirichlet character qnfdirchar(D,z) quadratic 
			number 
field                   Groebner basis augmentation dipnfgba(r,F,PL,P) 
			distributive polynomial over number 
field                   Groebner basis dipnfgb(r,F,PL) distributive 
			polynomial over number 
field                   Groebner basis recursion dipnfgbr(r,F,PL) 
			distributive polynomial over number 
field                   S-polynomial dipnfsp(r,F,P1,P2) distributive 
			polynomial over number 
field                   Tate's values b2, b4, b6 
			ecnftavb6(F,a1,a2,a3,a4,a6) elliptic curve over 
			number 
field                   Tate's values b2, b4, b6, b8 
			ecnftavb8(F,a1,a2,a3,a4,a6) elliptic curve over 
			number 
field                   Tate's values c4, c6 ecnftavc6(F,a1,a2,a3,a4,a6) 
			elliptic curve over number 
field                   additive valuation pfaval(p,a) p-adic 
field                   additive valuation qnfaval(D,p,a) quadratic number 
field                   birational transformation of coefficients 
			ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over number 
field                   characteristic polynomial mapnfchpol(r,F,M) (MACRO) 
			matrix of polynomials over number 
field                   conjugate element qnfconj(D,a) quadratic number 
field                   construction 1 mapnfcons1(r,F,n) (MACRO) matrix of 
			polynomials over number 
field                   degrees of the residue class fields 
			qnfdegrescf(D,p) quadratic number 
field                   derivation, main variable (rekursiv) 
			ppfderiv(r,p,P) polynomial over p-adic 
field                   derivation, main variable pnfderiv(r,F,P) 
			polynomial over number 
field                   derivation, selected variable ppfderivsv(r,p,P,n) 
			polynomial over p-adic 
field                   derivation, specified variable (rekursiv) 
			pnfderivsv(r,F,P,n) polynomial over number 
field                   determinant mapnfdet(r,F,M) matrix of polynomials 
			over number 
field                   difference (rekursiv) pnfdif(r,F,P1,P2) polynomial 
			over number 
field                   difference dipnfdif(r,F,P1,P2) distributive 
			polynomial over number 
field                   difference mapnfdif(r,F,M,N) (MACRO) matrix of 
			polynomials over number 
field                   difference ppfdif(r,p,P1,P2) polynomial over p-adic 
field                   difference udppfdif(p,P1,P2) univariate dense 
			polynomial over p-adic 
field                   difference vecpnfdif(r,F,U,V) (MACRO) vector of 
			polynomials over number 
field                   discriminant ecnfdisc(F,a1,a2,a3,a4,a6) elliptic 
			curve over number 
field                   discriminant ecqnfflddisc(E) (MACRO) elliptic curve 
			over quadratic number field, 
field                   discriminant modulo 4 ecqnfdmod4(E) (MACRO) 
			elliptic curve over quadratic number field, 
field                   discriminant nffielddiscr(F) number field, 
field                   discriminant qnfdisc(D) quadratic number 
field                   element comparison qnfelcomp(D,A,B) quadratic 
			number 
field                   element difference nfdif(F,a,b) number 
field                   element difference pfdif(p,a,b) p-adic 
field                   element difference qnfdif(D,a,b) (MACRO) quadratic 
			number 
field                   element evaluation first variable special version 
			mapinfevlfvs(r,F,M) matrix of polynomials over 
			integers number 
field                   element evaluation first variable special version 
			maprnfevlfvs(r,F,M) matrix of polynomials over 
			rationals number 
field                   element evaluation first variable special version 
			pinfevalfvs(r,F,P) polynomial over integers number 
field                   element evaluation first variable special version 
			prnfevalfvs(r,F,P) polynomial over rationals number 
field                   element evaluation first variable special version 
			vpinfevalfvs(r,F,V) vector of polynomials over 
			integers number 
field                   element evaluation first variable special version 
			vprnfevalfvs(r,F,V) vector of polynomials over 
			rationals number 
field                   element evaluation special upinfeevals(F,P,a) 
			univariate polynomial over the integers number 
field                   element evaluation upinfeval(P,F,a) univariate 
			polynomial over integers number 
field                   element evaluation uprnfeval(P,F,a) univariate 
			polynomial over rationals number 
field                   element exponentiation nfexp(F,a,n) number 
field                   element exponentiation pfexp(p,a,n) p-adic 
field                   element exponentiation qnfexp(D,a,e) quadratic 
			number 
field                   element exponentiation special nfeexpspec(F,a,e,M) 
			number 
field                   element factor exponent list fputqnffel(D,L,pf) 
			file put quadratic number 
field                   element factor exponent list putqnffel(D,L) (MACRO) 
			put quadratic number 
field                   element fgetnfel(F,V,pf) file get number 
field                   element fgetpfel(p,pf) file get p-adic 
field                   element fgetqnfel(D,pf) file get quadratic number 
field                   element fgetspfel(p,pf) file get special p-adic 
field                   element fputnfel(F,a,V,pf) file put number 
field                   element fputonfel(F,a,V,pf) file put original 
			number 
field                   element fputpfel(p,a,pf) file put p-adic 
field                   element fputqnfel(D,a,pf) file put quadratic number 
field                   element fputspfel(p,a,pf) file put special p-adic 
field                   element getnfel(F,V) (MACRO) get number 
field                   element getpfel(p) (MACRO) get p-adic 
field                   element getqnfel(D) (MACRO) get quadratic number 
field                   element getspfel(p) (MACRO) get special p-adic 
field                   element integer product nfeliprod(F,a,i) number 
field                   element integer product pfeliprod(p,a,i) p-adic 
field                   element integer? isqnfint(D,a) (MACRO) is quadratic 
			number 
field                   element integral element? isqnfiel(D,a) is 
			quadratic number 
field                   element inverse element qnfinv(D,a) quadratic 
			number 
field                   element inverse pfinv(p,a) p-adic 
field                   element itonf(A) (MACRO) integer to number 
field                   element itopfel(p,d,A) integer to p-adic 
field                   element itoqnf(D,a) (MACRO) integer to quadratic 
			number 
field                   element minimal polynomial modulo p-power 
			infeminpmpp(F,a,p,e,Q) integral number 
field                   element minimal polynomial modulo p-power with 
			respect to integer primes infempmppip(F,a,p,e,Q) 
			integral number 
field                   element minimal representation qnfminrep(D,a) 
			quadratic number 
field                   element modulo integer nfelmodi(F,a,M) number 
field                   element negation nfneg(F,a) number 
field                   element negation pfneg(p,a) p-adic 
field                   element negation qnfneg(D,a,b) quadratic number 
field                   element norm nfnorm(F,a) number 
field                   element normalized representation nfelnormal(L) 
			number 
field                   element one isnfone(F,A) is number 
field                   element one? isqnfone(D,a) (MACRO) is quadratic 
			number 
field                   element p-primality test and factorization of the 
			defining polynomial or the minimal polynomial 
			infepptfact(F,p,Q,ppot,a0,z) integral number 
field                   element p-primality test and factorization of the 
			defining polynomial or the minimal polynomial with 
			respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) integral number 
field                   element p-star valuation infepstarval(p,A) integral 
			number 
field                   element p-star valuation with respect to integer 
			primes infepstarvip(P,A) integral number 
field                   element power of prime ideal homomorphism zero? 
			isqnfppihom0(D,P,k,pi,z,a) is quadratic number 
field                   element prime ideal factorization qnfpifact(D,a) 
			quadratic number 
field                   element prime ideal order qnfpiord(D,P,pi,z,a) 
			quadratic number 
field                   element prime power product pfpprod(p,a,i) p-adic 
field                   element product (rekursiv) pnfnfprod(r,F,P,a) 
			polynomial over number field, number 
field                   element product dipnfnfprod(r,F,P,A) distributive 
			polynomial over number field, number 
field                   element product nfprod(F,a,b) number 
field                   element product pfprod(p,a,b) p-adic 
field                   element product ppfpfprod(r,p,P,b) polynomial over 
			p-adic field p-adic 
field                   element product qnfprod(D,a,b) quadratic number 
field                   element product special nfeprodspec(F,a,b,M) number 
field                   element product udppfpfprod(p,P,a) univariate dense 
			polynomial over p-adic field p-adic 
field                   element putnfel(F,a,V) (MACRO) put number 
field                   element putonfel(F,a,V) (MACRO) put original number 
field                   element putpfel(p,a) (MACRO) put p-adic 
field                   element putqnfel(D,a) (MACRO) put quadratic number 
field                   element putspfel(p,a) (MACRO) put special p-adic 
field                   element quotient (rekursiv) pnfnfquot(r,F,P,a) 
			polynomial over number field, number 
field                   element quotient qnfquot(D,a,b) (MACRO) quadratic 
			number 
field                   element rational isqnfrat(D,a) (MACRO) is quadratic 
			number 
field                   element rational number product nfelrprod(F,a,R) 
			number 
field                   element rational number product pfelrprod(p,a,R) 
			p-adic 
field                   element regulation with respect to integer primes 
			ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number 
field                   element regulation, version1 
			ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number 
field                   element regulation, version2 
			ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number 
field                   element rtonf(R) rational number to number 
field                   element rtopfel(p,d,R) rational to p-adic 
field                   element rtoqnf(D,A) (MACRO) rational number to 
			quadratic number 
field                   element special minimal polynomial, Collins 
			algorithm, version1 nfespecmpc1(F,a) number 
field                   element special minimal polynomial, Collins 
			algorithm, version2 nfespecmpc2(F,a) number 
field                   element square qnfsquare(D,a) quadratic number 
field                   element sum nfsum(F,a,b) number 
field                   element sum pfsum(p,a,b) p-adic 
field                   element sum qnfsum(D,a,b) quadratic number 
field                   element to matrix line nfeltomaln(n,a) number 
field                   element to univariate dense polynomial over 
			rationals nfeltoudpr(a) number 
field                   element trace nftrace(F,a) number 
field                   element udprtonfel(P) univariate dense polynomial 
			over rationals to number 
field                   element uprtonfel(F,P) univariate polynomial over 
			rationals to number 
field                   element, core algorithm ippnfecoreal(F,p,Q,mp) 
			integral p-primary number 
field                   element, core algorithm with respect to integer 
			primes ippnfecalip(F,P,Q,mp) integral P-primary 
			number 
field                   element, difference iqnfdif(D,a,b) (MACRO) integer, 
			quadratic number 
field                   element, difference rqnfdif(D,a,b) (MACRO) rational 
			number, quadratic number 
field                   element, increasing the denominator of the p-star 
			value ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) 
			integral p-primary number 
field                   element, increasing the denominator of the p-star 
			value with respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number 
field                   element, integer, difference qnfidif(D,a,b) (MACRO) 
			quadratic number 
field                   element, integer, product qnfiprod(D,a,b) quadratic 
			number 
field                   element, integer, quotient qnfiquot(D,a,b) 
			quadratic number 
field                   element, integer, sum qnfisum(D,a,b) quadratic 
			number 
field                   element, quotient iqnfquot(D,a,b) integer, 
			quadratic number 
field                   element, quotient rqnfquot(D,a,b) rational number, 
			quadratic number 
field                   element, rational number, difference qnfrdif(D,a,b) 
			(MACRO) quadratic number 
field                   element, rational number, product qnfrprod(D,a,b) 
			quadratic number 
field                   element, rational number, quotient qnfrquot(D,a,b) 
			(MACRO) quadratic number 
field                   element, rational number, sum qnfrsum(D,a,b) 
			quadratic number 
field                   element, sparse representation ? isnfels(F,a) is 
			number 
field                   element, sparse representation fgetnfels(F,V,pf) 
			file get number 
field                   element, sparse representation fputnfels(F,a,V,pf) 
			file put number 
field                   element, sparse representation getnfels(F,V) 
			(MACRO) get number 
field                   element, sparse representation itonfs(A) integer to 
			number 
field                   element, sparse representation putnfels(F,a,V) 
			(MACRO) put number 
field                   element, sparse representation rtonfs(R) rational 
			number to number 
field                   element, sparse representation, evaluation 
			upinfseval(P,F,a) univariate polynomial over 
			integers number 
field                   element, sparse representation, evaluation 
			uprnfseval(P,F,a) univariate polynomial over 
			rationals number 
field                   element? isnfel(F,a) is number 
field                   element? ispfel(p,a) is p-adic 
field                   elements ? ismanf(F,M) (MACRO) is matrix of number 
field                   elements ? isvecnf(F,V) (MACRO) is vector of number 
field                   elements characteristic polynomial manfchpol(F,M) 
			(MACRO) matrix of number 
field                   elements construction 1 manfcons1(F,n) (MACRO) 
			matrix of number 
field                   elements determinant manfdet(F,M) matrix of number 
field                   elements difference manfdif(F,M,N) (MACRO) matrix 
			of number 
field                   elements difference vecnfdif(F,U,V) (MACRO) vector 
			of number 
field                   elements exponentiation manfexp(F,M,n) matrix of 
			number 
field                   elements fgetmanf(F,VL,pf) (MACRO) file get matrix 
			of number 
field                   elements fgetvecnf(F,VL,pf) (MACRO) file get vector 
			of number 
field                   elements fputmanf(F,M,VL,pf) (MACRO) file put 
			matrix of number 
field                   elements fputvecnf(F,V,VL,pf) (MACRO) file put 
			vector of number 
field                   elements getmanf(F,VL) (MACRO) get matrix of number 
field                   elements getvecnf(F,VL) (MACRO) get vector of 
			number 
field                   elements inverse manfinv(F,M) matrix of number 
field                   elements linear combination vecnflc(F,s1,s2,L1,L2) 
			vector of number 
field                   elements maitomanf(M) matrix of integers to matrix 
			of number 
field                   elements martomanf(M) matrix of rationals to matrix 
			of number 
field                   elements maudprtomnf(M) matrix of univariate dense 
			polynomials over rationals to matrix of number 
field                   elements negation manfneg(F,M) (MACRO) matrix of 
			number 
field                   elements negation vecnfneg(F,V) (MACRO) vector of 
			number 
field                   elements null space basis manfnsb(F,M) matrix of 
			number 
field                   elements product manfprod(F,M,N) (MACRO) matrix of 
			number 
field                   elements putmanf(F,M,VL) (MACRO) put matrix of 
			number 
field                   elements putvecnf(F,V,VL) (MACRO) put vector of 
			number 
field                   elements rank manfrk(F,M) matrix of number 
field                   elements scalar multiplication manfsmul(F,M,el) 
			matrix of number 
field                   elements scalar multiplication vecnfsmul(F,V,el) 
			vector of number 
field                   elements scalar product vecnfsprod(F,V,W) vector of 
			number 
field                   elements solution of a system of linear equations 
			manfssle(F,A,b,pX,pN) matrix of number 
field                   elements sum manfsum(F,M,N) (MACRO) matrix of 
			number 
field                   elements sum vecnfsum(F,U,V) (MACRO) vector of 
			number 
field                   elements to matrix of univariate dense polynomials 
			over rationals manftomudpr(F,M) matrix of number 
field                   elements to vector of univariate dense polynomials 
			over rationals vnftovudpr(F,V) vector of number 
field                   elements vecitovecnf(V) vector of integers to 
			vector of number 
field                   elements vecrtovecnf(V) vector of rationals to 
			vector of number 
field                   elements vector multiplication manfvecmul(F,A,x) 
			(MACRO) matrix of number 
field                   elements vudprtovnf(V) vector of univariate dense 
			polynomials over rationals to vector of number 
field                   elements, sparse representation ? ismanfs(F,M) 
			(MACRO) is matrix of number 
field                   elements, sparse representation ? isvecnfs(F,V) 
			(MACRO) is vector of number 
field                   elements, sparse representation fgetmanfs(F,VL,pf) 
			(MACRO) file get matrix of number 
field                   elements, sparse representation fgetvecnfs(F,VL,pf) 
			(MACRO) file get vector of number 
field                   elements, sparse representation 
			fputmanfs(F,M,VL,pf) (MACRO) file put matrix of 
			number 
field                   elements, sparse representation 
			fputvecnfs(F,V,VL,pf) (MACRO) file put vector of 
			number 
field                   elements, sparse representation getmanfs(F,VL) 
			(MACRO) get matrix of number 
field                   elements, sparse representation getvecnfs(F,VL) 
			(MACRO) get vector of number 
field                   elements, sparse representation maitomanfs(M) 
			matrix of integers to matrix of number 
field                   elements, sparse representation martomanfs(M) 
			matrix of rationals to matrix of number 
field                   elements, sparse representation putmanfs(F,M,VL) 
			(MACRO) put matrix of number 
field                   elements, sparse representation putvecnfs(F,V,VL) 
			(MACRO) put vector of number 
field                   elements, sparse representation vecitovnfs(V) 
			vector of integers to vector of number 
field                   elements, sparse representation vecrtovnfs(V) 
			vector of rationals to vector of number 
field                   elements, sparse representation, construction 1 
			manfscons1(F,n) (MACRO) matrix of number 
field                   elements, sparse representation, determinant 
			manfsdet(F,M) matrix of number 
field                   elements, sparse representation, difference 
			manfsdif(F,M,N) (MACRO) matrix of number 
field                   elements, sparse representation, difference 
			vecnfsdif(F,U,V) (MACRO) vector of number 
field                   elements, sparse representation, exponentiation 
			manfsexp(F,M,n) matrix of number 
field                   elements, sparse representation, inverse 
			manfsinv(F,M) matrix of number 
field                   elements, sparse representation, linear combination 
			vecnfslc(F,s1,s2,L1,L2) vector of number 
field                   elements, sparse representation, negation 
			manfsneg(F,M) (MACRO) matrix of number 
field                   elements, sparse representation, negation 
			vecnfsneg(F,V) (MACRO) vector of number 
field                   elements, sparse representation, null space basis 
			manfsnsb(F,M) matrix of number 
field                   elements, sparse representation, product 
			manfsprod(F,M,N) (MACRO) matrix of number 
field                   elements, sparse representation, rank manfsrk(F,M) 
			matrix of number 
field                   elements, sparse representation, scalar 
			multiplication manfssmul(F,M,el) matrix of number 
field                   elements, sparse representation, scalar 
			multiplication vecnfssmul(F,V,el) vector of number 
field                   elements, sparse representation, scalar product 
			vecnfssprod(F,V,W) vector of number 
field                   elements, sparse representation, solution of a 
			system of linear equations manfsssle(F,A,b,pX,pN) 
			matrix of number 
field                   elements, sparse representation, sum 
			manfssum(F,M,N) (MACRO) matrix of number 
field                   elements, sparse representation, sum 
			vecnfssum(F,U,V) (MACRO) vector of number 
field                   elements, sparse representation, vector 
			multiplication manfsvecmul(F,A,x) (MACRO) matrix of 
			number 
field                   equal? isppecnfeq(F,P1,P2) is projective point of 
			an elliptic curve over number 
field                   evaluation upnfeval(F,P,A) univariate polynomial 
			over a number 
field                   evaluation, main variable pnfeval(r,F,P,a) 
			polynomial over number 
field                   evaluation, main variable ppfeval(r,p,P,A) 
			polynomial over p-adic 
field                   evaluation, selected variable ppfevalsv(r,p,P,n,A) 
			polynomial over p-adic 
field                   evaluation, specified variable (rekursiv) 
			pnfevalsv(r,F,P,n,a) polynomial over number 
field                   exponentiation mapnfexp(r,F,M,n) matrix of 
			polynomials over number 
field                   exponentiation pnfexp(r,F,P,n) polynomial over 
			number 
field                   exponentiation ppfexp(r,p,P,n) polynomial over 
			p-adic 
field                   exponentiation udppfexp(p,P,n) univariate dense 
			polynomial over p-adic 
field                   extension (rekursiv) pgf2efe(r,GmtoGn,P) polynomial 
			over Galois-field with characteristic 2 embedding 
			in 
field                   extension (rekursiv) pgfsefe(r,p,ALm,P,g) 
			polynomial over Galois-field with single 
			characteristic embedding in 
field                   extension ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) 
			elliptic curve over Galois field with 
			characteristic 2, number of points after 
field                   extension gf2efe(GmtoGn,gm) Galois-field with 
			characteristic 2 embedding in 
field                   extension gfsefe(p,ALm,a,g) Galois-field with 
			single characteristic embedding in 
field                   extension magfsefe(p,ALm,M,g) matrix over 
			Galois-field with single characteristic embedding 
			in 
field                   extension mapgfsefe(r,p,ALm,M,g) matrix over 
			polynomials over Galois-field with single 
			characteristic embedding in 
field                   extension vecgfsefe(p,ALm,V,g) vector over 
			Galois-field with single characteristic embedding 
			in 
field                   extension vecpgfsefe(r,p,ALm,V,g) vector over 
			polynomials over Galois-field with single 
			characteristic embedding in 
field                   fgetmapnf(r,F,V,Vnf,pf) (MACRO) file get matrix of 
			polynomials over number 
field                   fgetpnf(r,F,V,Vnf,pf) file get polynomial over 
			number 
field                   fgetppf(r,p,V,pf) file get polynomial over p-adic 
field                   fgetvecpnf(r,F,VL,VLnf,pf) (MACRO) file get vector 
			of polynomials over number 
field                   fitting ppffit(r,p,P,d) polynomial over p-adic 
field                   fitting udppffit(p,P,Pd) univariate dense 
			polynomial over p-adic 
field                   fputmapnf(r,F,M,V,Vnf,pf) (MACRO) file put matrix 
			of polynomials over number 
field                   fputpnf(r,F,P,V,Vnf,pf) file put polynomial over 
			number 
field                   fputppf(r,p,P,V,pf) file put polynomial over p-adic 
field                   fputvecpnf(r,F,W,VL,VLnf,pf) (MACRO) file put 
			vector of polynomials over number 
field                   fundamental unit rqnffu(D,pl) real quadratic number 
field                   getmapnf(r,F,V,Vnf) (MACRO) get matrix of 
			polynomials over number 
field                   getpnf(r,F,V,Vnf) (MACRO) get polynomial over 
			number 
field                   getppf(r,p,V) get polynomial over p-adic 
field                   getvecpnf(r,F,VL,VLnf) (MACRO) get vector of 
			polynomials over number 
field                   greatest common divisor and cofactors 
			upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate polynomial 
			over number 
field                   greatest common divisor upnfgcd(F,P1,P2) univariate 
			polynomial over number 
field                   ideal comparison qnfidcomp(D,A,B) quadratic number 
field                   ideal exponentiation qnfidexp(D,A,e) quadratic 
			number 
field                   ideal fputqnfid(D,A,pf) file put quadratic number 
field                   ideal one qnfidone(D) (MACRO) quadratic number 
field                   ideal one? isqnfidone(D,A) is quadratic number 
field                   ideal product qnfidprod(D,A,B) quadratic number 
field                   ideal putqnfid(D,A) (MACRO) put quadratic number 
field                   ideal square qnfidsquare(D,A) quadratic number 
field                   in graduated lexicographical order 
			dipnflotoglo(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over number 
field                   in lexicographical order to distributive polynomial 
			over number field in graduated lexicographical 
			order dipnflotoglo(r,F,P) distributive polynomial 
			over number 
field                   in lexicographical order to distributive polynomial 
			over number field in lexicographical order with 
			inverse exponent vector dipnflotolio(r,F,P) 
			distributive polynomial over number 
field                   in lexicographical order to distributive polynomial 
			over number field with total degree ordering 
			dipnflototdo(r,F,P) distributive polynomial over 
			number 
field                   in lexicographical order with inverse exponent 
			vector dipnflotolio(r,F,P) distributive polynomial 
			over number field in lexicographical order to 
			distributive polynomial over number 
field                   integer product ppfiprod(r,p,P,i) polynomial over 
			p-adic 
field                   integral basis qnfintbas(D) quadratic number 
field                   integral element prime ideal factorization, special 
			version qnfielpifacts(D,a,L) quadratic number 
field                   inverse mapnfinv(r,F,M) matrix of polynomials over 
			number 
field                   inverse nfinv(F,a) number 
field                   iprniqf(p,D) integer prime representation as a norm 
			in an imaginary quadratic 
field                   j-invariant ecnfjinv(F,a1,a2,a3,a4,a6) elliptic 
			curve over number 
field                   line through points ecnflp(F,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over number 
field                   linear combination vecpnflc(r,F,s1,s2,L1,L2) vector 
			of polynomials over number 
field                   list fgetdipnfl(r,F,VL,Vnf,pf) file get 
			distributive polynomial over number 
field                   list fputdipnfl(r,F,PL,VL,Vnf,pf) file put 
			distributive polynomial over number 
field                   list getdipnfl(r,F,VL,Vnf) (MACRO) get distributive 
			polynomial over number 
field                   list putdipnfl(r,F,PL,VL,Vnf) (MACRO) put 
			distributive polynomial over number 
field                   mapitomapnf(r,M) matrix of polynomials over 
			integers to matrix of polynomials over number 
field                   mapnftomapmp(r,F,P,M) matrix of polynomials over 
			number field to matrix of polynomials modulo 
			polynomial over number 
field                   maprtomapnf(r,M) matrix of polynomials over 
			rationals to matrix of polynomials over number 
field                   monic dipnfmonic(r,F,P) distributive polynomial 
			over number 
field                   monic pnfmonic(r,F,P) polynomial over number 
field                   multiplication-map ecnfmul(F,a1,a2,a3,a4,a6,n,P1) 
			elliptic curve over number 
field                   negation (rekursiv) pnfneg(r,F,P) polynomial over 
			number 
field                   negation dipnfneg(r,F,P) distributive polynomial 
			over number 
field                   negation mapnfneg(r,F,M) (MACRO) matrix of 
			polynomials over number 
field                   negation ppfneg(r,p,P) polynomial over p-adic 
field                   negation udppfneg(p,P) univariate dense polynomial 
			over p-adic 
field                   negation vecpnfneg(r,F,U) (MACRO) vector of 
			polynomials over number 
field                   negative point ecnfneg(F,a1,a2,a3,a4,a6,P) elliptic 
			curve over number 
field                   norm of an element qnfnorm(D,a) quadratic number 
field                   of degree 3 characteristic polynomial 
			nf3chpol(F,el) number 
field                   of degree 3 equal to number field of degree 3 
			isnf3eqnf3(F,P,pFD,pPD,pQ) is number 
field                   of degree 3 isnf3eqnf3(F,P,pFD,pPD,pQ) is number 
			field of degree 3 equal to number 
field                   of degree 3 square root nf3sqrt(F,el) number 
field                   order ppford(r,p,P) polynomial over p-adic 
field                   over modular single prime, transcendence degree 1, 
			decomposition law affmsp1decl(p,F,P) algebraic 
			function 
field                   over modular singles divisor class number 
			qffmsdcn(m,P) quadratic function 
field                   over modular singles divisor class number 
			subroutine 1 qffmsdcns1(m,P) quadratic function 
field                   over modular singles divisor class number 
			subroutine 2 qffmsdcns2(m,P) quadratic function 
field                   over modular singles divisor class number 
			subroutine 3 qffmsdcns3(m,P) quadratic function 
field                   over modular singles fundamental unit, baby step 
			version qffmsfubs(m,D) quadratic function 
field                   over modular singles fundamental unit, original 
			version qffmsfuobs(m,D) quadratic function 
field                   over modular singles ideal class group generators 
			and isomorphy type, imaginary case 
			qffmsicggii(m,D,H,L,pIT) quadratic function 
field                   over modular singles ideal class group generators 
			and isomorphy type, real case 
			qffmsicggir(m,D,d,H,L,pIT) quadratic function 
field                   over modular singles ideal class group structure, 
			imaginary case qffmsicgsti(m,D,L) quadratic 
			function 
field                   over modular singles ideal class group structure, 
			real case qffmsicgstr(m,D,d,LG,pHid) quadratic 
			function 
field                   over modular singles ideal class group system of 
			representatives qffmsicgrep(m,D,pHid) quadratic 
			function 
field                   over modular singles ideal class group system of 
			representatives, imaginary case 
			qffmsicgri(m,D,pHid) quadratic function 
field                   over modular singles ideal class group system of 
			representatives, real case qffmsicgrr(m,D,d) 
			quadratic function 
field                   over modular singles ideal class number 
			qffmsicn(m,P) quadratic function 
field                   over modular singles is element of an ideal class 
			qffmsiselic(m,D,L,Q,P) quadratic function 
field                   over modular singles is equal ideal special 
			qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic function 
field                   over modular singles order of one single ideal 
			class, imaginary case qffmsordsici(m,D,Q,P,OS) 
			quadratic function 
field                   over modular singles order of one single ideal 
			class, real case qffmsordsicr(m,D,d,LE,ID,OS) 
			quadratic function 
field                   over modular singles primitive ideal product 
			qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function 
field                   over modular singles primitive ideal product, 
			special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function 
field                   over modular singles primitive ideal square 
			qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
field                   over modular singles primitive ideal square, 
			special version qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) 
			quadratic function 
field                   over modular singles reduction of a real quadratic 
			irrational qffmsrqired(m,D,d,Q,P,pPr) quadratic 
			function 
field                   over modular singles regulator qffmsreg(m,P) 
			quadratic function 
field                   over modular singles regulator, baby step - giant 
			step version qffmsregbg(m,D) quadratic function 
field                   over modular singles regulator, baby step - giant 
			step version, first case qffmsregbg1(m,D,s) 
			quadratic function 
field                   over modular singles regulator, baby step - giant 
			step version, fourth case qffmsregbg4(m,D,s) 
			quadratic function 
field                   over modular singles regulator, baby step - giant 
			step version, second case qffmsregbg2(m,D,s) 
			quadratic function 
field                   over modular singles regulator, baby step - giant 
			step version, third case qffmsregbg3(m,D,s) 
			quadratic function 
field                   over modular singles regulator, baby step version 
			qffmsregbs(m,D) quadratic function 
field                   over modular singles regulator, original baby step 
			- giant step version qffmsregobg(m,D) quadratic 
			function 
field                   over modular singles regulator, original baby step 
			version qffmsregobs(m,D) quadratic function 
field                   over modular singles zero class group isomorphy 
			type, imaginary case qffmszcgiti(m,D,LG,IT) 
			quadratic function 
field                   over modular singles zero class group isomorphy 
			type, real case qffmszcgitr(m,D,d,H,LG,R,IT) 
			quadratic function 
field                   over modular singles, imaginary case, primitive 
			ideal reduction qffmsipidred(m,D,Q,P,pQr,pPr) 
			quadratic function 
field                   over modular singles, imaginary case, sparse 
			representation, reduction of a primitive ideal 
			qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic function 
field                   over modular singles, principal ideal generating 
			element, real case, qffmspidgenr(m,D,Q,P,G,pB) 
			quadratic function 
field                   over modular singles, real case, reduction of a 
			primitive ideal qffmsrpidred(m,D,d,Q,P,pQr,pPr) 
			quadratic function 
field                   over modular singles, real case, sparse 
			representation, reduction of a primitive ideal 
			qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function 
field                   over modular singles, sparse representation, 
			primitive ideal product 
			qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function 
field                   over modular singles, sparse representation, 
			primitive ideal product, special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function 
field                   over modular singles, sparse representation, 
			primitive ideal square 
			qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
field                   over modular singles, sparse representation, 
			primitive ideal square, special version 
			qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function 
field                   over modular singles, sparse representation, 
			reduction of a real quadratic irrational 
			qffmssrqired(m,D,d,Q,P,pPr) quadratic function 
field                   p-adic field element product ppfpfprod(r,p,P,b) 
			polynomial over p-adic 
field                   p-adic field element product udppfpfprod(p,P,a) 
			univariate dense polynomial over p-adic 
field                   pitoppf(r,P,p,d) polynomial over integers to 
			polynomial over p-adic 
field                   point at infinity ? isppecnfpai(P) is projective 
			point of an elliptic curve over number 
field                   prime ideal homomorphism qnfpihom(D,P,pi,z,a) 
			quadratic number 
field                   prime power product ppfpprod(r,p,P,i) polynomial 
			over p-adic 
field                   prime power product udppfpprod(p,P,i) univariate 
			dense polynomial over p-adic 
field                   product (rekursiv) pnfprod(r,F,P1,P2) polynomial 
			over number 
field                   product dipnfprod(r,F,P1,P2) distributive 
			polynomial over number 
field                   product mapnfprod(r,F,M,N) (MACRO) matrix of 
			polynomials over number 
field                   product ppfprod(r,p,P1,P2) polynomial over p-adic 
field                   product udppfprod(p,P1,P2) univariate dense 
			polynomial over p-adic 
field                   prtoppf(r,P,p,d) polynomial over rationals to 
			polynomial over p-adic 
field                   putmapnf(r,F,M,V,Vnf) (MACRO) put matrix of 
			polynomials over number 
field                   putpnf(r,F,P,V,Vnf) (MACRO) put polynomial over 
			number 
field                   putppf(r,p,P,V) put polynomial over p-adic 
field                   putvecpnf(r,F,W,VL,VLnf) (MACRO) put vector of 
			polynomials over number 
field                   quotient and remainder (rekursiv) 
			pnfqrem(r,F,P1,P2,pR) polynomial over number 
field                   quotient nfquot(F,a,b) number 
field                   quotient pfquot(p,a,b) p-adic 
field                   quotient pnfquot(r,F,P1,P2) (MACRO) polynomial over 
			number 
field                   ramification indices qnframind(D,p) quadratic 
			number 
field                   rational number product (rekursiv) 
			ppfrprod(r,p,P,R) polynomial over p-adic 
field                   relative class number abnfrelcl(q,g) abelian number 
field                   relative class number modulo prime 
			abnfrelclmp(m,q,g) abelian number 
field                   remainder pnfrem(r,F,P1,P2) (MACRO) polynomial over 
			number 
field                   scalar multiplication mapnfsmul(r,F,M,el) matrix of 
			polynomials over number 
field                   scalar multiplication vecpnfsmul(r,F,U,el) vector 
			of polynomials over number 
field                   scalar product vpnfsprod(r,F,V,W) vector of 
			polynomials over number 
field                   short normal form line through points 
			ecnfsnflp(F,a,b,P1,P2) elliptic curve over number 
field                   short normal form multiplication-map 
			ecnfsnfmul(F,a,b,n,P1) elliptic curve over number 
field                   short normal form negative point 
			ecnfsnfneg(F,a,b,P) elliptic curve over number 
field                   short normal form sum of points 
			ecnfsnfsum(F,a,b,P1,P2) elliptic curve over number 
field                   squarefree factorization upnfsfact(F,P) univariate 
			polynomial over number 
field                   standard representation of projective point 
			ecnfsrpp(F,P) elliptic curve over number 
field                   substitution, main variable ppfsubst(r,p,P1,P2) 
			polynomial over p-adic 
field                   substitution, selected variable 
			ppfsubstsv(r,p,P1,n,P2) polynomial over p-adic 
field                   sum (rekursiv) pnfsum(r,F,P1,P2) polynomial over 
			number 
field                   sum dipnfsum(r,F,P1,P2) distributive polynomial 
			over number 
field                   sum mapnfsum(r,F,M,N) (MACRO) matrix of polynomials 
			over number 
field                   sum of points ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over number 
field                   sum ppfsum(r,p,P1,P2) polynomial over p-adic 
field                   sum udppfsum(p,P1,P2) univariate dense polynomial 
			over p-adic 
field                   sum vecpnfsum(r,F,U,V) (MACRO) vector of 
			polynomials over number 
field                   system of representatives modulo a prime ideal 
			qnfsysrmodpi(D,P,pi,z,k) quadratic number 
field                   to elliptic curve with integral coefficients 
			ecqnftoeci(D,L) elliptic curve over quadratic 
			number 
field                   to matrix of polynomials modulo polynomial over 
			number field mapnftomapmp(r,F,P,M) matrix of 
			polynomials over number 
field                   to matrix of polynomials over rationals 
			mapnftomapr(r,M) matrix of polynomials over number 
field                   to polynomial over rationals pnftopr(r,P) 
			polynomial over number 
field                   to short normal form ecnftosnf(F,a1,a2,a3,a4,a6) 
			elliptic curve over number 
field                   to vector of polynomials modulo polynomial over 
			number field vecpnftovpmp(r,F,P,V) vector of 
			polynomials over number 
field                   to vector of polynomials over rationals 
			vecpnftovpr(r,V) vector of polynomials over number 
field                   trace of an element qnftrace(D,a) quadratic number 
field                   transformation 
			mapnftransf(r1,F,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over number 
field                   transformation 
			pnftransf(r1,F,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over number 
field                   transformation 
			ppftransf(r1,p,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over p-adic 
field                   transformation 
			vpnftransf(r1,F,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over number 
field                   translation, all variables ppftransav(r,p,P,Lpf) 
			polynomial over p-adic 
field                   translation, main variable ppftrans(r,p,P,A) 
			polynomial over p-adic 
field                   udpitoudppf(P,p,d) univariate dense polynomial over 
			integers to univariate dense polynomial over p-adic 
field                   udprtoudppf(P,p,d) univariate dense polynomial over 
			rationals to univariate dense polynomial over 
			p-adic 
field                   unit group qnfunit(D) quadratic number 
field                   vecpitovpnf(r,V) vector of polynomials over 
			integers to vector of polynomials over number 
field                   vecpnftovpmp(r,F,P,V) vector of polynomials over 
			number field to vector of polynomials modulo 
			polynomial over number 
field                   vecprtovpnf(r,V) vector of polynomials over 
			rationals to vector of polynomials over number 
field                   vector multiplication mapnfvecmul(r,F,A,x) (MACRO) 
			matrix of polynomials over number 
field                   with characteristic 2 isomorphic embedding of 
			subfield gf2ies(Gm,Gn,n) Galois 
field                   with characteristic 2, combined Schoof- Shanks- 
			algorithm ecgf2cssa(G,a6,s,pl,ts) elliptic curve 
			over Galois 
field                   with characteristic 2, number of points after field 
			extension ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) 
			elliptic curve over Galois 
field                   with total degree ordering dipnflototdo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order to distributive polynomial 
			over number 
field,                  Tate's algorithm ecqnftatealg(D,LC,LTV,P,pi,z,n) 
			elliptic curve over quadratic number 
field,                  actual model, Tate value b2 ecqnfacb2(E) elliptic 
			curve over quadratic number 
field,                  actual model, Tate value b4 ecqnfacb4(E) elliptic 
			curve over quadratic number 
field,                  actual model, Tate value b6 ecqnfacb6(E) elliptic 
			curve over quadratic number 
field,                  actual model, Tate value b8 ecqnfacb8(E) elliptic 
			curve over quadratic number 
field,                  actual model, Tate value c4 ecqnfacc4(E) elliptic 
			curve over quadratic number 
field,                  actual model, Tate value c6 ecqnfacc6(E) elliptic 
			curve over quadratic number 
field,                  actual model, discriminant ecqnfacdisc(E) elliptic 
			curve over quadratic number 
field,                  actual model, factorization of the norm of the 
			discriminant ecqnfacfndisc(E) elliptic curve over 
			quadratic number 
field,                  actual model, norm of the discriminant 
			ecqnfacndisc(E) elliptic curve over quadratic 
			number 
field,                  actual model, prime ideal factorization of the 
			discriminant ecqnfacpifdi(E) elliptic curve over 
			quadratic number 
field,                  conductor ecqnfcond(E) elliptic curve over 
			quadratic number 
field,                  field discriminant ecqnfflddisc(E) (MACRO) elliptic 
			curve over quadratic number 
field,                  field discriminant modulo 4 ecqnfdmod4(E) (MACRO) 
			elliptic curve over quadratic number 
field,                  field discriminant nffielddiscr(F) number 
field,                  initialization ecqnfinit(D,a1,a2,a3,a4,a6) elliptic 
			curve over quadratic number 
field,                  integer prime decomposition law nfipdeclaw(F,P) 
			number 
field,                  integral element, prime ideal order 
			qnfielpiord(D,P,pi,z,a) quadratic number 
field,                  j-invariant ecqnfjinv(E) elliptic curve over 
			quadratic number 
field,                  number field element product (rekursiv) 
			pnfnfprod(r,F,P,a) polynomial over number 
field,                  number field element product dipnfnfprod(r,F,P,A) 
			distributive polynomial over number 
field,                  number field element quotient (rekursiv) 
			pnfnfquot(r,F,P,a) polynomial over number 
field,                  short normal form ? iselecnfsnf(F,a,b,P) is element 
			of an elliptic curve over number 
field,                  short normal form, discriminant ecnfsnfdisc(F,a,b) 
			elliptic curve over number 
field,                  short normal form, j-invariant ecnfsnfjinv(F,a,b) 
			elliptic curve over number 
field,                  single prime decomposition law nfspdeclaw(F,p) 
			number 
field,                  sparse representation, difference nfsdif(F,a,b) 
			(MACRO) number 
field,                  sparse representation, inverse nfsinv(F,a) number 
field,                  sparse representation, negation as function 
			nfsnegf(F,a) number 
field,                  sparse representation, negation nfsneg(F,a) (MACRO) 
			number 
field,                  sparse representation, product nfsprod(F,a,b) 
			number 
field,                  sparse representation, quotient nfsquot(F,a,b) 
			number 
field,                  sparse representation, sum as function 
			nfssumf(F,a,b) number 
field,                  sparse representation, sum nfssum(F,a,b) (MACRO) 
			number 
fields                  qnfdegrescf(D,p) quadratic number field degrees of 
			the residue class 
fifth                   lfifth(L) (MACRO) list 
file                    get Galois-field with characteristic 2 element 
			fgetgf2el(G,V,pf) 
file                    get Galois-field with single characteristic element 
			fgetgfsel(p,AL,V,pf) 
file                    get atom fgeta(pf) 
file                    get character fgetc(pf) (MACRO) 
file                    get character, skipping blanks fgetcb(pf) 
file                    get character, skipping space fgetcs(pf) 
file                    get distributive polynomial over Galois-field with 
			single characteristic list 
			fgetdipgfsl(r,p,AL,VL,Vgfs,pf) 
file                    get distributive polynomial over integers list 
			fgetdipil(r,VL,pf) 
file                    get distributive polynomial over modular integer 
			primes list fgetdipmipl(r,p,VL,pf) 
file                    get distributive polynomial over modular single 
			primes list fgetdipmspl(r,p,VL,pf) 
file                    get distributive polynomial over number field list 
			fgetdipnfl(r,F,VL,Vnf,pf) 
file                    get distributive polynomial over polynomials over 
			integers case distinction 
			fgetdippicd(r1,r2,VL1,VL2,fac,pf) 
file                    get distributive polynomial over polynomials over 
			integers list fgetdippil(r1,r2,VL1,VL2,pf) 
file                    get distributive polynomial over rational functions 
			over the rationals list 
			fgetdiprfrl(r1,r2,VL1,VL2,pf) 
file                    get distributive polynomial over rationals list 
			fgetdiprl(r,VL,pf) 
file                    get elliptic curve over rational numbers 
			fgetecr(pf) 
file                    get floating point fgetfl(pf) 
file                    get integer fgeti(pf) 
file                    get list (rekursiv) fgetl(pf) 
file                    get list of integers fgetli(pf) 
file                    get list of rational numbers fgetlr(pf) 
file                    get matrix 
			fgetma(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) 
file                    get matrix of Galois-field with single 
			characteristic elements fgetmagfs(p,AL,V,pf) 
			(MACRO) 
file                    get matrix of integers fgetmai(pf) (MACRO) 
file                    get matrix of modular integers fgetmami(m,pf) 
			(MACRO) 
file                    get matrix of modular singles fgetmams(m,pf) 
			(MACRO) 
file                    get matrix of number field elements 
			fgetmanf(F,VL,pf) (MACRO) 
file                    get matrix of number field elements, sparse 
			representation fgetmanfs(F,VL,pf) (MACRO) 
file                    get matrix of polynomials over Galois-field with 
			single characteristic fgetmapgfs(r,p,AL,V,Vgfs,pf) 
			(MACRO) 
file                    get matrix of polynomials over integers 
			fgetmapi(r,V,pf) (MACRO) 
file                    get matrix of polynomials over modular integers 
			fgetmapmi(r,m,V,pf) (MACRO) 
file                    get matrix of polynomials over modular singles 
			fgetmapms(r,m,V,pf) (MACRO) 
file                    get matrix of polynomials over number field 
			fgetmapnf(r,F,V,Vnf,pf) (MACRO) 
file                    get matrix of polynomials over rationals 
			fgetmapr(r,V,pf) (MACRO) 
file                    get matrix of rational functions over modular 
			single primes, transcendence degree 1 
			fgetmarfmsp1(p,V,pf) (MACRO) 
file                    get matrix of rational functions over rationals 
			fgetmarfr(r,V,pf) (MACRO) 
file                    get matrix of rationals fgetmar(pf) (MACRO) 
file                    get matrix special 
			fgetmaspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
file                    get modular integer fgetmi(M,pf) 
file                    get modular single fgetms(m,pf) 
file                    get number field element fgetnfel(F,V,pf) 
file                    get number field element, sparse representation 
			fgetnfels(F,V,pf) 
file                    get object fgeto(pf) 
file                    get p-adic field element fgetpfel(p,pf) 
file                    get point on elliptic curve over rational numbers 
			fgetecrp(pf) 
file                    get polynomial over Galois-field with 
			characteristic 2 fgetpgf2(r,G,V,Vgf2,pf) 
file                    get polynomial over Galois-field with single 
			characteristic fgetpgfs(r,p,AL,V,Vgfs,pf) 
file                    get polynomial over integers fgetpi(r,V,pf) 
file                    get polynomial over modular integers 
			fgetpmi(r,M,V,pf) 
file                    get polynomial over modular singles 
			fgetpms(r,m,V,pf) 
file                    get polynomial over number field 
			fgetpnf(r,F,V,Vnf,pf) 
file                    get polynomial over p-adic field fgetppf(r,p,V,pf) 
file                    get polynomial over rationals fgetpr(r,V,pf) 
file                    get quadratic number field element fgetqnfel(D,pf) 
file                    get rational function over modular single primes, 
			transcendence degree 1 fgetrfmsp1(p,V,pf) 
file                    get rational function over rationals 
			fgetrfr(r,V,pf) 
file                    get rational number fgetr(pf) 
file                    get single fgetsi(pf) 
file                    get special p-adic field element fgetspfel(p,pf) 
file                    get string fgets(s,n,pf) (MACRO) 
file                    get variable list fgetvl(pf) 
file                    get vector 
			fgetvec(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) 
file                    get vector of Galois-field with single 
			characteristic elements fgetvecgfs(p,AL,VL,pf) 
			(MACRO) 
file                    get vector of integers fgetveci(pf) (MACRO) 
file                    get vector of modular integers fgetvecmi(m,pf) 
			(MACRO) 
file                    get vector of modular singles fgetvecms(m,pf) 
			(MACRO) 
file                    get vector of number field elements 
			fgetvecnf(F,VL,pf) (MACRO) 
file                    get vector of number field elements, sparse 
			representation fgetvecnfs(F,VL,pf) (MACRO) 
file                    get vector of polynomials over Galois-field with 
			single characteristic fgetvpgfs(r,p,AL,V,Vgfs,pf) 
			(MACRO) 
file                    get vector of polynomials over integers 
			fgetvecpi(r,VL,pf) (MACRO) 
file                    get vector of polynomials over modular integers 
			fgetvecpmi(r,m,VL,pf) (MACRO) 
file                    get vector of polynomials over modular singles 
			fgetvecpms(r,m,VL,pf) (MACRO) 
file                    get vector of polynomials over number field 
			fgetvecpnf(r,F,VL,VLnf,pf) (MACRO) 
file                    get vector of polynomials over rationals 
			fgetvecpr(r,VL,pf) (MACRO) 
file                    get vector of rational functions over modular 
			single primes, transcendence degree 1 
			fgetvrfmsp1(p,VL,pf) (MACRO) 
file                    get vector of rational functions over rationals 
			fgetvecrfr(r,VL,pf) (MACRO) 
file                    get vector of rationals fgetvecr(pf) (MACRO) 
file                    get vector special 
			fgetvecspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
file                    lines flines(k,pf) 
file                    print formated fprintf(pf,format[,arg]...) (MACRO) 
file                    put Galois-field with characteristic 2 element 
			fputgf2el(G,a,V,pf) 
file                    put Galois-field with single characteristic element 
			fputgfsel(p,AL,a,V,pf) 
file                    put atom fputa(a,pf) 
file                    put bits fputbits(s,pf) 
file                    put character fputc(c,pf) (MACRO) 
file                    put complex number fputcn(a,v,n,pf) 
file                    put distributive polynomial dimension 
			fputdipdim(r,dim,S,M,VL,pf) 
file                    put distributive polynomial over Galois-field with 
			single characteristic list 
			fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) 
file                    put distributive polynomial over integers list 
			fputdipil(r,PL,VL,pf) 
file                    put distributive polynomial over modular integer 
			primes list fputdipmipl(r,p,PL,VL,pf) 
file                    put distributive polynomial over modular single 
			primes list fputdipmspl(r,p,PL,VL,pf) 
file                    put distributive polynomial over number field list 
			fputdipnfl(r,F,PL,VL,Vnf,pf) 
file                    put distributive polynomial over polynomials over 
			integers Groebner system 
			fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) 
file                    put distributive polynomial over polynomials over 
			integers Groebner test 
			fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) 
file                    put distributive polynomial over polynomials over 
			integers comprehensive Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) 
file                    put distributive polynomial over polynomials over 
			integers dimension 
			fputdippidim(r1,r2,DIML,VL1,VL2,pf) 
file                    put distributive polynomial over polynomials over 
			integers list fputdippil(r1,r2,PL,VL1,VL2,pf) 
file                    put distributive polynomial over polynomials over 
			integers parametric ideal membership test 
			fputdippipim(r1,r2,NOUT,VL1,VL2,pf) 
file                    put distributive polynomial over polynomials over 
			integers quantifier free formula 
			fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) 
file                    put distributive polynomial over rational functions 
			over the rationals list 
			fputdiprfrl(r1,r2,PL,VL1,VL2,pf) 
file                    put distributive polynomial over rationals list 
			fputdiprl(r,PL,VL,pf) 
file                    put elliptic curve fputecr(E,pf) 
file                    put elliptic curve over rational numbers, actual 
			curve fputecrac(E,pf) 
file                    put elliptic curve over rational numbers, point 
			fputecrp(P,pf) 
file                    put elliptic curve over the rational numbers, 
			invariants fputecrinv(E,pf) 
file                    put elliptic curve over the rational numbers, list 
			of points fputecrlistp(P,modus,pf) 
file                    put elliptic curve with integer coefficients, 
			minimal model fputecimin(E,pf) 
file                    put elliptic curve with integer coefficients, short 
			normal form fputecisnf(E,*pf) 
file                    put factor list fputfactl(L,pf) 
file                    put floating point by fix point 
			fputflfx(f,vk,nk,pf) 
file                    put floating point fputfl(f,n,pf) 
file                    put integer factor exponent list fputifel(L,pf) 
file                    put integer fputi(A,pf) 
file                    put list (rekursiv) fputl(L,pf) 
file                    put list of integers fputli(L,pf) 
file                    put list of polynomials over integers 
			fputlpi(r,L,V,pf) 
file                    put list of polynomials over rationals 
			fputlpr(r,L,V,pf) 
file                    put list of rationals fputlr(L,pf) 
file                    put list structure (rekursiv) fputlstruct(L,pf) 
file                    put matrix 
			fputma(M,pf,fputfkt,anzahlargs,arg1,arg2,arg3) 
file                    put matrix of Galois-field with single 
			characteristic elements fputmagfs(p,AL,M,V,pf) 
			(MACRO) 
file                    put matrix of floatings by fix point 
			fputmaflfx(M,v,n,pf) 
file                    put matrix of integers fputmai(M,pf) (MACRO) 
file                    put matrix of modular integers fputmami(m,M,pf) 
			(MACRO) 
file                    put matrix of modular singles fputmams(m,M,pf) 
			(MACRO) 
file                    put matrix of number field elements 
			fputmanf(F,M,VL,pf) (MACRO) 
file                    put matrix of number field elements, sparse 
			representation fputmanfs(F,M,VL,pf) (MACRO) 
file                    put matrix of polynomials over Galois-field with 
			single characteristic 
			fputmapgfs(r,p,AL,M,V,Vgfs,pf) (MACRO) 
file                    put matrix of polynomials over integers 
			fputmapi(r,M,V,pf) (MACRO) 
file                    put matrix of polynomials over modular integers 
			fputmapmi(r,m,M,V,pf) (MACRO) 
file                    put matrix of polynomials over modular singles 
			fputmapms(r,m,M,V,pf) (MACRO) 
file                    put matrix of polynomials over number field 
			fputmapnf(r,F,M,V,Vnf,pf) (MACRO) 
file                    put matrix of polynomials over rationals 
			fputmapr(r,M,V,pf) (MACRO) 
file                    put matrix of rational functions over modular 
			single primes, transcendence degree 1 
			fputmarfmsp1(p,M,V,pf) (MACRO) 
file                    put matrix of rational functions over rationals 
			fputmarfr(r,M,V,pf) (MACRO) 
file                    put matrix of rationals fputmar(M,pf) (MACRO) 
file                    put matrix of singles fputmas(M) 
file                    put matrix special 
			fputmaspec(M,pf,fputfkt,anzahlargs,arg1,...,arg8) 
file                    put modular integer fputmi(M,A,pf) 
file                    put modular single fputms(m,a,pf) 
file                    put number field element fputnfel(F,a,V,pf) 
file                    put number field element, sparse representation 
			fputnfels(F,a,V,pf) 
file                    put object fputo(a,pf) (MACRO) 
file                    put original number field element 
			fputonfel(F,a,V,pf) 
file                    put p-adic field element fputpfel(p,a,pf) 
file                    put polynomial over Galois-field 
			fputpgfs(r,p,AL,P,V,Vgfs,pf) 
file                    put polynomial over Galois-field with 
			characteristic 2 fputpgf2(r,G,P,V,Vgf2,pf) 
file                    put polynomial over integers fputpi(r,P,V,pf) 
file                    put polynomial over modular integers 
			fputpmi(r,M,P,V,pf) 
file                    put polynomial over modular singles 
			fputpms(r,m,P,V,pf) 
file                    put polynomial over number field 
			fputpnf(r,F,P,V,Vnf,pf) 
file                    put polynomial over p-adic field 
			fputppf(r,p,P,V,pf) 
file                    put polynomial over rationals fputpr(r,P,V,pf) 
file                    put quadratic number field element factor exponent 
			list fputqnffel(D,L,pf) 
file                    put quadratic number field element 
			fputqnfel(D,a,pf) 
file                    put quadratic number field ideal fputqnfid(D,A,pf) 
file                    put rational function over modular single prime, 
			transcendence degree 1 fputrfmsp1(p,R,V,pf) (MACRO) 
file                    put rational function over rationals 
			fputrfr(r,R,V,pf) 
file                    put rational number decimal fputrd(R,n,pf) 
file                    put rational number fputr(R,pf) 
file                    put single precision fputsi(n,pf) 
file                    put special p-adic field element fputspfel(p,a,pf) 
file                    put string fputs(s,pf) (MACRO) 
file                    put vector 
			fputvec(V,pf,fputfkt,anzahlargs,arg1,arg2,arg3) 
file                    put vector of Galois-field with single 
			characteristic elements fputvecgfs(p,AL,V,VL,pf) 
			(MACRO) 
file                    put vector of integers fputveci(V,pf) (MACRO) 
file                    put vector of modular integers fputvecmi(m,V,pf) 
			(MACRO) 
file                    put vector of modular singles fputvecms(m,V,pf) 
			(MACRO) 
file                    put vector of number field elements 
			fputvecnf(F,V,VL,pf) (MACRO) 
file                    put vector of number field elements, sparse 
			representation fputvecnfs(F,V,VL,pf) (MACRO) 
file                    put vector of polynomials over Galois-field with 
			single characteristic fputvpgfs(r,p,AL,W,V,Vgfs,pf) 
			(MACRO) 
file                    put vector of polynomials over integers 
			fputvecpi(r,V,VL,pf) (MACRO) 
file                    put vector of polynomials over modular integers 
			fputvecpmi(r,m,V,VL,pf) (MACRO) 
file                    put vector of polynomials over modular singles 
			fputvecpms(r,m,V,VL,pf) (MACRO) 
file                    put vector of polynomials over number field 
			fputvecpnf(r,F,W,VL,VLnf,pf) (MACRO) 
file                    put vector of polynomials over rationals 
			fputvecpr(r,V,VL,pf) (MACRO) 
file                    put vector of rational functions over modular 
			single primes, transcendence degree 1 
			fputvrfmsp1(p,V,VL,pf) (MACRO) 
file                    put vector of rational functions over rationals 
			fputvecrfr(r,V,VL,pf) (MACRO) 
file                    put vector of rationals fputvecr(V,pf) (MACRO) 
file                    put vector special 
			fputvecspec(V,pf,fputfkt,anzahlargs,arg1,...,arg8) 
file                    tabulator ftab(n,pf) 
find                    non square mipfnsquare(p) modular integer prime 
find                    point ecgf2fp(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with characteristic 2, 
find                    point ecmpfp(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular primes, 
find                    point ecmpsnffp(p,a4,a6) elliptic curve over 
			modular primes, short normal form, 
find                    point iecfindp(p,a,b) integer elliptic curve 
find                    square mipfsquare(p) modular integer prime 
finding                 (rekursiv) upgfsrf(p,AL,P) univariate polynomial 
			over Galois-field with single characteristic root 
finding                 (rekursiv) upmirf(ip,P) univariate polynomial over 
			modular integers, root 
finding                 (rekursiv) upmsrf(m,P) univariate polynomial over 
			modular singles, root 
finding                 a multiple of the order of a point with the Pollard 
			Lambda method ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) 
			elliptic curve over Galois-field with 
			characteristic 2, 
finding                 a multiple of the order of a point with the Pollard 
			Lambda method ecmpsnffmopl(p,a4,a6,P,L,N) elliptic 
			curve over modular primes, short normal form, 
finding                 a multiple of the order of a point with the Pollard 
			Rho method ecmpsnffmopr(p,a4,a6,P,k) elliptic curve 
			over modular primes, short normal form, 
finding,                special (rekursiv) upmirfspec(ip,P) univariate 
			polynomial over modular integers, root 
first                   case qffmsregbg1(m,D,s) quadratic function field 
			over modular singles regulator, baby step - giant 
			step version, 
first                   derivative ecrlserfd(E) elliptic curve over 
			rational numbers, L-series, 
first                   derivative, special version ecrlserfds(E,A,result) 
			elliptic curve over the rationals, L-series, 
first                   lfirst(L) (MACRO) list 
first                   lsfirst(L,a) (MACRO) list set 
first                   part ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) 
			elliptic curve over Galois-field with 
			characteristic 2, modified Shanks' algorithm, 
first                   part ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic 
			curve over modular primes, short normal form, 
			modified Shanks' algorithm, 
first                   variable special version (rekursiv) 
			pigf2evalfvs(r,G,P) polynomial over integers 
			Galois-field with characteristic 2 element 
			evaluation 
first                   variable special version (rekursiv) 
			pigfsevalfvs(r,p,AL,P) polynomial over integers 
			Galois-field with single characteristic element 
			evaluation 
first                   variable special version mapigfsevfvs(r,p,AL,M) 
			matrix over polynomials over integers Galois-field 
			with single characteristic element evaluation 
first                   variable special version mapinfevlfvs(r,F,M) matrix 
			of polynomials over integers number field element 
			evaluation 
first                   variable special version maprnfevlfvs(r,F,M) matrix 
			of polynomials over rationals number field element 
			evaluation 
first                   variable special version pinfevalfvs(r,F,P) 
			polynomial over integers number field element 
			evaluation 
first                   variable special version prnfevalfvs(r,F,P) 
			polynomial over rationals number field element 
			evaluation 
first                   variable special version vecpigfsefvs(r,p,AL,V) 
			vector over polynomials over integers Galois-field 
			with single characteristic element evaluation 
first                   variable special version vpinfevalfvs(r,F,V) vector 
			of polynomials over integers number field element 
			evaluation 
first                   variable special version vprnfevalfvs(r,F,V) vector 
			of polynomials over rationals number field element 
			evaluation 
fitting                 ppffit(r,p,P,d) polynomial over p-adic field 
fitting                 udppffit(p,P,Pd) univariate dense polynomial over 
			p-adic field 
fix                     point fputflfx(f,vk,nk,pf) file put floating point 
			by 
fix                     point fputmaflfx(M,v,n,pf) file put matrix of 
			floatings by 
fix                     point putflfx(f,vk,nk) (MACRO) put floating point 
			by 
fix                     point putmaflfx(M,v,n) (MACRO) put matrix of 
			floatings by 
flPAFfu(func,anzahlargs,arg1,arg2) floating point using Papanikolaou 
			floating point functions 
flPi()                  floating point Pi 
flabs(f)                (MACRO) floating point absolute value 
flagm(a,b)              floating point aritho-geometric mean 
flath_sp(f)             floating point area tangens hyperbolicus special 
			version 
flatn_sp(f)             floating point arcus tangens special version 
flcomp(f,g)             floating point comparison 
flcons(A,e,lA)          floating point construction 
flcos(a)                floating point cosinus 
flcos_sp(f)             floating point cosinus special version 
flcut(A,e,lA)           floating point construction by cutting 
fldif(f,g)              (MACRO) floating point difference 
flerr()                 (MACRO) floating point overflow error handling 
flexp(f)                floating point exponential function 
flexpo(f)               (MACRO) floating point exponent 
flfloor(f)              floating point floor 
flines(k,pf)            file lines 
flinit(k)               floating point initialization 
fllog(f)                floating point natural logarithm (rekursiv) 
flmant(f)               (MACRO) floating point mantissa 
flneg(f)                floating point negation 
floating                point ? isfloat(A) is 
floating                point Cfltofl(x) C-floating point to 
floating                point PAFtofl(x) Papanikolaou floating point to ( 
			SIMATH ) 
floating                point Pi flPi() 
floating                point absolute value flabs(f) (MACRO) 
floating                point arcus tangens special version flatn_sp(f) 
floating                point area tangens hyperbolicus special version 
			flath_sp(f) 
floating                point aritho-geometric mean flagm(a,b) 
floating                point by fix point fputflfx(f,vk,nk,pf) file put 
floating                point by fix point putflfx(f,vk,nk) (MACRO) put 
floating                point chartofl(A) character to 
floating                point comparison flcomp(f,g) 
floating                point construction by cutting flcut(A,e,lA) 
floating                point construction flcons(A,e,lA) 
floating                point cosinus flcos(a) 
floating                point cosinus special version flcos_sp(f) 
floating                point difference fldif(f,g) (MACRO) 
floating                point exponent flexpo(f) (MACRO) 
floating                point exponential function flexp(f) 
floating                point fgetfl(pf) file get 
floating                point floor flfloor(f) 
floating                point fltoPAF(f,x) ( SIMATH ) floating point to 
			Papanikolaou 
floating                point fltofl(f) (MACRO) floating point to 
floating                point fputfl(f,n,pf) file put 
floating                point functions flPAFfu(func,anzahlargs,arg1,arg2) 
			floating point using Papanikolaou 
floating                point getfl() (MACRO) get 
floating                point initialization flinit(k) 
floating                point itofl(A) (MACRO) integer to 
floating                point mantissa flmant(f) (MACRO) 
floating                point natural logarithm (rekursiv) fllog(f) 
floating                point negation flneg(f) 
floating                point overflow error floverflow(a) 
floating                point overflow error handling flerr() (MACRO) 
floating                point package: I/O-functions PAFio() Papanikolaou 
floating                point package: addition PAFadd() Papanikolaou 
floating                point package: assignments PAFassign() Papanikolaou 
floating                point package: comparisons PAFcomp() Papanikolaou 
floating                point package: construction PAFcon() Papanikolaou 
floating                point package: division PAFdiv() Papanikolaou 
floating                point package: globals PAFglob() Papanikolaou 
floating                point package: multiplication PAFmul() Papanikolaou 
floating                point package: shiftings PAFshift() Papanikolaou 
floating                point package: subtraction PAFsub() Papanikolaou 
floating                point package: transcendental functions 1 
			PAFtrans1() Papanikolaou 
floating                point package: transcendental functions 2 
			PAFtrans2() Papanikolaou 
floating                point package: transcendental functions 3 
			PAFtrans3() Papanikolaou 
floating                point package: typer PAFtype() Papanikolaou 
floating                point package: utilities PAFutil() Papanikolaou 
floating                point power flpow(f,g) 
floating                point product flprod(f,g) 
floating                point putfl(f,n) (MACRO) put 
floating                point quotient flquot(f,g) 
floating                point round flround(f) 
floating                point rtofl(r) rational number to 
floating                point set precision flsetprec(k,N) 
floating                point sgetfl(ps) string get 
floating                point sign flsign(f) (MACRO) 
floating                point single exponentiation flsexp(f,n) 
floating                point single quotient flsquot(f,n) 
floating                point sinus flsin(a) 
floating                point sinus special version flsin_sp(f) 
floating                point special version sgetflsp(ps) string get 
floating                point special version sputflsp(prec,f,str) string 
			put 
floating                point square root flsqrt(f) 
floating                point sum flsum(f,g) 
floating                point to ( SIMATH ) floating point PAFtofl(x) 
			Papanikolaou 
floating                point to C-floating point fltoCfl(f) 
floating                point to Papanikolaou floating point fltoPAF(f,x) ( 
			SIMATH ) 
floating                point to floating point fltofl(f) (MACRO) 
floating                point to rational number fltor(f) 
floating                point trigonometric functions fltrig(Ffunc,f) 
			(MACRO) 
floating                point using Papanikolaou floating point functions 
			flPAFfu(func,anzahlargs,arg1,arg2) 
floating                points sum (rekursiv) pflsum(r,P1,P2) polynomial 
			over 
floating                quotient and remainder flqrem(A,B,pQ,pR) 
floatings               by fix point fputmaflfx(M,v,n,pf) file put matrix 
			of 
floatings               by fix point putmaflfx(M,v,n) (MACRO) put matrix of 
floatings               determinant mafldet(M) matrix of 
floor                   flfloor(f) floating point 
floor                   rfloor(R) rational number 
floverflow(a)           floating point overflow error 
flpow(f,g)              floating point power 
flprod(f,g)             floating point product 
flqrem(A,B,pQ,pR)       floating quotient and remainder 
flquot(f,g)             floating point quotient 
flround(f)              floating point round 
flsetprec(k,N)          floating point set precision 
flsexp(f,n)             floating point single exponentiation 
flsign(f)               (MACRO) floating point sign 
flsin(a)                floating point sinus 
flsin_sp(f)             floating point sinus special version 
flsqrt(f)               floating point square root 
flsquot(f,n)            floating point single quotient 
flsum(f,g)              floating point sum 
fltoCfl(f)              floating point to C-floating point 
fltoPAF(f,x)            ( SIMATH ) floating point to Papanikolaou floating 
			point 
fltofl(f)               (MACRO) floating point to floating point 
fltor(f)                floating point to rational number 
fltrig(Ffunc,f)         (MACRO) floating point trigonometric functions 
form                    ( lower triangular form with negative entries ) 
			maihermltne(A) (MACRO) matrix of integers Hermite 
			normal 
form                    ( lower triangular form with positive entries ) 
			maihermltpe(A) (MACRO) matrix of integers Hermite 
			normal 
form                    ? iselecmpsnf(p,a,b,P) is element of an elliptic 
			curve over modular primes, short normal 
form                    ? iselecnfsnf(F,a,b,P) is element of an elliptic 
			curve over number field, short normal 
form                    and cofactors maiedfcf(M,pA,pB) matrix of integers 
			elementary divisor 
form                    and cofactors maupmipedfcf(p,M,pA,pB) matrix of 
			univariate polynomials over modular integer primes 
			elementary divisor 
form                    and cofactors maupmspedfcf(p,M,pA,pB) matrix of 
			univariate polynomials over modular single primes 
			elementary divisor 
form                    and cofactors maupredfcf(M,pA,pB) matrix of 
			univariate polynomials over rationals elementary 
			divisor 
form                    eciminbtsnf(E) elliptic curve with integer 
			coefficients, minimal model, birational 
			transformation to short normal 
form                    ecimintosnf(E) elliptic curve with integer 
			coefficients, minimal model to short normal 
form                    ecmptosnf(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular primes to short normal 
form                    ecnftosnf(F,a1,a2,a3,a4,a6) elliptic curve over 
			number field to short normal 
form                    ecracbtsnf(E) elliptic curve over rational numbers, 
			actual curve, birational transformation to short 
			normal 
form                    fputecisnf(E,*pf) file put elliptic curve with 
			integer coefficients, short normal 
form                    isponecisnf(E,P) is point on elliptic curve with 
			integer coefficients, model in short normal 
form                    line through points ecnfsnflp(F,a,b,P1,P2) elliptic 
			curve over number field short normal 
form                    maiherm(A,ne) matrix of integers Hermite normal 
form                    multiplication-map ecnfsnfmul(F,a,b,n,P1) elliptic 
			curve over number field short normal 
form                    negative point ecnfsnfneg(F,a,b,P) elliptic curve 
			over number field short normal 
form                    number of points special version 
			ecmipsnfnpsv(p,a4,a6) elliptic curve over modular 
			integer primes short normal 
form                    putecisnf(E) (MACRO) put elliptic curve with 
			integer coefficients, short normal 
form                    sum of points ecnfsnfsum(F,a,b,P1,P2) elliptic 
			curve over number field short normal 
form                    with negative entries ) maihermltne(A) (MACRO) 
			matrix of integers Hermite normal form ( lower 
			triangular 
form                    with positive entries ) maihermltpe(A) (MACRO) 
			matrix of integers Hermite normal form ( lower 
			triangular 
form,                   Mordell-Weil-group, base ecisnfmwgbase(E) elliptic 
			curve with integer coefficients, short normal 
form,                   Shanks' algorithm ecmspsnfsha(p,a4,a6) (MACRO) 
			elliptic curve over modular single primes, short 
			normal 
form,                   a4 ecisnfa4(E) elliptic curve with integer 
			coefficients, short normal 
form,                   a6 ecisnfa6(E) elliptic curve with integer 
			coefficients, short normal 
form,                   b2 ecisnfb2(E) elliptic curve with integer 
			coefficients, short normal 
form,                   b4 ecisnfb4(E) elliptic curve with integer 
			coefficients, short normal 
form,                   b6 ecisnfb6(E) elliptic curve with integer 
			coefficients, short normal 
form,                   b8 ecisnfb8(E) elliptic curve with integer 
			coefficients, short normal 
form,                   birational transformation of coefficients 
			ecisnfbtco(E,BT) elliptic curve with integer 
			coefficients, short normal 
form,                   birational transformation to actual ( rational ) 
			model ecisnfbtac(E) elliptic curve with integer 
			coefficients, short normal 
form,                   birational transformation to minimal model 
			ecisnfbtmin(E) elliptic curve with integer 
			coefficients, short normal 
form,                   c4 ecisnfc4(E) elliptic curve with integer 
			coefficients, short normal 
form,                   c6 ecisnfc6(E) elliptic curve with integer 
			coefficients, short normal 
form,                   combined Schoof- Shanks- algorithm 
			ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic curve over 
			modular primes, short normal 
form,                   construction of division polynomials 
			ecmpsnfcdivp(P,a4,a6,n) elliptic curve over modular 
			primes, short normal 
form,                   difference between Weil height and Neron-Tate 
			height ecisnfdwhnth(E) elliptic curve with integer 
			coefficients, short normal 
form,                   discriminant ecisnfdisc(E) elliptic curve with 
			integer coefficients, short normal 
form,                   discriminant ecmpsnfdisc(p,a4,a6) elliptic curve 
			over modular primes, short normal 
form,                   discriminant ecnfsnfdisc(F,a,b) elliptic curve over 
			number field, short normal 
form,                   double of point ecisnfdouble(E,P) elliptic curve 
			with integer coefficients, short normal 
form,                   elliptic logarithm of point ecisnfelogp(E,P,n) 
			elliptic curve with integer coefficients, short 
			normal 
form,                   factorization of discriminant ecisnffdisc(E) 
			elliptic curve with integer coefficients, short 
			normal 
form,                   find point ecmpsnffp(p,a4,a6) elliptic curve over 
			modular primes, short normal 
form,                   finding a multiple of the order of a point with the 
			Pollard Lambda method ecmpsnffmopl(p,a4,a6,P,L,N) 
			elliptic curve over modular primes, short normal 
form,                   finding a multiple of the order of a point with the 
			Pollard Rho method ecmpsnffmopr(p,a4,a6,P,k) 
			elliptic curve over modular primes, short normal 
form,                   generators of the torsion group ecisnfgentor(E) 
			elliptic curve with integer coefficients, short 
			normal 
form,                   j-invariant ecmpsnfjinv(p,a4,a6) elliptic curve 
			over modular primes, short normal 
form,                   j-invariant ecnfsnfjinv(F,a,b) elliptic curve over 
			number field, short normal 
form,                   line through points ecmpsnflp(p,a4,a6,P1,P2) 
			elliptic curve over modular primes, short normal 
form,                   modified Shanks' algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over modular primes, short normal 
form,                   multiple of the order of a point to exact order of 
			the point ecmpsnfmopto(p,a4,a6,P,mul) elliptic 
			curve over modular primes, short normal 
form,                   multiplication-map ecisnfmul(E,P,n) elliptic curve 
			with integer coefficients, short normal 
form,                   multiplication-map ecmpsnfmul(p,a4,a6,n,P1) 
			elliptic curve over modular primes, short normal 
form,                   multiplication-map, special version 
			ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve over 
			Galois-field with characteristic 2, special 
form,                   multiplication-map, special version 
			ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve over 
			modular primes, short normal 
form,                   negative of point ecisnfneg(E,P) elliptic curve 
			with integer coefficients, short normal 
form,                   negative point ecmpsnfneg(p,a4,a6,P) elliptic curve 
			over modular primes, short normal 
form,                   number of points ecmspsnfnp(p,a4,a6) elliptic curve 
			over modular single primes, short normal 
form,                   number of points modulo 2 ecmpsnfnpm2(P,a4,a6) 
			elliptic curve over modular primes, short normal 
form,                   number of points modulo a single prime determined 
			with the Schoof algorithm ecmpsnfnpmsp(P,a4,a6,p,L) 
			elliptic curve over modular primes, short normal 
form,                   number of points modulo an integer determined with 
			the Schoof algorithm ecmpsnfnpmi(P,a4,a6,S,pM) 
			elliptic curve over modular primes, short normal 
form,                   points of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve 
			with integer coefficients, short normal 
form,                   real roots of the right side ecrsnfrroots(a,b) 
			elliptic curve over rational numbers, short normal 
form,                   sum of points ecisnfsum(E,P,Q) elliptic curve with 
			integer coefficients, short normal 
form,                   sum of points ecmpsnfsum(p,a4,a6,P1,P2) elliptic 
			curve over modular primes, short normal 
form,                   sum of points, special version 
			ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic curve over 
			Galois-field with characteristic 2, special 
form,                   sum of points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve 
			over modular primes, short normal 
form,                   torsion group ecisnftorgr(E) elliptic curve with 
			integer coefficients, short normal 
formated                fprintf(pf,format[,arg]...) (MACRO) file print 
formated                printf(format[,arg]...) (MACRO) print 
forms                   iprpdbqf(D,h1,h2) integer primitive reduced 
			positive definite binary quadratic 
formula                 dippiqff(r1,r2,s,PL,CONDS,fac) distributive 
			polynomial over polynomials over integers 
			quantifier free 
formula                 fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers quantifier free 
formula                 putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers quantifier free 
fourth                  case qffmsregbg4(m,D,s) quadratic function field 
			over modular singles regulator, baby step - giant 
			step version, 
fourth                  lfourth(L) (MACRO) list 
fprintf(pf,format[,arg]...) (MACRO) file print formated 
fputa(a,pf)             file put atom 
fputbits(s,pf)          file put bits 
fputc(c,pf)             (MACRO) file put character 
fputcn(a,v,n,pf)        file put complex number 
fputdipdim(r,dim,S,M,VL,pf) file put distributive polynomial dimension 
fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put distributive polynomial over 
			Galois-field with single characteristic list 
fputdipil(r,PL,VL,pf)   file put distributive polynomial over integers list 
fputdipmipl(r,p,PL,VL,pf) file put distributive polynomial over modular 
			integer primes list 
fputdipmspl(r,p,PL,VL,pf) file put distributive polynomial over modular 
			single primes list 
fputdipnfl(r,F,PL,VL,Vnf,pf) file put distributive polynomial over number 
			field list 
fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put distributive polynomial over 
			polynomials over integers comprehensive Groebner 
			basis 
fputdippidim(r1,r2,DIML,VL1,VL2,pf) file put distributive polynomial over 
			polynomials over integers dimension 
fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file put distributive polynomial over 
			polynomials over integers Groebner system 
fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) file put distributive 
			polynomial over polynomials over integers Groebner 
			test 
fputdippil(r1,r2,PL,VL1,VL2,pf) file put distributive polynomial over 
			polynomials over integers list 
fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put distributive polynomial over 
			polynomials over integers parametric ideal 
			membership test 
fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file put distributive polynomial over 
			polynomials over integers quantifier free formula 
fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file put distributive polynomial over 
			rational functions over the rationals list 
fputdiprl(r,PL,VL,pf)   file put distributive polynomial over rationals 
			list 
fputecimin(E,pf)        file put elliptic curve with integer coefficients, 
			minimal model 
fputecisnf(E,*pf)       file put elliptic curve with integer coefficients, 
			short normal form 
fputecr(E,pf)           file put elliptic curve 
fputecrac(E,pf)         file put elliptic curve over rational numbers, 
			actual curve 
fputecrinv(E,pf)        file put elliptic curve over the rational numbers, 
			invariants 
fputecrlistp(P,modus,pf) file put elliptic curve over the rational numbers, 
			list of points 
fputecrp(P,pf)          file put elliptic curve over rational numbers, 
			point 
fputfactl(L,pf)         file put factor list 
fputfl(f,n,pf)          file put floating point 
fputflfx(f,vk,nk,pf)    file put floating point by fix point 
fputgf2el(G,a,V,pf)     file put Galois-field with characteristic 2 element 
fputgfsel(p,AL,a,V,pf)  file put Galois-field with single characteristic 
			element 
fputi(A,pf)             file put integer 
fputifel(L,pf)          file put integer factor exponent list 
fputl(L,pf)             file put list (rekursiv) 
fputli(L,pf)            file put list of integers 
fputlpi(r,L,V,pf)       file put list of polynomials over integers 
fputlpr(r,L,V,pf)       file put list of polynomials over rationals 
fputlr(L,pf)            file put list of rationals 
fputlstruct(L,pf)       file put list structure (rekursiv) 
fputma(M,pf,fputfkt,anzahlargs,arg1,arg2,arg3) file put matrix 
fputmaflfx(M,v,n,pf)    file put matrix of floatings by fix point 
fputmagfs(p,AL,M,V,pf)  (MACRO) file put matrix of Galois-field with single 
			characteristic elements 
fputmai(M,pf)           (MACRO) file put matrix of integers 
fputmami(m,M,pf)        (MACRO) file put matrix of modular integers 
fputmams(m,M,pf)        (MACRO) file put matrix of modular singles 
fputmanf(F,M,VL,pf)     (MACRO) file put matrix of number field elements 
fputmanfs(F,M,VL,pf)    (MACRO) file put matrix of number field elements, 
			sparse representation 
fputmapgfs(r,p,AL,M,V,Vgfs,pf) (MACRO) file put matrix of polynomials over 
			Galois-field with single characteristic 
fputmapi(r,M,V,pf)      (MACRO) file put matrix of polynomials over 
			integers 
fputmapmi(r,m,M,V,pf)   (MACRO) file put matrix of polynomials over modular 
			integers 
fputmapms(r,m,M,V,pf)   (MACRO) file put matrix of polynomials over modular 
			singles 
fputmapnf(r,F,M,V,Vnf,pf) (MACRO) file put matrix of polynomials over number 
			field 
fputmapr(r,M,V,pf)      (MACRO) file put matrix of polynomials over 
			rationals 
fputmar(M,pf)           (MACRO) file put matrix of rationals 
fputmarfmsp1(p,M,V,pf)  (MACRO) file put matrix of rational functions over 
			modular single primes, transcendence degree 1 
fputmarfr(r,M,V,pf)     (MACRO) file put matrix of rational functions over 
			rationals 
fputmas(M)              file put matrix of singles 
fputmaspec(M,pf,fputfkt,anzahlargs,arg1,...,arg8) file put matrix special 
fputmi(M,A,pf)          file put modular integer 
fputms(m,a,pf)          file put modular single 
fputnfel(F,a,V,pf)      file put number field element 
fputnfels(F,a,V,pf)     file put number field element, sparse 
			representation 
fputo(a,pf)             (MACRO) file put object 
fputonfel(F,a,V,pf)     file put original number field element 
fputpfel(p,a,pf)        file put p-adic field element 
fputpgf2(r,G,P,V,Vgf2,pf) file put polynomial over Galois-field with 
			characteristic 2 
fputpgfs(r,p,AL,P,V,Vgfs,pf) file put polynomial over Galois-field 
fputpi(r,P,V,pf)        file put polynomial over integers 
fputpmi(r,M,P,V,pf)     file put polynomial over modular integers 
fputpms(r,m,P,V,pf)     file put polynomial over modular singles 
fputpnf(r,F,P,V,Vnf,pf) file put polynomial over number field 
fputppf(r,p,P,V,pf)     file put polynomial over p-adic field 
fputpr(r,P,V,pf)        file put polynomial over rationals 
fputqnfel(D,a,pf)       file put quadratic number field element 
fputqnffel(D,L,pf)      file put quadratic number field element factor 
			exponent list 
fputqnfid(D,A,pf)       file put quadratic number field ideal 
fputr(R,pf)             file put rational number 
fputrd(R,n,pf)          file put rational number decimal 
fputrfmsp1(p,R,V,pf)    (MACRO) file put rational function over modular 
			single prime, transcendence degree 1 
fputrfr(r,R,V,pf)       file put rational function over rationals 
fputs(s,pf)             (MACRO) file put string 
fputsi(n,pf)            file put single precision 
fputspfel(p,a,pf)       file put special p-adic field element 
fputvec(V,pf,fputfkt,anzahlargs,arg1,arg2,arg3) file put vector 
fputvecgfs(p,AL,V,VL,pf) (MACRO) file put vector of Galois-field with single 
			characteristic elements 
fputveci(V,pf)          (MACRO) file put vector of integers 
fputvecmi(m,V,pf)       (MACRO) file put vector of modular integers 
fputvecms(m,V,pf)       (MACRO) file put vector of modular singles 
fputvecnf(F,V,VL,pf)    (MACRO) file put vector of number field elements 
fputvecnfs(F,V,VL,pf)   (MACRO) file put vector of number field elements, 
			sparse representation 
fputvecpi(r,V,VL,pf)    (MACRO) file put vector of polynomials over 
			integers 
fputvecpmi(r,m,V,VL,pf) (MACRO) file put vector of polynomials over modular 
			integers 
fputvecpms(r,m,V,VL,pf) (MACRO) file put vector of polynomials over modular 
			singles 
fputvecpnf(r,F,W,VL,VLnf,pf) (MACRO) file put vector of polynomials over 
			number field 
fputvecpr(r,V,VL,pf)    (MACRO) file put vector of polynomials over 
			rationals 
fputvecr(V,pf)          (MACRO) file put vector of rationals 
fputvecrfr(r,V,VL,pf)   (MACRO) file put vector of rational functions over 
			rationals 
fputvecspec(V,pf,fputfkt,anzahlargs,arg1,...,arg8) file put vector special 
fputvpgfs(r,p,AL,W,V,Vgfs,pf) (MACRO) file put vector of polynomials over 
			Galois-field with single characteristic 
fputvrfmsp1(p,V,VL,pf)  (MACRO) file put vector of rational functions over 
			modular single primes, transcendence degree 1 
fraction                expansion ifactcfe(n,Large_P,K,mode) integer 
			factorization continued 
free                    formula dippiqff(r1,r2,s,PL,CONDS,fac) distributive 
			polynomial over polynomials over integers 
			quantifier 
free                    formula fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file 
			put distributive polynomial over polynomials over 
			integers quantifier 
free                    formula putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers quantifier 
freeing                 blocks gcfree() garbage collector with 
ftab(n,pf)              file tabulator 
function                cexp(z) complex exponential 
function                f cweberf(z) complex Weber 
function                f1 cweberf1(z) complex Weber 
function                f2 cweberf2(z) complex Weber 
function                field over modular single prime, transcendence 
			degree 1, decomposition law affmsp1decl(p,F,P) 
			algebraic 
function                field over modular singles divisor class number 
			qffmsdcn(m,P) quadratic 
function                field over modular singles divisor class number 
			subroutine 1 qffmsdcns1(m,P) quadratic 
function                field over modular singles divisor class number 
			subroutine 2 qffmsdcns2(m,P) quadratic 
function                field over modular singles divisor class number 
			subroutine 3 qffmsdcns3(m,P) quadratic 
function                field over modular singles fundamental unit, baby 
			step version qffmsfubs(m,D) quadratic 
function                field over modular singles fundamental unit, 
			original version qffmsfuobs(m,D) quadratic 
function                field over modular singles ideal class group 
			generators and isomorphy type, imaginary case 
			qffmsicggii(m,D,H,L,pIT) quadratic 
function                field over modular singles ideal class group 
			generators and isomorphy type, real case 
			qffmsicggir(m,D,d,H,L,pIT) quadratic 
function                field over modular singles ideal class group 
			structure, imaginary case qffmsicgsti(m,D,L) 
			quadratic 
function                field over modular singles ideal class group 
			structure, real case qffmsicgstr(m,D,d,LG,pHid) 
			quadratic 
function                field over modular singles ideal class group system 
			of representatives qffmsicgrep(m,D,pHid) quadratic 
function                field over modular singles ideal class group system 
			of representatives, imaginary case 
			qffmsicgri(m,D,pHid) quadratic 
function                field over modular singles ideal class group system 
			of representatives, real case qffmsicgrr(m,D,d) 
			quadratic 
function                field over modular singles ideal class number 
			qffmsicn(m,P) quadratic 
function                field over modular singles is element of an ideal 
			class qffmsiselic(m,D,L,Q,P) quadratic 
function                field over modular singles is equal ideal special 
			qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic 
function                field over modular singles order of one single 
			ideal class, imaginary case 
			qffmsordsici(m,D,Q,P,OS) quadratic 
function                field over modular singles order of one single 
			ideal class, real case qffmsordsicr(m,D,d,LE,ID,OS) 
			quadratic 
function                field over modular singles primitive ideal product 
			qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
function                field over modular singles primitive ideal product, 
			special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
function                field over modular singles primitive ideal square 
			qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic 
function                field over modular singles primitive ideal square, 
			special version qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) 
			quadratic 
function                field over modular singles reduction of a real 
			quadratic irrational qffmsrqired(m,D,d,Q,P,pPr) 
			quadratic 
function                field over modular singles regulator qffmsreg(m,P) 
			quadratic 
function                field over modular singles regulator, baby step - 
			giant step version qffmsregbg(m,D) quadratic 
function                field over modular singles regulator, baby step - 
			giant step version, first case qffmsregbg1(m,D,s) 
			quadratic 
function                field over modular singles regulator, baby step - 
			giant step version, fourth case qffmsregbg4(m,D,s) 
			quadratic 
function                field over modular singles regulator, baby step - 
			giant step version, second case qffmsregbg2(m,D,s) 
			quadratic 
function                field over modular singles regulator, baby step - 
			giant step version, third case qffmsregbg3(m,D,s) 
			quadratic 
function                field over modular singles regulator, baby step 
			version qffmsregbs(m,D) quadratic 
function                field over modular singles regulator, original baby 
			step - giant step version qffmsregobg(m,D) 
			quadratic 
function                field over modular singles regulator, original baby 
			step version qffmsregobs(m,D) quadratic 
function                field over modular singles zero class group 
			isomorphy type, imaginary case 
			qffmszcgiti(m,D,LG,IT) quadratic 
function                field over modular singles zero class group 
			isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) quadratic 
function                field over modular singles, imaginary case, 
			primitive ideal reduction 
			qffmsipidred(m,D,Q,P,pQr,pPr) quadratic 
function                field over modular singles, imaginary case, sparse 
			representation, reduction of a primitive ideal 
			qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic 
function                field over modular singles, principal ideal 
			generating element, real case, 
			qffmspidgenr(m,D,Q,P,G,pB) quadratic 
function                field over modular singles, real case, reduction of 
			a primitive ideal qffmsrpidred(m,D,d,Q,P,pQr,pPr) 
			quadratic 
function                field over modular singles, real case, sparse 
			representation, reduction of a primitive ideal 
			qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic 
function                field over modular singles, sparse representation, 
			primitive ideal product 
			qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
function                field over modular singles, sparse representation, 
			primitive ideal product, special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
function                field over modular singles, sparse representation, 
			primitive ideal square 
			qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic 
function                field over modular singles, sparse representation, 
			primitive ideal square, special version 
			qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic 
function                field over modular singles, sparse representation, 
			reduction of a real quadratic irrational 
			qffmssrqired(m,D,d,Q,P,pPr) quadratic 
function                flexp(f) floating point exponential 
function                gfsnegf(p,AL,a) Galois-field with single 
			characteristic negation as 
function                gfssumf(p,AL,a,b) Galois-field with single 
			characteristic sum as 
function                minegf(M,A) modular integer negation as 
function                miprodf(M,A,B) modular integer product as 
function                misumf(M,A,B) modular integer sum as 
function                msnegf(m,a) modular single negation as 
function                mssumf(m,a,b) modular single sum as 
function                nfsnegf(F,a) number field, sparse representation, 
			negation as 
function                nfssumf(F,a,b) number field, sparse representation, 
			sum as 
function                over modular single prime construction, 
			transcendence degree 1 rfmsp1cons(p,P1,P2) rational 
function                over modular single prime difference, transcendence 
			degree 1 rfmsp1dif(p,R1,R2) rational 
function                over modular single prime negation, transcendence 
			degree 1 rfmsp1neg(p,R) rational 
function                over modular single prime product, transcendence 
			degree 1 rfmsp1prod(p,R1,R2) rational 
function                over modular single prime quotient, transcendence 
			degree 1 rfmsp1quot(p,R1,R2) rational 
function                over modular single prime sum, transcendence degree 
			1 rfmsp1sum(p,R1,R2) rational 
function                over modular single prime, transcendence degree 1 ? 
			isrfmsp1(p,R) is rational 
function                over modular single prime, transcendence degree 1 
			fputrfmsp1(p,R,V,pf) (MACRO) file put rational 
function                over modular single prime, transcendence degree 1 
			pmstorfmsp1(p,P) (MACRO) polynomial over modular 
			singles to rational 
function                over modular single prime, transcendence degree 1 
			putrfmsp1(p,R,V) (MACRO) put rational 
function                over modular single prime, transcendence degree 1, 
			P-primality test and factorization of the defining 
			polynomial or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic 
function                over modular single prime, transcendence degree 1, 
			P-star valuation iafmsp1psval(p,P,A) integral 
			algebraic 
function                over modular single prime, transcendence degree 1, 
			evaluation special upprmsp1afes(p,F,P,a) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, algebraic 
function                over modular single prime, transcendence degree 1, 
			exponentiation special afmsp1expsp(p,F,a,e,M) 
			algebraic 
function                over modular single prime, transcendence degree 1, 
			product (rekursiv) prfmsp1rfprd(r,p,P,a) polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, rational 
function                over modular single prime, transcendence degree 1, 
			product special afmsp1prodsp(p,F,a,b,M) algebraic 
function                over modular single primes, transcendence degree 1 
			fgetrfmsp1(p,V,pf) file get rational 
function                over modular single primes, transcendence degree 1 
			getrfmsp1(p,V) (MACRO) get rational 
function                over modular single primes, transcendence degree 1, 
			core algorithm afmsp1coreal(p,F,P,Q,mp) algebraic 
function                over modular single primes, transcendence degree 1, 
			increasing the denominator of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
function                over modular single primes, transcendence degree 1, 
			inverse rfmsp1inv(p,R) rational 
function                over modular single primes, transcendence degree 1, 
			minimal polynomial afmsp1minpol(p,F,a) algebraic 
function                over modular single primes, transcendence degree 1, 
			minimal polynomial iafmsp1mpol(p,F,a,Q) integral 
			algebraic 
function                over modular single primes, transcendence degree 1, 
			minimal polynomial modulo power of an univariate 
			prime polynomial over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
function                over modular single primes, transcendence degree 1, 
			regulation afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) 
			algebraic 
function                over rationals fgetrfr(r,V,pf) file get rational 
function                over rationals fputrfr(r,R,V,pf) file put rational 
function                over rationals getrfr(r,V) (MACRO) get rational 
function                over rationals one isrfrone(r,A) is rational 
function                over rationals putrfr(r,R,V) (MACRO) put rational 
function                over rationals rtorfr(r,R) rational number to 
			rational 
function                over the rationals ? isrfr(r,R) is rational 
function                over the rationals construction rfrcons(r,P1,P2) 
			rational 
function                over the rationals difference rfrdif(r,R1,R2) 
			rational 
function                over the rationals diprfrtorfr(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals to rational 
function                over the rationals inverse rfrinv(r,R) rational 
function                over the rationals negation rfrneg(r,R) rational 
function                over the rationals pitorfr(r,P) polynomial over 
			integers to rational 
function                over the rationals product diprfrrfprod(r1,r2,P,A) 
			distributive polynomial over rational functions 
			over the rationals rational 
function                over the rationals product rfrprod(r,R1,R2) 
			rational 
function                over the rationals prtorfr(r,P) polynomial over the 
			rationals to rational 
function                over the rationals quotient rfrquot(r,R1,R2) 
			rational 
function                over the rationals sum rfrsum(r,R1,R2) rational 
function                over the rationals to distributive polynomial over 
			rational functions over the rationals 
			rfrtodiprfr(r1,r2,F) rational 
function                over the rationals transformation 
			rfrtransf(r1,R1,V1,r2,R2,V2,Vn,pV3) rational 
function                special cdedeetas(q,ln_q) complex Dedekind eta 
function                special version cexpsv(z,n) complex exponential 
function                upgfstf(p,AL,G,d,M) univariate polynomial over 
			Galois-field with single characteristic, trace 
function,               special upgf2tf(G,F,d,M) polynomial over 
			Galois-field with characteristic 2, trace 
function,               special upmitfsp(ip,G,d,M) univariate polynomial 
			over modular integers, trace 
functional              equation ecrsign(E) elliptic curve over rational 
			numbers, sign of the 
functional              equation, special version ecrsigns(E,A,C) elliptic 
			curve over the rationals, sign of the 
functions               1 PAFtrans1() Papanikolaou floating point package: 
			transcendental 
functions               2 PAFtrans2() Papanikolaou floating point package: 
			transcendental 
functions               3 PAFtrans3() Papanikolaou floating point package: 
			transcendental 
functions               HDidigit() Heidelberg arithmetic package: digit 
functions               HDidigitvec() Heidelberg arithmetic package: vector 
functions               HDiio() Heidelberg arithmetic package: I/O 
functions               flPAFfu(func,anzahlargs,arg1,arg2) floating point 
			using Papanikolaou floating point 
functions               fltrig(Ffunc,f) (MACRO) floating point 
			trigonometric 
functions               iHDfu(func,anzahlargs,arg1,arg2) integer using 
			Heidelberg arithmetic 
functions               over modular single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from univariate polynomial 
			over rational 
functions               over modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, list from common 
			denominator matrix of rational 
functions               over modular single prime, transcendence degree 1 
			clfcdprfmsp1(P,n) coefficient list from common 
			denominator polynomial over rational 
functions               over modular single prime, transcendence degree 1 
			sclfuprfmsp1(P,n) special coefficient list from 
			univariate polynomial over rational 
functions               over modular single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, from common denominator 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			derivation, main variable prfmsp1deriv(r,p,P) 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			difference (rekursiv) prfmsp1dif(r,p,P1,P2) 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			extended greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over rational 
functions               over modular single prime, transcendence degree 1, 
			from coefficient list cdprfmsp1fcl(L,p) common 
			denominator polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			from common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 uprfmsp1fcdp(p,P) univariate polynomial 
			over rational 
functions               over modular single prime, transcendence degree 1, 
			from special coefficient list uprfmsp1fscl(L) 
			univariate polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			from univariate polynomial over rational functions 
			over modular single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common denominator polynomial 
			over rational 
functions               over modular single prime, transcendence degree 1, 
			hermitian reduction cdmarfmsp1hr(p,M) common 
			denominator matrix of rational 
functions               over modular single prime, transcendence degree 1, 
			identity construction cdmarfmsp1id(n) common 
			denominator matrix of rational 
functions               over modular single prime, transcendence degree 1, 
			inverse cdprfmsp1inv(p,F,A) common denominator 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			list from common denominator matrix of rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1lfm(M,p) common denominator 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			negation (rekursiv) prfmsp1neg(r,p,P) polynomial 
			over rational 
functions               over modular single prime, transcendence degree 1, 
			product (rekursiv) prfmsp1prod(r,p,P1,P2) 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			quotient and remainder (rekursiv) 
			prfmsp1qrem(r,p,P1,P2,pR) polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			rational function over modular single prime, 
			transcendence degree 1, product (rekursiv) 
			prfmsp1rfprd(r,p,P,a) polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			sum (rekursiv) prfmsp1sum(r,p,P1,P2) polynomial 
			over rational 
functions               over modular single prime, transcendence degree 1, 
			sum cdprfmsp1sum(p,P1,P2) common denominator 
			polynomial over rational 
functions               over modular single prime, transcendence degree 1, 
			univariate polynomial over modular single prime 
			quotient cdprfmsp1upq(p,F,P) common denominator 
			polynomial over rational 
functions               over modular single primes transcendence degree 1, 
			determinant marfmsp1det(p,M) matrix of rational 
functions               over modular single primes transcendence degree 1, 
			difference marfmsp1dif(p,M,N) (MACRO) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1 
			? ismarfmsp1(p,M) (MACRO) is matrix of rational 
functions               over modular single primes, transcendence degree 1 
			? isvecrfmsp1(p,V) (MACRO) is vector of rational 
functions               over modular single primes, transcendence degree 1 
			fgetmarfmsp1(p,V,pf) (MACRO) file get matrix of 
			rational 
functions               over modular single primes, transcendence degree 1 
			fgetvrfmsp1(p,VL,pf) (MACRO) file get vector of 
			rational 
functions               over modular single primes, transcendence degree 1 
			fputmarfmsp1(p,M,V,pf) (MACRO) file put matrix of 
			rational 
functions               over modular single primes, transcendence degree 1 
			fputvrfmsp1(p,V,VL,pf) (MACRO) file put vector of 
			rational 
functions               over modular single primes, transcendence degree 1 
			getmarfmsp1(p,V) (MACRO) get matrix of rational 
functions               over modular single primes, transcendence degree 1 
			getvecrfmsp1(p,VL) (MACRO) get vector of rational 
functions               over modular single primes, transcendence degree 1 
			mpmstmrfmsp1(p,M) matrix of polynomials over 
			modular singles to matrix of rational 
functions               over modular single primes, transcendence degree 1 
			putmarfmsp1(p,M,V) (MACRO) put matrix of rational 
functions               over modular single primes, transcendence degree 1 
			putvecrfmsp1(p,V,VL) (MACRO) put vector of rational 
functions               over modular single primes, transcendence degree 1 
			vpmstvrfmsp1(p,V) vector of polynomials over 
			modular singles to vector of rational 
functions               over modular single primes, transcendence degree 1, 
			construction 1 marfmsp1c1(p,n) (MACRO) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			difference vecrfmsp1dif(p,U,V) (MACRO) vector of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			exponentiation marfmsp1exp(p,M,n) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			inverse marfmsp1inv(p,M) matrix of rational 
functions               over modular single primes, transcendence degree 1, 
			linear combination vecrfmsp1lc(p,F1,F2,V1,V2) 
			vector of rational 
functions               over modular single primes, transcendence degree 1, 
			module homomorphism cdprfmsp1mh(p,P,M) common 
			denominator polynomial over rational 
functions               over modular single primes, transcendence degree 1, 
			negation marfmsp1neg(p,M) (MACRO) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			negation vecrfmsp1neg(p,V) (MACRO) vector of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			null space basis marfmsp1nsb(p,M) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			product marfmsp1prod(p,M,N) (MACRO) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			rank marfmsp1rk(p,M) matrix of rational 
functions               over modular single primes, transcendence degree 1, 
			scalar multiplication marfmsp1smul(p,M,F) matrix of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			scalar multiplication vecrfmsp1sm(p,F,V) vector of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			scalar product vecrfmsp1sp(p,V,W) vector of 
			rational 
functions               over modular single primes, transcendence degree 1, 
			solution of a system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
functions               over modular single primes, transcendence degree 1, 
			sum marfmsp1sum(p,M,N) (MACRO) matrix of rational 
functions               over modular single primes, transcendence degree 1, 
			sum vecrfmsp1sum(p,U,V) (MACRO) vector of rational 
functions               over modular single primes, transcendence degree 1, 
			vector multiplication marfmsp1vmul(p,A,x) (MACRO) 
			matrix of rational 
functions               over rationals ? ismarfr(r,M) (MACRO) is matrix of 
			rational 
functions               over rationals ? isvecrfr(r,V) (MACRO) is vector of 
			rational 
functions               over rationals characteristic polynomial 
			marfrchpol(r,M) matrix of rational 
functions               over rationals construction 1 marfrcons1(r,n) 
			(MACRO) matrix of rational 
functions               over rationals determinant marfrdet(r,M) matrix of 
			rational 
functions               over rationals difference marfrdif(r,M,N) (MACRO) 
			matrix of rational 
functions               over rationals difference vecrfrdif(r,U,V) (MACRO) 
			vector of rational 
functions               over rationals exponentiation marfrexp(r,M,n) 
			matrix of rational 
functions               over rationals fgetmarfr(r,V,pf) (MACRO) file get 
			matrix of rational 
functions               over rationals fgetvecrfr(r,VL,pf) (MACRO) file get 
			vector of rational 
functions               over rationals fputmarfr(r,M,V,pf) (MACRO) file put 
			matrix of rational 
functions               over rationals fputvecrfr(r,V,VL,pf) (MACRO) file 
			put vector of rational 
functions               over rationals getmarfr(r,V) (MACRO) get matrix of 
			rational 
functions               over rationals getvecrfr(r,VL) (MACRO) get vector 
			of rational 
functions               over rationals inverse marfrinv(r,M) matrix of 
			rational 
functions               over rationals linear combination 
			vecrfrlc(r,F1,F2,V1,V2) vector of rational 
functions               over rationals mapitomarfr(r,M) matrix of 
			polynomials over integers to matrix of rational 
functions               over rationals maprtomarfr(r,M) matrix of 
			polynomials over rationals to matrix of rational 
functions               over rationals negation marfrneg(r,M) (MACRO) 
			matrix of rational 
functions               over rationals negation vecrfrneg(r,V) (MACRO) 
			vector of rational 
functions               over rationals product marfrprod(r,M,N) (MACRO) 
			matrix of rational 
functions               over rationals putmarfr(r,M,V) (MACRO) put matrix 
			of rational 
functions               over rationals putvecrfr(r,V,VL) (MACRO) put vector 
			of rational 
functions               over rationals rank marfrrk(r,M) matrix of rational 
functions               over rationals scalar multiplication 
			marfrsmul(r,M,F) matrix of rational 
functions               over rationals scalar multiplication 
			vecrfrsmul(r,F,V) vector of rational 
functions               over rationals scalar product vecrfrsprod(r,V,W) 
			vector of rational 
functions               over rationals solution of a system of linear 
			equations marfrssle(r,A,b,pX,pN) matrix of rational 
functions               over rationals sum marfrsum(r,M,N) (MACRO) matrix 
			of rational 
functions               over rationals sum vecrfrsum(r,U,V) (MACRO) vector 
			of rational 
functions               over rationals vecpitovrfr(r,V) vector of 
			polynomials over integers to vector of rational 
functions               over rationals vecprtovrfr(r,V) vector of 
			polynomials over rationals to vector of rational 
functions               over rationals vector multiplication 
			marfrvecmul(r,A,x) (MACRO) matrix of rational 
functions               over rationals, null space basis marfrnsb(r,M) 
			matrix of rational 
functions               over the rationals Groebner basis augmentation 
			diprfrgba(r1,r2,PL,P) distributive polynomial over 
			rational 
functions               over the rationals Groebner basis 
			diprfrgb(r1,r2,PL) distributive polynomial over 
			rational 
functions               over the rationals Groebner basis recursion 
			diprfrgbr(r1,r2,PL) distributive polynomial over 
			rational 
functions               over the rationals S-polynomial 
			diprfrsp(r1,r2,P1,P2) distributive polynomial over 
			rational 
functions               over the rationals difference 
			diprfrdif(r1,r2,P1,P2) distributive polynomial over 
			rational 
functions               over the rationals in graduated lexicographical 
			order diprfrlotglo(r1,r2,P) distributive polynomial 
			over rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational 
functions               over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals in graduated lexicographical 
			order diprfrlotglo(r1,r2,P) distributive polynomial 
			over rational 
functions               over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order with 
			inverse exponent vector diprfrlotlio(r1,r2,P) 
			distributive polynomial over rational 
functions               over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals with total degree ordering 
			diprfrlottdo(r1,r2,P) distributive polynomial over 
			rational 
functions               over the rationals in lexicographical order with 
			inverse exponent vector diprfrlotlio(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational 
functions               over the rationals list 
			fgetdiprfrl(r1,r2,VL1,VL2,pf) file get distributive 
			polynomial over rational 
functions               over the rationals list 
			fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file put 
			distributive polynomial over rational 
functions               over the rationals list getdiprfrl(r1,r2,VL1,VL2) 
			(MACRO) get distributive polynomial over rational 
functions               over the rationals list 
			putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive polynomial over rational 
functions               over the rationals monic diprfrmonic(r1,r2,P) 
			distributive polynomial over rational 
functions               over the rationals negation diprfrneg(r1,r2,P) 
			distributive polynomial over rational 
functions               over the rationals one ? isdiprfrone(r1,r2,P) is 
			distributive polynomial over rational 
functions               over the rationals product diprfrprod(r1,r2,P1,P2) 
			distributive polynomial over rational 
functions               over the rationals rational function over the 
			rationals product diprfrrfprod(r1,r2,P,A) 
			distributive polynomial over rational 
functions               over the rationals rfrtodiprfr(r1,r2,F) rational 
			function over the rationals to distributive 
			polynomial over rational 
functions               over the rationals sum diprfrsum(r1,r2,P1,P2) 
			distributive polynomial over rational 
functions               over the rationals to rational function over the 
			rationals diprfrtorfr(r1,r2,P) distributive 
			polynomial over rational 
functions               over the rationals transformation 
			marfrtransf(r1,M1,V1,r2,R2,V2,Vn,pV3) matrix of 
			rational 
functions               over the rationals transformation 
			vecrfrtrnsf(r1,W1,V1,r2,R2,V2,Vn,pV3) vector of 
			rational 
functions               over the rationals with total degree ordering 
			diprfrlottdo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational 
fundamental             unit rqnffu(D,pl) real quadratic number field 
fundamental             unit, baby step version qffmsfubs(m,D) quadratic 
			function field over modular singles 
fundamental             unit, original version qffmsfuobs(m,D) quadratic 
			function field over modular singles 
garbage                 collector gc() 
garbage                 collector reinitialization gcreinit(bls,blnrm) 
garbage                 collector with freeing blocks gcfree() 
garbage                 collector: compressing gccpr() 
gc()                    garbage collector 
gccpr()                 garbage collector: compressing 
gcfree()                garbage collector with freeing blocks 
gcreinit(bls,blnrm)     garbage collector reinitialization 
general                 lreduct(L,k) list reductum, 
generating              element, real case, qffmspidgenr(m,D,Q,P,G,pB) 
			quadratic function field over modular singles, 
			principal ideal 
generator               gf2algen(n,H) Galois-field with characteristic 2 
			arithmetic list 
generator               gf2impsbgen(n,H) Galois-field with characteristic 2 
			irreducible and monic polynomial in special 
			bit-representation 
generator               gfsalgen(p,n,G) Galois-field with single 
			characteristic arithmetic list 
generator               ipgen(u,o) integer prime 
generator               isomorphic embedding of subfield 
			gfsalgenies(p,m,n,ALn) Galois-field with single 
			characteristic arithmetic list 
generator               lepermg(L) list element permutations 
generator               spgen(a,b) single prime 
generator               upgf2gen(G,m) univariate polynomial over 
			Galois-field with characteristic 2, random 
generator               upm2imgen(n) univariate polynomial over modular 2, 
			irreducible and monic, 
generator               upm2imtgen(n) univariate polynomial over modular 2, 
			irreducible and monic trinomial, 
generator               upmsimgen(p,n) univariate polynomial over modular 
			singles, irreducible and monic, 
generator               upmsimtgen(p,n) univariate polynomial over modular 
			singles, irreducible and monic trinomial, 
generators              and isomorphy type, imaginary case 
			qffmsicggii(m,D,H,L,pIT) quadratic function field 
			over modular singles ideal class group 
generators              and isomorphy type, real case 
			qffmsicggir(m,D,d,H,L,pIT) quadratic function field 
			over modular singles ideal class group 
generators              of p-maximal orders of the p-adic divisors of the 
			defining polynomial and p-minimal polynomials of 
			the generators ouspiapfgmic(p,P,k) order of an 
			univariate separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, 
generators              of the torsion group ecisnfgentor(E) elliptic curve 
			with integer coefficients, short normal form, 
generators              of torsion group ecimingentor(E) elliptic curve 
			with integer coefficients, minimal model, 
generators              of torsion group ecracgentor(E) elliptic curve over 
			rational numbers, actual curve, 
generators              oibasisfgen(F,L) order over the integers basis from 
generators              oprmsp1basfg(p,F,L) order over polynomial ring over 
			modular single prime, transcendence degree 1, basis 
			from 
generators              ouspiapfgmic(p,P,k) order of an univariate 
			separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal orders 
			of the p-adic divisors of the defining polynomial 
			and p-minimal polynomials of the 
get                     Galois-field with characteristic 2 element 
			fgetgf2el(G,V,pf) file 
get                     Galois-field with characteristic 2 element 
			getgf2el(G,V) (MACRO) 
get                     Galois-field with single characteristic element 
			fgetgfsel(p,AL,V,pf) file 
get                     Galois-field with single characteristic element 
			getgfsel(p,AL,V) (MACRO) 
get                     atom fgeta(pf) file 
get                     atom geta() (MACRO) 
get                     atom sgeta(ps) string 
get                     character fgetc(pf) (MACRO) file 
get                     character getc(pf) (MACRO) 
get                     character getchar() (MACRO) 
get                     character sgetc(ps) string 
get                     character unsgetc(c,ps) undo string 
get                     character, skipping blanks fgetcb(pf) file 
get                     character, skipping blanks getcb() (MACRO) 
get                     character, skipping blanks sgetcb(pf) string 
get                     character, skipping space fgetcs(pf) file 
get                     character, skipping space getcs() (MACRO) 
get                     character, skipping space sgetcs(ps) string 
get                     distributive polynomial over Galois-field with 
			single characteristic list 
			fgetdipgfsl(r,p,AL,VL,Vgfs,pf) file 
get                     distributive polynomial over Galois-field with 
			single characteristic list 
			getdipgfsl(r,p,AL,VL,Vgfs) (MACRO) 
get                     distributive polynomial over integers list 
			fgetdipil(r,VL,pf) file 
get                     distributive polynomial over integers list 
			getdipil(r,VL) (MACRO) 
get                     distributive polynomial over modular integer primes 
			list fgetdipmipl(r,p,VL,pf) file 
get                     distributive polynomial over modular integer primes 
			list getdipmipl(r,p,VL) (MACRO) 
get                     distributive polynomial over modular single primes 
			list fgetdipmspl(r,p,VL,pf) file 
get                     distributive polynomial over modular single primes 
			list getdipmspl(r,p,VL) (MACRO) 
get                     distributive polynomial over number field list 
			fgetdipnfl(r,F,VL,Vnf,pf) file 
get                     distributive polynomial over number field list 
			getdipnfl(r,F,VL,Vnf) (MACRO) 
get                     distributive polynomial over polynomials over 
			integers case distinction 
			fgetdippicd(r1,r2,VL1,VL2,fac,pf) file 
get                     distributive polynomial over polynomials over 
			integers case distinction 
			getdippicd(r1,r2,VL1,VL2,fac) (MACRO) 
get                     distributive polynomial over polynomials over 
			integers list fgetdippil(r1,r2,VL1,VL2,pf) file 
get                     distributive polynomial over polynomials over 
			integers list getdippil(r1,r2,VL1,VL2) (MACRO) 
get                     distributive polynomial over rational functions 
			over the rationals list 
			fgetdiprfrl(r1,r2,VL1,VL2,pf) file 
get                     distributive polynomial over rational functions 
			over the rationals list getdiprfrl(r1,r2,VL1,VL2) 
			(MACRO) 
get                     distributive polynomial over rationals list 
			fgetdiprl(r,VL,pf) file 
get                     distributive polynomial over rationals list 
			getdiprl(r,VL) (MACRO) 
get                     elliptic curve over rational numbers fgetecr(pf) 
			file 
get                     elliptic curve over rational numbers getecr() 
get                     elliptic curve over rational numbers point 
			getecrp() (MACRO) 
get                     floating point fgetfl(pf) file 
get                     floating point getfl() (MACRO) 
get                     floating point sgetfl(ps) string 
get                     floating point special version sgetflsp(ps) string 
get                     integer fgeti(pf) file 
get                     integer geti() (MACRO) 
get                     integer sgeti(ps) string 
get                     list (rekursiv) fgetl(pf) file 
get                     list (rekursiv) sgetl(ps) string 
get                     list getl() (MACRO) 
get                     list of integers fgetli(pf) file 
get                     list of integers getli() (MACRO) 
get                     list of rational numbers fgetlr(pf) file 
get                     list of rational numbers getlr() (MACRO) 
get                     matrix fgetma(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) 
			file 
get                     matrix of Galois-field with single characteristic 
			elements fgetmagfs(p,AL,V,pf) (MACRO) file 
get                     matrix of Galois-field with single characteristic 
			elements getmagfs(p,AL,V) (MACRO) 
get                     matrix of integers fgetmai(pf) (MACRO) file 
get                     matrix of integers getmai() (MACRO) 
get                     matrix of modular integers fgetmami(m,pf) (MACRO) 
			file 
get                     matrix of modular integers getmami(m) (MACRO) 
get                     matrix of modular singles fgetmams(m,pf) (MACRO) 
			file 
get                     matrix of modular singles getmams(m) (MACRO) 
get                     matrix of number field elements fgetmanf(F,VL,pf) 
			(MACRO) file 
get                     matrix of number field elements getmanf(F,VL) 
			(MACRO) 
get                     matrix of number field elements, sparse 
			representation fgetmanfs(F,VL,pf) (MACRO) file 
get                     matrix of number field elements, sparse 
			representation getmanfs(F,VL) (MACRO) 
get                     matrix of polynomials over Galois-field with single 
			characteristic fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) 
			file 
get                     matrix of polynomials over Galois-field with single 
			characteristic getmapgfs(r,p,AL,V,Vgfs) (MACRO) 
get                     matrix of polynomials over integers 
			fgetmapi(r,V,pf) (MACRO) file 
get                     matrix of polynomials over integers getmapi(r,V) 
			(MACRO) 
get                     matrix of polynomials over modular integers 
			fgetmapmi(r,m,V,pf) (MACRO) file 
get                     matrix of polynomials over modular integers 
			getmapmi(r,m,V) (MACRO) 
get                     matrix of polynomials over modular singles 
			fgetmapms(r,m,V,pf) (MACRO) file 
get                     matrix of polynomials over modular singles 
			getmapms(r,m,V) (MACRO) 
get                     matrix of polynomials over number field 
			fgetmapnf(r,F,V,Vnf,pf) (MACRO) file 
get                     matrix of polynomials over number field 
			getmapnf(r,F,V,Vnf) (MACRO) 
get                     matrix of polynomials over rationals 
			fgetmapr(r,V,pf) (MACRO) file 
get                     matrix of polynomials over rationals getmapr(r,V) 
			(MACRO) 
get                     matrix of rational functions over modular single 
			primes, transcendence degree 1 fgetmarfmsp1(p,V,pf) 
			(MACRO) file 
get                     matrix of rational functions over modular single 
			primes, transcendence degree 1 getmarfmsp1(p,V) 
			(MACRO) 
get                     matrix of rational functions over rationals 
			fgetmarfr(r,V,pf) (MACRO) file 
get                     matrix of rational functions over rationals 
			getmarfr(r,V) (MACRO) 
get                     matrix of rationals fgetmar(pf) (MACRO) file 
get                     matrix of rationals getmar() (MACRO) 
get                     matrix special 
			fgetmaspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
			file 
get                     modular integer fgetmi(M,pf) file 
get                     modular integer getmi(M) (MACRO) 
get                     modular single fgetms(m,pf) file 
get                     modular single getms(m) (MACRO) 
get                     number field element fgetnfel(F,V,pf) file 
get                     number field element getnfel(F,V) (MACRO) 
get                     number field element, sparse representation 
			fgetnfels(F,V,pf) file 
get                     number field element, sparse representation 
			getnfels(F,V) (MACRO) 
get                     object fgeto(pf) file 
get                     object geto() (MACRO) 
get                     output-counter getocnt(pf) 
get                     p-adic field element fgetpfel(p,pf) file 
get                     p-adic field element getpfel(p) (MACRO) 
get                     point on elliptic curve over rational numbers 
			fgetecrp(pf) file 
get                     polynomial over Galois-field with characteristic 2 
			fgetpgf2(r,G,V,Vgf2,pf) file 
get                     polynomial over Galois-field with characteristic 2 
			getpgf2(r,G,V,Vgf2) (MACRO) 
get                     polynomial over Galois-field with single 
			characteristic fgetpgfs(r,p,AL,V,Vgfs,pf) file 
get                     polynomial over Galois-field with single 
			characteristic getpgfs(r,p,AL,V,Vgfs) (MACRO) 
get                     polynomial over integers fgetpi(r,V,pf) file 
get                     polynomial over integers getpi(r,V) (MACRO) 
get                     polynomial over modular integers fgetpmi(r,M,V,pf) 
			file 
get                     polynomial over modular integers getpmi(r,M,V) 
			(MACRO) 
get                     polynomial over modular singles fgetpms(r,m,V,pf) 
			file 
get                     polynomial over modular singles getpms(r,m,V) 
			(MACRO) 
get                     polynomial over number field fgetpnf(r,F,V,Vnf,pf) 
			file 
get                     polynomial over number field getpnf(r,F,V,Vnf) 
			(MACRO) 
get                     polynomial over p-adic field fgetppf(r,p,V,pf) file 
get                     polynomial over p-adic field getppf(r,p,V) 
get                     polynomial over rationals fgetpr(r,V,pf) file 
get                     polynomial over rationals getpr(r,V) (MACRO) 
get                     quadratic number field element fgetqnfel(D,pf) file 
get                     quadratic number field element getqnfel(D) (MACRO) 
get                     rational function over modular single primes, 
			transcendence degree 1 fgetrfmsp1(p,V,pf) file 
get                     rational function over modular single primes, 
			transcendence degree 1 getrfmsp1(p,V) (MACRO) 
get                     rational function over rationals fgetrfr(r,V,pf) 
			file 
get                     rational function over rationals getrfr(r,V) 
			(MACRO) 
get                     rational number fgetr(pf) file 
get                     rational number getr() (MACRO) 
get                     rational number sgetr(ps) string 
get                     single fgetsi(pf) file 
get                     single precision getsi() (MACRO) 
get                     single sgetsi(ps) string 
get                     special p-adic field element fgetspfel(p,pf) file 
get                     special p-adic field element getspfel(p) (MACRO) 
get                     string fgets(s,n,pf) (MACRO) file 
get                     string gets(s) (MACRO) 
get                     variable list fgetvl(pf) file 
get                     variable list getvl() (MACRO) 
get                     vector 
			fgetvec(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) file 
get                     vector of Galois-field with single characteristic 
			elements fgetvecgfs(p,AL,VL,pf) (MACRO) file 
get                     vector of Galois-field with single characteristic 
			elements getvecgfs(p,AL,VL) (MACRO) 
get                     vector of integers fgetveci(pf) (MACRO) file 
get                     vector of integers getveci() (MACRO) 
get                     vector of modular integers fgetvecmi(m,pf) (MACRO) 
			file 
get                     vector of modular integers getvecmi(m) (MACRO) 
get                     vector of modular singles fgetvecms(m,pf) (MACRO) 
			file 
get                     vector of modular singles getvecms(m) (MACRO) 
get                     vector of number field elements fgetvecnf(F,VL,pf) 
			(MACRO) file 
get                     vector of number field elements getvecnf(F,VL) 
			(MACRO) 
get                     vector of number field elements, sparse 
			representation fgetvecnfs(F,VL,pf) (MACRO) file 
get                     vector of number field elements, sparse 
			representation getvecnfs(F,VL) (MACRO) 
get                     vector of polynomials over Galois-field with single 
			characteristic fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) 
			file 
get                     vector of polynomials over Galois-field with single 
			characteristic getvpgfs(r,p,AL,V,Vgfs) (MACRO) 
get                     vector of polynomials over integers 
			fgetvecpi(r,VL,pf) (MACRO) file 
get                     vector of polynomials over integers getvecpi(r,VL) 
			(MACRO) 
get                     vector of polynomials over modular integers 
			fgetvecpmi(r,m,VL,pf) (MACRO) file 
get                     vector of polynomials over modular integers 
			getvecpmi(r,m,VL) (MACRO) 
get                     vector of polynomials over modular singles 
			fgetvecpms(r,m,VL,pf) (MACRO) file 
get                     vector of polynomials over modular singles 
			getvecpms(r,m,VL) (MACRO) 
get                     vector of polynomials over number field 
			fgetvecpnf(r,F,VL,VLnf,pf) (MACRO) file 
get                     vector of polynomials over number field 
			getvecpnf(r,F,VL,VLnf) (MACRO) 
get                     vector of polynomials over rationals 
			fgetvecpr(r,VL,pf) (MACRO) file 
get                     vector of polynomials over rationals getvecpr(r,VL) 
			(MACRO) 
get                     vector of rational functions over modular single 
			primes, transcendence degree 1 fgetvrfmsp1(p,VL,pf) 
			(MACRO) file 
get                     vector of rational functions over modular single 
			primes, transcendence degree 1 getvecrfmsp1(p,VL) 
			(MACRO) 
get                     vector of rational functions over rationals 
			fgetvecrfr(r,VL,pf) (MACRO) file 
get                     vector of rational functions over rationals 
			getvecrfr(r,VL) (MACRO) 
get                     vector of rationals fgetvecr(pf) (MACRO) file 
get                     vector of rationals getvecr() (MACRO) 
get                     vector special 
			fgetvecspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
			file 
geta()                  (MACRO) get atom 
getc(pf)                (MACRO) get character 
getcb()                 (MACRO) get character, skipping blanks 
getchar()               (MACRO) get character 
getcs()                 (MACRO) get character, skipping space 
getdipgfsl(r,p,AL,VL,Vgfs) (MACRO) get distributive polynomial over 
			Galois-field with single characteristic list 
getdipil(r,VL)          (MACRO) get distributive polynomial over integers 
			list 
getdipmipl(r,p,VL)      (MACRO) get distributive polynomial over modular 
			integer primes list 
getdipmspl(r,p,VL)      (MACRO) get distributive polynomial over modular 
			single primes list 
getdipnfl(r,F,VL,Vnf)   (MACRO) get distributive polynomial over number 
			field list 
getdippicd(r1,r2,VL1,VL2,fac) (MACRO) get distributive polynomial over 
			polynomials over integers case distinction 
getdippil(r1,r2,VL1,VL2) (MACRO) get distributive polynomial over 
			polynomials over integers list 
getdiprfrl(r1,r2,VL1,VL2) (MACRO) get distributive polynomial over rational 
			functions over the rationals list 
getdiprl(r,VL)          (MACRO) get distributive polynomial over rationals 
			list 
getecr()                get elliptic curve over rational numbers 
getecrp()               (MACRO) get elliptic curve over rational numbers 
			point 
getfl()                 (MACRO) get floating point 
getgf2el(G,V)           (MACRO) get Galois-field with characteristic 2 
			element 
getgfsel(p,AL,V)        (MACRO) get Galois-field with single characteristic 
			element 
geti()                  (MACRO) get integer 
getl()                  (MACRO) get list 
getli()                 (MACRO) get list of integers 
getlr()                 (MACRO) get list of rational numbers 
getmagfs(p,AL,V)        (MACRO) get matrix of Galois-field with single 
			characteristic elements 
getmai()                (MACRO) get matrix of integers 
getmami(m)              (MACRO) get matrix of modular integers 
getmams(m)              (MACRO) get matrix of modular singles 
getmanf(F,VL)           (MACRO) get matrix of number field elements 
getmanfs(F,VL)          (MACRO) get matrix of number field elements, sparse 
			representation 
getmapgfs(r,p,AL,V,Vgfs) (MACRO) get matrix of polynomials over Galois-field 
			with single characteristic 
getmapi(r,V)            (MACRO) get matrix of polynomials over integers 
getmapmi(r,m,V)         (MACRO) get matrix of polynomials over modular 
			integers 
getmapms(r,m,V)         (MACRO) get matrix of polynomials over modular 
			singles 
getmapnf(r,F,V,Vnf)     (MACRO) get matrix of polynomials over number field 
getmapr(r,V)            (MACRO) get matrix of polynomials over rationals 
getmar()                (MACRO) get matrix of rationals 
getmarfmsp1(p,V)        (MACRO) get matrix of rational functions over 
			modular single primes, transcendence degree 1 
getmarfr(r,V)           (MACRO) get matrix of rational functions over 
			rationals 
getmi(M)                (MACRO) get modular integer 
getms(m)                (MACRO) get modular single 
getnfel(F,V)            (MACRO) get number field element 
getnfels(F,V)           (MACRO) get number field element, sparse 
			representation 
geto()                  (MACRO) get object 
getocnt(pf)             get output-counter 
getpfel(p)              (MACRO) get p-adic field element 
getpgf2(r,G,V,Vgf2)     (MACRO) get polynomial over Galois-field with 
			characteristic 2 
getpgfs(r,p,AL,V,Vgfs)  (MACRO) get polynomial over Galois-field with 
			single characteristic 
getpi(r,V)              (MACRO) get polynomial over integers 
getpmi(r,M,V)           (MACRO) get polynomial over modular integers 
getpms(r,m,V)           (MACRO) get polynomial over modular singles 
getpnf(r,F,V,Vnf)       (MACRO) get polynomial over number field 
getppf(r,p,V)           get polynomial over p-adic field 
getpr(r,V)              (MACRO) get polynomial over rationals 
getqnfel(D)             (MACRO) get quadratic number field element 
getr()                  (MACRO) get rational number 
getrfmsp1(p,V)          (MACRO) get rational function over modular single 
			primes, transcendence degree 1 
getrfr(r,V)             (MACRO) get rational function over rationals 
gets(s)                 (MACRO) get string 
getsi()                 (MACRO) get single precision 
getspfel(p)             (MACRO) get special p-adic field element 
getvecgfs(p,AL,VL)      (MACRO) get vector of Galois-field with single 
			characteristic elements 
getveci()               (MACRO) get vector of integers 
getvecmi(m)             (MACRO) get vector of modular integers 
getvecms(m)             (MACRO) get vector of modular singles 
getvecnf(F,VL)          (MACRO) get vector of number field elements 
getvecnfs(F,VL)         (MACRO) get vector of number field elements, sparse 
			representation 
getvecpi(r,VL)          (MACRO) get vector of polynomials over integers 
getvecpmi(r,m,VL)       (MACRO) get vector of polynomials over modular 
			integers 
getvecpms(r,m,VL)       (MACRO) get vector of polynomials over modular 
			singles 
getvecpnf(r,F,VL,VLnf)  (MACRO) get vector of polynomials over number field 
getvecpr(r,VL)          (MACRO) get vector of polynomials over rationals 
getvecr()               (MACRO) get vector of rationals 
getvecrfmsp1(p,VL)      (MACRO) get vector of rational functions over 
			modular single primes, transcendence degree 1 
getvecrfr(r,VL)         (MACRO) get vector of rational functions over 
			rationals 
getvl()                 (MACRO) get variable list 
getvpgfs(r,p,AL,V,Vgfs) (MACRO) get vector of polynomials over Galois-field 
			with single characteristic 
gf2algen(n,H)           Galois-field with characteristic 2 arithmetic list 
			generator 
gf2dif(G,a,b)           (MACRO) Galois-field with characteristic 2 
			difference 
gf2efe(GmtoGn,gm)       Galois-field with characteristic 2 embedding in 
			field extension 
gf2elrand(G)            Galois-field with characteristic 2 element 
			randomize 
gf2eltogfsel(G,a)       (MACRO) Galois-field with characteristic 2 element 
			to Galois-field with single characteristic element 
gf2eltoudpm2(G,a)       Galois-field with characteristic 2 element to 
			univariate dense polynomial over modular 2 
gf2exp(G,a,m)           Galois-field with characteristic 2 exponentiation 
gf2ies(Gm,Gn,n)         Galois field with characteristic 2 isomorphic 
			embedding of subfield 
gf2impsbgen(n,H)        Galois-field with characteristic 2 irreducible and 
			monic polynomial in special bit-representation 
			generator 
gf2inv(G,a)             Galois-field with characteristic 2 inverse 
gf2neg(G,a)             (MACRO) Galois-field with characteristic 2 negation 
gf2prod(G,a,b)          Galois-field with characteristic 2 product 
gf2prodAL(AL,a,b)       Galois-field with characteristic 2 product with 
			arithmetic list 
gf2quot(G,a,b)          Galois-field with characteristic 2 quotient 
gf2squ(G,a)             Galois-field with characteristic 2 square 
gf2squAL(AL,a)          Galois-field with characteristic 2 square with 
			arithmetic list 
gf2sum(G,a,b)           Galois-field with characteristic 2 sum 
gfsalgen(p,n,G)         Galois-field with single characteristic arithmetic 
			list generator 
gfsalgenies(p,m,n,ALn)  Galois-field with single characteristic arithmetic 
			list generator isomorphic embedding of subfield 
gfsdif(p,AL,a,b)        (MACRO) Galois-field with single characteristic 
			difference 
gfsefe(p,ALm,a,g)       Galois-field with single characteristic embedding 
			in field extension 
gfselrand(p,AL)         Galois-field with single characteristic, element 
			randomize 
gfseltogf2el(G,a)       Galois-field with single characteristic element to 
			Galois-field with characteristic 2 element 
gfsexp(p,AL,a,m)        Galois-field with single characteristic 
			exponentiation 
gfsinv(p,AL,a)          Galois-field with single characteristic inverse 
gfsneg(p,AL,a)          (MACRO) Galois-field with single characteristic 
			negation 
gfsnegf(p,AL,a)         Galois-field with single characteristic negation as 
			function 
gfsprod(p,AL,a,b)       Galois-field with single characteristic product 
gfsquot(p,AL,a,b)       Galois-field with single characteristic quotient 
gfssum(p,AL,a,b)        (MACRO) Galois-field with single characteristic sum 
gfssumf(p,AL,a,b)       Galois-field with single characteristic sum as 
			function 
giant                   step version qffmsregbg(m,D) quadratic function 
			field over modular singles regulator, baby step - 
giant                   step version qffmsregobg(m,D) quadratic function 
			field over modular singles regulator, original baby 
			step - 
giant                   step version, first case qffmsregbg1(m,D,s) 
			quadratic function field over modular singles 
			regulator, baby step - 
giant                   step version, fourth case qffmsregbg4(m,D,s) 
			quadratic function field over modular singles 
			regulator, baby step - 
giant                   step version, second case qffmsregbg2(m,D,s) 
			quadratic function field over modular singles 
			regulator, baby step - 
giant                   step version, third case qffmsregbg3(m,D,s) 
			quadratic function field over modular singles 
			regulator, baby step - 
given                   number of points, j-invariant iecgnpj(p,m,h1,h2,D) 
			integer elliptic curve of 
global                  and static variables globbind(pL) bind for 
global                  and static variables globinit(pL) init for 
global                  minimal model ( Laska's algorithm ) 
			ecractoecimin(E) elliptic curve over rational 
			numbers, actual curve to 
globals                 PAFglob() Papanikolaou floating point package: 
globbind(pL)            bind for global and static variables 
globinit(pL)            init for global and static variables 
graduated               lexicographical order dipgfslotglo(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in 
graduated               lexicographical order dipilotoglo(r,P) distributive 
			polynomial over integers in lexicographical order 
			to distributive polynomial over integers in 
graduated               lexicographical order dipmiplotglo(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over modular integer primes in 
graduated               lexicographical order dipmsplotglo(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order to distributive polynomial 
			over modular single primes in 
graduated               lexicographical order dipnflotoglo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order to distributive polynomial 
			over number field in 
graduated               lexicographical order dippilotoglo(r1,r2,P) 
			distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
			polynomial over polynomials over integers in 
graduated               lexicographical order diprfrlotglo(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals in 
graduated               lexicographical order diprlotoglo(r,P) distributive 
			polynomial over rationals in lexicographical order 
			to distributive polynomial over rationals in 
greatest                common divisor HDigcd() Heidelberg arithmetic 
			package: 
greatest                common divisor and cofactors (rekursiv) 
			pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
			integers 
greatest                common divisor and cofactors (rekursiv) 
			pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
			singles 
greatest                common divisor and cofactors igcdcf(A,B,pU,pV) 
			integer 
greatest                common divisor and cofactors 
			pigcdcf(r,P1,P2,pQ1,pQ2) polynomial over integers 
greatest                common divisor and cofactors 
			upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate polynomial 
			over number field 
greatest                common divisor iegcd(A,B,pU,pV) integer extended 
greatest                common divisor igcd(A,B) integer 
greatest                common divisor ihegcd(A,B,pV) integer half extended 
greatest                common divisor segcd(a,b,pu,pv) single-precision 
			extended 
greatest                common divisor sgcd(a,b) single-precision 
greatest                common divisor udpmiegcd(m,P1,P2,pPX,pPY) 
			univariate dense polynomial over modular integers 
			extended 
greatest                common divisor udpmigcd(m,P1,P2) univariate dense 
			polynomial over modular integers 
greatest                common divisor udpmihegcd(m,P1,P2,pP3) univariate 
			dense polynomial over modular integers half 
			extended 
greatest                common divisor udpmsegcd(m,P1,P2,pPX,pPY) 
			univariate dense polynomial over modular singles 
			extended 
greatest                common divisor udpmsgcd(m,P1,P2) univariate dense 
			polynomial over modular singles 
greatest                common divisor udpmshegcd(m,P1,P2,pP3) univariate 
			dense polynomial over modular singles half extended 
greatest                common divisor upgf2gcd(G,P1,P2) univariate 
			polynomial over Galois-field with characteristic 2 
greatest                common divisor upgfsegcd(p,AL,P1,P2,pP3,pP4) 
			univariate polynomial over Galois-field with single 
			characteristic extended 
greatest                common divisor upgfsgcd(p,AL,P1,P2) univariate 
			polynomial over Galois-field with single 
			characteristic 
greatest                common divisor upgfshegcd(p,AL,P1,P2,pP3) 
			univariate polynomial over Galois-field with single 
			characteristic half extended 
greatest                common divisor upmiegcd(P,P1,P2,pP3,pP4) univariate 
			polynomial over modular integers extended 
greatest                common divisor upmigcd(ip,P1,P2) univariate 
			polynomial over modular integers 
greatest                common divisor upmihegcd(P,P1,P2,pP3) univariate 
			polynomial over modular integers half extended 
greatest                common divisor upmsegcd(m,P1,P2,pP3,pP4) univariate 
			polynomial over modular singles extended 
greatest                common divisor upmsgcd(m,P1,P2) univariate 
			polynomial over modular singles 
greatest                common divisor upmshegcd(m,P1,P2,pP3) univariate 
			polynomial over modular singles half extended 
greatest                common divisor upnfgcd(F,P1,P2) univariate 
			polynomial over number field 
greatest                common divisor uprfmsp1egcd(p,P1,P2,pF1,pF2) 
			univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1, 
			extended 
greatest                common divisor, lists only igcd_lo(A,B) integer 
greatest                squarefree divisor (rekursiv) upgfsgsd(p,AL,P) 
			univariate polynomial over Galois-field with single 
			characteristic 
greatest                squarefree divisor (rekursiv) upmigsd(ip,P) 
			univariate polynomial over modular integers 
greatest                squarefree divisor (rekursiv) upmsgsd(m,P) 
			univariate polynomial over modular singles 
group                   ecimingentor(E) elliptic curve with integer 
			coefficients, minimal model, generators of torsion 
group                   ecimintorgr(E) elliptic curve with integer 
			coefficients, minimal model, torsion 
group                   ecisnfgentor(E) elliptic curve with integer 
			coefficients, short normal form, generators of the 
			torsion 
group                   ecisnftorgr(E) elliptic curve with integer 
			coefficients, short normal form, torsion 
group                   ecracgentor(E) elliptic curve over rational 
			numbers, actual curve, generators of torsion 
group                   ecractorgr(E) elliptic curve over rational numbers, 
			actual curve, torsion 
group                   ecrexptor(E) elliptic curve over rational numbers, 
			exponent of torsion 
group                   ecrordtor(E) elliptic curve over rational numbers, 
			order of torsion 
group                   ecrordtsg(E) elliptic curve over the rational 
			numbers, order of Tate- Shafarevic 
group                   ecrstrtor(E) elliptic curve over rational numbers, 
			structure of torsion 
group                   generators and isomorphy type, imaginary case 
			qffmsicggii(m,D,H,L,pIT) quadratic function field 
			over modular singles ideal class 
group                   generators and isomorphy type, real case 
			qffmsicggir(m,D,d,H,L,pIT) quadratic function field 
			over modular singles ideal class 
group                   isomorphy type, imaginary case 
			qffmszcgiti(m,D,LG,IT) quadratic function field 
			over modular singles zero class 
group                   isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function 
			field over modular singles zero class 
group                   qnfunit(D) quadratic number field unit 
group                   structure, imaginary case qffmsicgsti(m,D,L) 
			quadratic function field over modular singles ideal 
			class 
group                   structure, real case qffmsicgstr(m,D,d,LG,pHid) 
			quadratic function field over modular singles ideal 
			class 
group                   system of representatives qffmsicgrep(m,D,pHid) 
			quadratic function field over modular singles ideal 
			class 
group                   system of representatives, imaginary case 
			qffmsicgri(m,D,pHid) quadratic function field over 
			modular singles ideal class 
group                   system of representatives, real case 
			qffmsicgrr(m,D,d) quadratic function field over 
			modular singles ideal class 
half                    extended greatest common divisor ihegcd(A,B,pV) 
			integer 
half                    extended greatest common divisor 
			udpmihegcd(m,P1,P2,pP3) univariate dense polynomial 
			over modular integers 
half                    extended greatest common divisor 
			udpmshegcd(m,P1,P2,pP3) univariate dense polynomial 
			over modular singles 
half                    extended greatest common divisor 
			upgfshegcd(p,AL,P1,P2,pP3) univariate polynomial 
			over Galois-field with single characteristic 
half                    extended greatest common divisor 
			upmihegcd(P,P1,P2,pP3) univariate polynomial over 
			modular integers 
half                    extended greatest common divisor 
			upmshegcd(m,P1,P2,pP3) univariate polynomial over 
			modular singles 
handling                flerr() (MACRO) floating point overflow error 
height                  and Neron-Tate height ecimindwhnth(E) elliptic 
			curve with integer coefficients, minimal model, 
			difference between Weil 
height                  and Neron-Tate height ecisnfdwhnth(E) elliptic 
			curve with integer coefficients, short normal form, 
			difference between Weil 
height                  at the archimedean absolute value eciminlhaav(E,P) 
			elliptic curve with integer coefficients, minimal 
			model, local 
height                  ecimindwhnth(E) elliptic curve with integer 
			coefficients, minimal model, difference between 
			Weil height and Neron-Tate 
height                  eciminnetahe(E,P) elliptic curve with integer 
			coefficients, minimal model, Neron-Tate 
height                  ecisnfdwhnth(E) elliptic curve with integer 
			coefficients, short normal form, difference between 
			Weil height and Neron-Tate 
height                  ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve 
			with integer coefficients, short normal form, 
			points of bounded Weil 
height                  ecracweilhe(E,P) elliptic curve over the rational 
			numbers, Weil 
height                  rabsheight(r) rational number absolute 
heights                 at all non archimedean absolute values 
			eciminlhnaav(E,P) elliptic curve with integer 
			coefficients, minimal model, local 
hermitian               reduction cdmarfmsp1hr(p,M) common denominator 
			matrix of rational functions over modular single 
			prime, transcendence degree 1, 
hermitian               reduction cdmarhermred(M) common denominator matrix 
			of rationals, 
hermitian               reduction, special maihermspec(M,r,pD) matrix of 
			integers 
hermitian               reduction, special maupmshermsp(p,M,r,pD) matrix of 
			univariate polynomials over modular single primes 
higher                  derivative ecrlserhd(E,r) elliptic curve over 
			rational numbers, L-series, 
higher                  derivative, large conductor 
			ecrlserhdlc(E,A,s,result) elliptic curve over the 
			rationals, L-series, 
higher                  derivative, small conductor 
			ecrlserhdsc(E,A,r,result) elliptic curve over 
			rational numbers, L-series, 
homogenize              diphomog(r,P) distributive polynomial 
homogenize              specified variable diphomogsv(r,P,n) distributive 
			polynomial 
homomorphism            cdprfmsp1mh(p,P,M) common denominator polynomial 
			over rational functions over modular single primes, 
			transcendence degree 1, module 
homomorphism            cdprzmodhom(P,M) common denominator polynomial over 
			the rationals Z-module 
homomorphism            m4hom(a) (MACRO) modular 4 
homomorphism            mihom(M,A) modular integer 
homomorphism            mshom(m,A) modular single 
homomorphism            pimidhom(r,S,P) polynomial over integers modular 
			ideal 
homomorphism            qnfpihom(D,P,pi,z,a) quadratic number field prime 
			ideal 
homomorphism            zero? isqnfppihom0(D,P,k,pi,z,a) is quadratic 
			number field element power of prime ideal 
homomorphism,           symmetric remainder system mihoms(M,A) modular 
			integer 
homomorphism,           symmetric remainder system mshoms(m,A) (MACRO) 
			modular single-precision 
hyperbolicus            special version flath_sp(f) floating point area 
			tangens 
i-node                  comparison inocmp(dk1,dk2) 
i22prod(A,B)            integer 2x2 product 
iHDfu(func,anzahlargs,arg1,arg2) integer using Heidelberg arithmetic 
			functions 
iabs(A)                 (MACRO) integer absolute value 
iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic function over modular single 
			primes, transcendence degree 1, minimal polynomial 
			modulo power of an univariate prime polynomial over 
			modular single primes 
iafmsp1mpol(p,F,a,Q)    integral algebraic function over modular single 
			primes, transcendence degree 1, minimal polynomial 
iafmsp1psval(p,P,A)     integral algebraic function over modular single 
			prime, transcendence degree 1, P-star valuation 
iaval(m,A)              integer additive m-adic value 
iavalint(M,I)           integer additive value with respect to integer 
ibinom(n,k)             integer binomial coefficient 
icomp(A,B)              integer comparison 
ideal                   class group generators and isomorphy type, 
			imaginary case qffmsicggii(m,D,H,L,pIT) quadratic 
			function field over modular singles 
ideal                   class group generators and isomorphy type, real 
			case qffmsicggir(m,D,d,H,L,pIT) quadratic function 
			field over modular singles 
ideal                   class group structure, imaginary case 
			qffmsicgsti(m,D,L) quadratic function field over 
			modular singles 
ideal                   class group structure, real case 
			qffmsicgstr(m,D,d,LG,pHid) quadratic function field 
			over modular singles 
ideal                   class group system of representatives 
			qffmsicgrep(m,D,pHid) quadratic function field over 
			modular singles 
ideal                   class group system of representatives, imaginary 
			case qffmsicgri(m,D,pHid) quadratic function field 
			over modular singles 
ideal                   class group system of representatives, real case 
			qffmsicgrr(m,D,d) quadratic function field over 
			modular singles 
ideal                   class number qffmsicn(m,P) quadratic function field 
			over modular singles 
ideal                   class qffmsiselic(m,D,L,Q,P) quadratic function 
			field over modular singles is element of an 
ideal                   class, imaginary case qffmsordsici(m,D,Q,P,OS) 
			quadratic function field over modular singles order 
			of one single 
ideal                   class, real case qffmsordsicr(m,D,d,LE,ID,OS) 
			quadratic function field over modular singles order 
			of one single 
ideal                   comparison qnfidcomp(D,A,B) quadratic number field 
ideal                   dipdimpolid(r,G,pS,pM) distributive polynomial 
			dimension of a polynomial 
ideal                   exponentiation qnfidexp(D,A,e) quadratic number 
			field 
ideal                   factorization of the discriminant ecqnfacpifdi(E) 
			elliptic curve over quadratic number field, actual 
			model, prime 
ideal                   factorization qnfpifact(D,a) quadratic number field 
			element prime 
ideal                   factorization, special version qnfielpifacts(D,a,L) 
			quadratic number field integral element prime 
ideal                   fputqnfid(D,A,pf) file put quadratic number field 
ideal                   generating element, real case, 
			qffmspidgenr(m,D,Q,P,G,pB) quadratic function field 
			over modular singles, principal 
ideal                   homomorphism pimidhom(r,S,P) polynomial over 
			integers modular 
ideal                   homomorphism qnfpihom(D,P,pi,z,a) quadratic number 
			field prime 
ideal                   homomorphism zero? isqnfppihom0(D,P,k,pi,z,a) is 
			quadratic number field element power of prime 
ideal                   membership test dippipim(r1,r2,s,PL,PTL,CONDS,OPL) 
			distributive polynomial over polynomials over 
			integers parametric 
ideal                   membership test fputdippipim(r1,r2,NOUT,VL1,VL2,pf) 
			file put distributive polynomial over polynomials 
			over integers parametric 
ideal                   membership test putdippipim(r1,r2,NOUT,VL1,VL2) 
			(MACRO) put distributive polynomial over 
			polynomials over integers parametric 
ideal                   one qnfidone(D) (MACRO) quadratic number field 
ideal                   one? isqnfidone(D,A) is quadratic number field 
ideal                   order qnfielpiord(D,P,pi,z,a) quadratic number 
			field, integral element, prime 
ideal                   order qnfpiord(D,P,pi,z,a) quadratic number field 
			element prime 
ideal                   product pimidprod(r,S,P1,P2) polynomial over 
			integers modular 
ideal                   product pmimidprod(r,M,S,P1,P2) polynomial over 
			modular integers, modular 
ideal                   product qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles primitive 
ideal                   product qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over modular singles, 
			sparse representation, primitive 
ideal                   product qnfidprod(D,A,B) quadratic number field 
ideal                   product, special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles primitive 
ideal                   product, special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, primitive 
ideal                   putqnfid(D,A) (MACRO) put quadratic number field 
ideal                   qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular singles, imaginary case, sparse 
			representation, reduction of a primitive 
ideal                   qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real case, reduction of 
			a primitive 
ideal                   qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real case, sparse 
			representation, reduction of a primitive 
ideal                   qnfsysrmodpi(D,P,pi,z,k) quadratic number field 
			system of representatives modulo a prime 
ideal                   quotient and remainder pmimidqrem(r,M,S,P1,P2,pR) 
			polynomial over modular integers monic, modular 
ideal                   reduction qffmsipidred(m,D,Q,P,pQr,pPr) quadratic 
			function field over modular singles, imaginary 
			case, primitive 
ideal                   solution of equation 
			pmimidse(r,M,S,P1,P2,F1,F2,H,pV) polynomial over 
			modular integers modular 
ideal                   special qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic 
			function field over modular singles is equal 
ideal                   square qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic 
			function field over modular singles primitive 
ideal                   square qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, primitive 
ideal                   square qnfidsquare(D,A) quadratic number field 
ideal                   square, special version 
			qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles primitive 
ideal                   square, special version 
			qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, sparse representation, 
			primitive 
ideal,                  Hensel lemma quadratic step on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
			modular integers, modular 
ideal,                  Hensel lemma quadratic step 
			pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial over 
			integers, modular 
ideal,                  Hensel lemma quadratic step 
			pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial 
			over modular integers, modular 
identity                construction cdmarfmsp1id(n) common denominator 
			matrix of rational functions over modular single 
			prime, transcendence degree 1, 
identity                construction cdmarid(n) common denominator matrix 
			of rationals, 
idif(A,B)               integer difference 
iecfindp(p,a,b)         integer elliptic curve find point 
iecgnpj(p,m,h1,h2,D)    integer elliptic curve of given number of points, 
			j-invariant 
iecjtoeq(p,j)           integer elliptic curve j-invariant to equation 
iecjtoeqsv(p,j,pi)      integer elliptic curve j-invariant to equation 
			special version 
iecpprod(p,E,P,a)       integer elliptic curve point product 
iecpsum(p,P,Q,a)        integer elliptic curve point sum 
iecpt(n,m,lp,a,b,anz)   integer elliptic curve primality test 
iegcd(A,B,pU,pV)        integer extended greatest common divisor 
ieven(A)                integer even 
iexp(A,n)               integer exponentiation 
ifact([-brk,][-imp,][-elc,][-rho,]N) integer factorization (rekursiv) 
ifact60(N)              integer factorization, N < 2^60 
ifact_o(N)              integer factorization, old version (rekursiv) 
ifactcfe(n,Large_P,K,mode) integer factorization continued fraction 
			expansion 
ifactl(a)               integer factorial 
ifactlf(n,G,p,quot)     integer factorization large factor 
ifactpp(N)              integer factorization into pseudoprimes (rekursiv) 
ifel(LP)                integer factor exponent list 
ifelprod(a,b)           integer factor exponent list product 
ifrl(N,pm)              integer Fermat residue list 
iftpt(n,L,anz)          integer Fermat's theorem primality test 
igcd(A,B)               integer greatest common divisor 
igcd_lo(A,B)            integer greatest common divisor, lists only 
igcdcf(A,B,pU,pV)       integer greatest common divisor and cofactors 
igkapt(n,msg)           integer Goldwasser Kilian Atkin primality test 
			(rekursiv) 
ihegcd(A,B,pV)          integer half extended greatest common divisor 
ijacsym(A,B)            integer Jacobi-symbol 
ijacsym_lo(A,B)         integer Jacobi-symbol ( lists only ) 
ilcm(A,B)               integer least common multiple 
ilcomb(A,B,m,n)         integer linear combination 
ilkprime()              integer largest known prime 
ilog10(n)               integer logarithm, base 10 
ilog2(A)                integer logarithm, base 2 
ilpds(N,A,B,pP,pN1)     integer large prime divisor search 
imaginary               case qffmsicggii(m,D,H,L,pIT) quadratic function 
			field over modular singles ideal class group 
			generators and isomorphy type, 
imaginary               case qffmsicgri(m,D,pHid) quadratic function field 
			over modular singles ideal class group system of 
			representatives, 
imaginary               case qffmsicgsti(m,D,L) quadratic function field 
			over modular singles ideal class group structure, 
imaginary               case qffmsordsici(m,D,Q,P,OS) quadratic function 
			field over modular singles order of one single 
			ideal class, 
imaginary               case qffmszcgiti(m,D,LG,IT) quadratic function 
			field over modular singles zero class group 
			isomorphy type, 
imaginary               case, primitive ideal reduction 
			qffmsipidred(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular singles, 
imaginary               case, sparse representation, reduction of a 
			primitive ideal qffmsispidrd(m,D,Q,P,pQr,pPr) 
			quadratic function field over modular singles, 
imaginary               part ccri(re,im) (MACRO) complex construction from 
			real and 
imaginary               part cimag(z) (MACRO) complex 
imaginary               quadratic field iprniqf(p,D) integer prime 
			representation as a norm in an 
imax(A,B)               (MACRO) integer maximum 
imin(A,B)               (MACRO) integer minimum 
imp2d(A)                integer maximal power of 2 divisibility 
impds(N,A,B,pP,pQ)      integer medium prime divisor search 
imspds(N,a,b)           integer medium single prime divisor search 
increasing              the denominator of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over modular single primes, transcendence 
			degree 1, 
increasing              the denominator of the p-star value 
			ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, 
increasing              the denominator of the p-star value with respect to 
			integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, 
indices                 qnframind(D,p) quadratic number field ramification 
inearesttor(r)          integer nearest to rational number 
ineg(A)                 integer negation 
infeminpmpp(F,a,p,e,Q)  integral number field element minimal polynomial 
			modulo p-power 
infempmppip(F,a,p,e,Q)  integral number field element minimal polynomial 
			modulo p-power with respect to integer primes 
infepptfact(F,p,Q,ppot,a0,z) integral number field element p-primality test 
			and factorization of the defining polynomial or the 
			minimal polynomial 
infepptfip(F,p,Q,ppot,a0,z) integral number field element p-primality test 
			and factorization of the defining polynomial or the 
			minimal polynomial with respect to integer primes 
infepstarval(p,A)       integral number field element p-star valuation 
infepstarvip(P,A)       integral number field element p-star valuation with 
			respect to integer primes 
infinity                ? ispecrpai(P) (MACRO) is point of an elliptic 
			curve over the rationals point at 
infinity                ? isppecgf2pai(G,P) is projective point of an 
			elliptic curve over Galois-field with 
			characteristic 2 point at 
infinity                ? isppecmppai(p,P) is projective point of an 
			elliptic curve over modular primes point at 
infinity                ? isppecnfpai(P) is projective point of an elliptic 
			curve over number field point at 
init                    for global and static variables globinit(pL) 
initialization          ecqnfinit(D,a1,a2,a3,a4,a6) elliptic curve over 
			quadratic number field, 
initialization          ecrinit(a1r,a2r,a3r,a4r,a6r) elliptic curve over 
			the rational numbers 
initialization          flinit(k) floating point 
initialization          upihli(p,P,L) univariate polynomial over integers, 
			Hensel lemma 
initialization          upprmsp1hli(p,F,P,L) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, Hensel lemma 
initialization          with respect to integer prime upihliip(P,F,L) 
			univariate polynomial over integers, Hensel lemma 
inocmp(dk1,dk2)         i-node comparison 
insert                  lecins(L,k,a) list element constructive 
insert                  leins(L,k,a) list element 
insert                  lsins(n,L) list of single precisions 
insert                  point eciminplinsp(P,h,PL) elliptic curve with 
			integer coefficients, minimal model, point list, 
insert,                 2nd position leins2(a,L) list element 
insertion               of new variables (rekursiv) pvinsert(r,P,k) 
			polynomial 
integer                 2x2 product i22prod(A,B) 
integer                 ? (rekursiv) ispmi(r,m,P) is polynomial over 
			modular 
integer                 ? isint(A) is 
integer                 ? ismi(m,a) is modular 
integer                 Etoi(e) Essen integer to SIMATH 
integer                 Fermat residue ? ismifr(M,A,B) is modular 
integer                 Fermat residue list ifrl(N,pm) 
integer                 Fermat's theorem primality test iftpt(n,L,anz) 
integer                 Goldwasser Kilian Atkin primality test (rekursiv) 
			igkapt(n,msg) 
integer                 Itoi(h) ( Heidelberg ) Integer to ( SIMATH ) 
integer                 Jacobi-symbol ( lists only ) ijacsym_lo(A,B) 
integer                 Jacobi-symbol ijacsym(A,B) 
integer                 P-part with respect to an integer intppint(P,A) 
integer                 Selfridge primality test ispt(M,M1,F) 
integer                 absolute value iabs(A) (MACRO) 
integer                 addition HDiadd() Heidelberg arithmetic package: 
integer                 additive m-adic value iaval(m,A) 
integer                 additive value with respect to integer 
			iavalint(M,I) 
integer                 binomial coefficient ibinom(n,k) 
integer                 chinese remainder algorithm micra(M1,M2,N1,A1,A2) 
			modular 
integer                 chinese remainder algorithm, n arguments (rekursiv) 
			micran(n,LM,LA) modular 
integer                 coefficients Tate's algorithm 
			ecitatealg(a1,a2,a3,a4,a6,p,n) elliptic curve with 
integer                 coefficients, Tate's values b2, b4, b6, b8 
			ecitavalb(a1,a2,a3,a4,a6) elliptic curve with 
integer                 coefficients, actual curve, difference of points 
			ecracdif(E,P,Q) elliptic curve with 
integer                 coefficients, minimal model fputecimin(E,pf) file 
			put elliptic curve with 
integer                 coefficients, minimal model isecimintorp(E,P) is 
			torsion point on elliptic curve with 
integer                 coefficients, minimal model isineciminpl(E,P,h,PL) 
			is in list of points on elliptic curve with 
integer                 coefficients, minimal model isponecimin(E,P) is 
			point on elliptic curve with 
integer                 coefficients, minimal model putecimin(E) (MACRO) 
			put elliptic curve with 
integer                 coefficients, minimal model to short normal form 
			ecimintosnf(E) elliptic curve with 
integer                 coefficients, minimal model, Mordell-Weil-group, 
			base eciminmwgbase(E) elliptic curve with 
integer                 coefficients, minimal model, Neron-Tate height 
			eciminnetahe(E,P) elliptic curve with 
integer                 coefficients, minimal model, Neron-Tate pairing 
			eciminnetapa(E,P,Q) elliptic curve with 
integer                 coefficients, minimal model, Tate's algorithm 
			ecimintatealg(E,p,n) elliptic curve with 
integer                 coefficients, minimal model, Tate's values c4, c6 
			ecitavalc(a1,a2,a3,a4,a6) elliptic curve with 
integer                 coefficients, minimal model, a1 ecimina1(E) 
			elliptic curve with 
integer                 coefficients, minimal model, a2 ecimina2(E) 
			elliptic curve with 
integer                 coefficients, minimal model, a3 ecimina3(E) 
			elliptic curve with 
integer                 coefficients, minimal model, a4 ecimina4(E) 
			elliptic curve with 
integer                 coefficients, minimal model, a6 ecimina6(E) 
			elliptic curve with 
integer                 coefficients, minimal model, b2 eciminb2(E) 
			elliptic curve with 
integer                 coefficients, minimal model, b4 eciminb4(E) 
			elliptic curve with 
integer                 coefficients, minimal model, b6 eciminb6(E) 
			elliptic curve with 
integer                 coefficients, minimal model, b8 eciminb8(E) 
			elliptic curve with 
integer                 coefficients, minimal model, bad reduction type 
			modulo prime eciminbrtmp(E,p,n) elliptic curve with 
integer                 coefficients, minimal model, birational 
			transformation of coefficients eciminbtco(E,BT) 
			elliptic curve with 
integer                 coefficients, minimal model, birational 
			transformation to actual ( rational ) model 
			eciminbtac(E) elliptic curve with 
integer                 coefficients, minimal model, birational 
			transformation to short normal form eciminbtsnf(E) 
			elliptic curve with 
integer                 coefficients, minimal model, c4 eciminc4(E) 
			elliptic curve with 
integer                 coefficients, minimal model, c6 eciminc6(E) 
			elliptic curve with 
integer                 coefficients, minimal model, difference between 
			Weil height and Neron-Tate height ecimindwhnth(E) 
			elliptic curve with 
integer                 coefficients, minimal model, difference of points 
			ecimindif(E,P,Q) elliptic curve with 
integer                 coefficients, minimal model, difference of points 
			ecisnfdif(E,P,Q) elliptic curve with 
integer                 coefficients, minimal model, discriminant 
			ecimindisc(E) elliptic curve with 
integer                 coefficients, minimal model, division by 2 of a 
			point ecimindivby2(E,P,h,PL,H) elliptic curve with 
integer                 coefficients, minimal model, division of a point by 
			an integer ecimindiv(E,P,n) elliptic curve with 
integer                 coefficients, minimal model, division of a point by 
			an integer, special version 
			ecimindivs(E,P,h,ug,PL,n) elliptic curve with 
integer                 coefficients, minimal model, double of a point 
			ecimindouble(E,P) elliptic curve with 
integer                 coefficients, minimal model, factorization of 
			discriminant eciminfdisc(E) elliptic curve with 
integer                 coefficients, minimal model, generators of torsion 
			group ecimingentor(E) elliptic curve with 
integer                 coefficients, minimal model, local height at the 
			archimedean absolute value eciminlhaav(E,P) 
			elliptic curve with 
integer                 coefficients, minimal model, local heights at all 
			non archimedean absolute values eciminlhnaav(E,P) 
			elliptic curve with 
integer                 coefficients, minimal model, multiplication-map 
			eciminmul(E,P,n) elliptic curve with 
integer                 coefficients, minimal model, multiplicative 
			reduction type modulo prime eciminmrtmp(E,p) 
			elliptic curve with 
integer                 coefficients, minimal model, negative point 
			eciminneg(E,P) elliptic curve with 
integer                 coefficients, minimal model, point comparison 
			modulo torsion eciminpcompmt(E,P1,P2) elliptic 
			curve with 
integer                 coefficients, minimal model, point list union 
			eciminplunion(E,L1,L2,modus) elliptic curve with 
integer                 coefficients, minimal model, point list, insert 
			point eciminplinsp(P,h,PL) elliptic curve with 
integer                 coefficients, minimal model, reduction type 
			eciminredtype(E) elliptic curve with 
integer                 coefficients, minimal model, regulator 
			eciminreg(E,LP,n,modus) elliptic curve with 
integer                 coefficients, minimal model, set NTH_EPS 
			eciminntheps(E,d) elliptic curve with 
integer                 coefficients, minimal model, sum of points 
			eciminsum(E,P,Q) elliptic curve with 
integer                 coefficients, minimal model, torsion group 
			ecimintorgr(E) elliptic curve with 
integer                 coefficients, model in short normal form 
			isponecisnf(E,P) is point on elliptic curve with 
integer                 coefficients, point normalization ecipnorm(P) 
			elliptic curve with 
integer                 coefficients, short normal form fputecisnf(E,*pf) 
			file put elliptic curve with 
integer                 coefficients, short normal form putecisnf(E) 
			(MACRO) put elliptic curve with 
integer                 coefficients, short normal form, 
			Mordell-Weil-group, base ecisnfmwgbase(E) elliptic 
			curve with 
integer                 coefficients, short normal form, a4 ecisnfa4(E) 
			elliptic curve with 
integer                 coefficients, short normal form, a6 ecisnfa6(E) 
			elliptic curve with 
integer                 coefficients, short normal form, b2 ecisnfb2(E) 
			elliptic curve with 
integer                 coefficients, short normal form, b4 ecisnfb4(E) 
			elliptic curve with 
integer                 coefficients, short normal form, b6 ecisnfb6(E) 
			elliptic curve with 
integer                 coefficients, short normal form, b8 ecisnfb8(E) 
			elliptic curve with 
integer                 coefficients, short normal form, birational 
			transformation of coefficients ecisnfbtco(E,BT) 
			elliptic curve with 
integer                 coefficients, short normal form, birational 
			transformation to actual ( rational ) model 
			ecisnfbtac(E) elliptic curve with 
integer                 coefficients, short normal form, birational 
			transformation to minimal model ecisnfbtmin(E) 
			elliptic curve with 
integer                 coefficients, short normal form, c4 ecisnfc4(E) 
			elliptic curve with 
integer                 coefficients, short normal form, c6 ecisnfc6(E) 
			elliptic curve with 
integer                 coefficients, short normal form, difference between 
			Weil height and Neron-Tate height ecisnfdwhnth(E) 
			elliptic curve with 
integer                 coefficients, short normal form, discriminant 
			ecisnfdisc(E) elliptic curve with 
integer                 coefficients, short normal form, double of point 
			ecisnfdouble(E,P) elliptic curve with 
integer                 coefficients, short normal form, elliptic logarithm 
			of point ecisnfelogp(E,P,n) elliptic curve with 
integer                 coefficients, short normal form, factorization of 
			discriminant ecisnffdisc(E) elliptic curve with 
integer                 coefficients, short normal form, generators of the 
			torsion group ecisnfgentor(E) elliptic curve with 
integer                 coefficients, short normal form, multiplication-map 
			ecisnfmul(E,P,n) elliptic curve with 
integer                 coefficients, short normal form, negative of point 
			ecisnfneg(E,P) elliptic curve with 
integer                 coefficients, short normal form, points of bounded 
			Weil height ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) 
			elliptic curve with 
integer                 coefficients, short normal form, sum of points 
			ecisnfsum(E,P,Q) elliptic curve with 
integer                 coefficients, short normal form, torsion group 
			ecisnftorgr(E) elliptic curve with 
integer                 comparison icomp(A,B) 
integer                 content (rekursiv) piicont(r,P) polynomial over 
			integers 
integer                 determined with the Schoof algorithm 
			ecgf2npmi(G,a6,S,v,pM) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo an 
integer                 determined with the Schoof algorithm 
			ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve over 
			modular primes, short normal form, number of points 
			modulo an 
integer                 difference idif(A,B) 
integer                 difference midif(M,A,B) modular 
integer                 division HDidiv() Heidelberg arithmetic package: 
integer                 ecimindiv(E,P,n) elliptic curve with integer 
			coefficients, minimal model, division of a point by 
			an 
integer                 elliptic curve find point iecfindp(p,a,b) 
integer                 elliptic curve j-invariant to equation 
			iecjtoeq(p,j) 
integer                 elliptic curve j-invariant to equation special 
			version iecjtoeqsv(p,j,pi) 
integer                 elliptic curve of given number of points, 
			j-invariant iecgnpj(p,m,h1,h2,D) 
integer                 elliptic curve point product iecpprod(p,E,P,a) 
integer                 elliptic curve point sum iecpsum(p,P,Q,a) 
integer                 elliptic curve primality test iecpt(n,m,lp,a,b,anz) 
integer                 eulerian phi-value iphi(N) 
integer                 even ieven(A) 
integer                 exponentiation ( lists only ) miexp_lo(M,A,E) 
			modular 
integer                 exponentiation iexp(A,n) 
integer                 exponentiation miexp(M,A,E) modular 
integer                 exponentiation, polynomial, remainder 
			upgfsmieprem(p,AL,a,t,P) univariate polynomial over 
			Galois-field, monomial, 
integer                 extended greatest common divisor iegcd(A,B,pU,pV) 
integer                 factor exponent list fputifel(L,pf) file put 
integer                 factor exponent list ifel(LP) 
integer                 factor exponent list product ifelprod(a,b) 
integer                 factor exponent list putifel(L) (MACRO) put 
integer                 factorial ifactl(a) 
integer                 factorization (rekursiv) 
			ifact([-brk,][-imp,][-elc,][-rho,]N) 
integer                 factorization continued fraction expansion 
			ifactcfe(n,Large_P,K,mode) 
integer                 factorization into pseudoprimes (rekursiv) 
			ifactpp(N) 
integer                 factorization large factor ifactlf(n,G,p,quot) 
integer                 factorization, N < 2^60 ifact60(N) 
integer                 factorization, old version (rekursiv) ifact_o(N) 
integer                 fgeti(pf) file get 
integer                 fgetmi(M,pf) file get modular 
integer                 fputi(A,pf) file put 
integer                 fputmi(M,A,pf) file put modular 
integer                 geti() (MACRO) get 
integer                 getmi(M) (MACRO) get modular 
integer                 greatest common divisor and cofactors 
			igcdcf(A,B,pU,pV) 
integer                 greatest common divisor igcd(A,B) 
integer                 greatest common divisor, lists only igcd_lo(A,B) 
integer                 half extended greatest common divisor 
			ihegcd(A,B,pV) 
integer                 homomorphism mihom(M,A) modular 
integer                 homomorphism, symmetric remainder system 
			mihoms(M,A) modular 
integer                 iavalint(M,I) integer additive value with respect 
			to 
integer                 intppint(P,A) integer P-part with respect to an 
integer                 inverse miinv(M,A) modular 
integer                 inverse, lists only miinv_lo(M,A) modular 
integer                 itoE(A,e) ( SIMATH ) integer to Essen 
integer                 itopi(r,A) (MACRO) integer to polynomial over 
integer                 large prime divisor search ilpds(N,A,B,pP,pN1) 
integer                 largest known prime ilkprime() 
integer                 least common multiple ilcm(A,B) 
integer                 linear combination ilcomb(A,B,m,n) 
integer                 list chinese remainder algorithm 
			milcra(m1,m2,L1,L2) modular 
integer                 logarithm, base 10 ilog10(n) 
integer                 logarithm, base 2 ilog2(A) 
integer                 maximal power of 2 divisibility imp2d(A) 
integer                 maximum imax(A,B) (MACRO) 
integer                 medium prime divisor search impds(N,A,B,pP,pQ) 
integer                 medium single prime divisor search imspds(N,a,b) 
integer                 minimum imin(A,B) (MACRO) 
integer                 multiplication HDimul() Heidelberg arithmetic 
			package: 
integer                 nearest to rational number inearesttor(r) 
integer                 negation Etoineg(e) Essen integer to SIMATH 
integer                 negation as function minegf(M,A) modular 
integer                 negation ineg(A) 
integer                 negation mineg(M,A) (MACRO) modular 
integer                 nfelmodi(F,a,M) number field element modulo 
integer                 odd iodd(A) (MACRO) 
integer                 p-part intpp(p,m) 
integer                 pairs power maximum lipairspmax(L) list of 
integer                 power of 2 product ip2prod(A,n) 
integer                 power of 2 quotient ip2quot(A,n) 
integer                 prime ? isiprime(n) is 
integer                 prime Jacobi-symbol ( Legendre-symbol ) 
			ipjacsym(a,p) 
integer                 prime additive valuation upmiaddval(p,P1,P) 
			univariate polynomial over modular 
integer                 prime construction iprimeconstr(bits,f,pL,n) 
integer                 prime decomposition law nfipdeclaw(F,P) number 
			field, 
integer                 prime divisor search dpipds(a,N) double precision 
integer                 prime find non square mipfnsquare(p) modular 
integer                 prime find square mipfsquare(p) modular 
integer                 prime generator ipgen(u,o) 
integer                 prime representation as a norm in an imaginary 
			quadratic field iprniqf(p,D) 
integer                 prime square root mipsqrt(p,r) modular 
integer                 prime upihlfaip(p,P,L,k) univariate polynomial over 
			integers, Hensel lemma factorization approximation 
			with respect to 
integer                 prime upihliip(P,F,L) univariate polynomial over 
			integers, Hensel lemma initialization with respect 
			to 
integer                 prime upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over integers, Hensel lemma quadratic 
			step with respect to 
integer                 prime, printing messages isiprimemsg(n) (MACRO) is 
integer                 primes Euklid- Gauss- step for columns 
			maupmipegsc(p,M,A,B) matrix of univariate 
			polynomials over modular 
integer                 primes Euklid- Gauss- step for rows 
			maupmipegsr(p,M,A,B) matrix of univariate 
			polynomials over modular 
integer                 primes Groebner basis augmentation 
			dipmipgba(r,p,PL,P) distributive polynomial over 
			modular 
integer                 primes Groebner basis dipmipgb(r,p,PL) distributive 
			polynomial over modular 
integer                 primes Groebner basis recursion dipmipgbr(r,p,PL) 
			distributive polynomial over modular 
integer                 primes S-polynomial dipmipsp(r,p,P1,P2) 
			distributive polynomial over modular 
integer                 primes difference dipmipdif(r,p,P1,P2) distributive 
			polynomial over modular 
integer                 primes elementary divisor form and cofactors 
			maupmipedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over modular 
integer                 primes in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular 
integer                 primes in lexicographical order to distributive 
			polynomial over modular integer primes in graduated 
			lexicographical order dipmiplotglo(r,p,P) 
			distributive polynomial over modular 
integer                 primes in lexicographical order to distributive 
			polynomial over modular integer primes in 
			lexicographical order with inverse exponent vector 
			dipmiplotlio(r,p,P) distributive polynomial over 
			modular 
integer                 primes in lexicographical order to distributive 
			polynomial over modular integer primes with total 
			degree ordering dipmiplottdo(r,p,P) distributive 
			polynomial over modular 
integer                 primes in lexicographical order with inverse 
			exponent vector dipmiplotlio(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular 
integer                 primes infempmppip(F,a,p,e,Q) integral number field 
			element minimal polynomial modulo p-power with 
			respect to 
integer                 primes infepptfip(F,p,Q,ppot,a0,z) integral number 
			field element p-primality test and factorization of 
			the defining polynomial or the minimal polynomial 
			with respect to 
integer                 primes infepstarvip(P,A) integral number field 
			element p-star valuation with respect to 
integer                 primes ippnfecalip(F,P,Q,mp) integral P-primary 
			number field element, core algorithm with respect 
			to 
integer                 primes ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) 
			integral p-primary number field element, increasing 
			the denominator of the p-star value with respect to 
integer                 primes ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field element regulation with 
			respect to 
integer                 primes list fgetdipmipl(r,p,VL,pf) file get 
			distributive polynomial over modular 
integer                 primes list fputdipmipl(r,p,PL,VL,pf) file put 
			distributive polynomial over modular 
integer                 primes list getdipmipl(r,p,VL) (MACRO) get 
			distributive polynomial over modular 
integer                 primes list putdipmipl(r,p,PL,VL) (MACRO) put 
			distributive polynomial over modular 
integer                 primes monic dipmipmonic(r,p,P) distributive 
			polynomial over modular 
integer                 primes negation dipmipneg(r,p,P) distributive 
			polynomial over modular 
integer                 primes ouspibaslmoi(F,P,Q,pk) order of an 
			univariate separable polynomial over the integers 
			basis of a local maximal over-order with respect to 
integer                 primes product dipmipmiprod(r,p,P,A) distributive 
			polynomial over modular integer primes, modular 
integer                 primes product dipmipprod(r,p,P1,P2) distributive 
			polynomial over modular 
integer                 primes short normal form number of points special 
			version ecmipsnfnpsv(p,a4,a6) elliptic curve over 
			modular 
integer                 primes sum dipmipsum(r,p,P1,P2) distributive 
			polynomial over modular 
integer                 primes with total degree ordering 
			dipmiplottdo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular 
integer                 primes, modular integer primes product 
			dipmipmiprod(r,p,P,A) distributive polynomial over 
			modular 
integer                 primitive reduced positive definite binary 
			quadratic forms iprpdbqf(D,h1,h2) 
integer                 primitive root miproot(Q) modular 
integer                 product (rekursiv) piiprod(r,P,A) polynomial over 
			integers, 
integer                 product as function miprodf(M,A,B) modular 
integer                 product ciprod(v,i) complex 
integer                 product dipiiprod(r,P,A) distributive polynomial 
			over integers, 
integer                 product iprod(A,B) 
integer                 product miprod(M,A,B) modular 
integer                 product nfeliprod(F,a,i) number field element 
integer                 product pfeliprod(p,a,i) p-adic field element 
integer                 product ppfiprod(r,p,P,i) polynomial over p-adic 
			field 
integer                 product udpiiprod(P,A) univariate dense polynomial 
			over integers 
integer                 product udpmimiprod(m,P,a) univariate dense 
			polynomial over modular integers, modular 
integer                 product, lists only iprod_lo(A,B) 
integer                 pseudo prime ? isipprime(n,a) is 
integer                 puti(A) (MACRO) put 
integer                 putmi(M,A) (MACRO) put modular 
integer                 quotient (rekursiv) piiquot(r,P,A) polynomial over 
			integers, 
integer                 quotient (rekursiv) pmimiquot(r,m,P,a) polynomial 
			over modular integers, modular 
integer                 quotient and remainder iqrem(A,B,pQ,pR) 
integer                 quotient and remainder special version 3 
			iqrem_3(A,B,pQ,pR) 
integer                 quotient and remainder, lists only 
			iqrem_lo(A,B,pQ,pR) 
integer                 quotient and remainder, old version 
			iqrem_2(A,B,pQ,pR) 
integer                 quotient cdpriquot(P,I) common denominator 
			polynomial over the rationals 
integer                 quotient ciquot(v,i) complex 
integer                 quotient iquot(A,B) (MACRO) 
integer                 quotient miquot(M,A,B) (MACRO) modular 
integer                 random divisor search (rekursiv) irds(n,G,p) 
integer                 random prime irandprime(a1,a2,n) 
integer                 randomize irand(G) 
integer                 randomize, alternative version irand_2(u) 
integer                 ravalint(M,R) rational additive value with respect 
			to 
integer                 remainder irem(A,B) (MACRO) 
integer                 right shift irshift(A) 
integer                 root iroot(A,n,ps) 
integer                 rtomi(R,M) rational number to modular 
integer                 sgeti(ps) string get 
integer                 sign isign(A) 
integer                 single chinese remainder algorithm 
			miscra(M,m,m1,A,a) modular 
integer                 single-precision product isprod(A,b) 
integer                 single-precision quotient and remainder 
			isqrem(A,b,pQ,pr) 
integer                 single-precision quotient isquot(A,b) (MACRO) 
integer                 single-precision remainder isrem(A,b) (MACRO) 
integer                 small prime divisors ( lists only ) ispd_lo(N,pM) 
integer                 small prime divisors search ispd(N,pM) 
integer                 sputi(A,str) string put 
integer                 square ? isisqr(A) is 
integer                 square ? ismisquare(M,A) is modular 
integer                 square root ( lists only ) isqrt_lo(A) 
integer                 square root all solutions misqrtas(N,r) modular 
integer                 square root isqrt(A) 
integer                 square root misqrt(m,a) modular 
integer                 square root search misqrtsrch(m,a) modular 
integer                 squarefree part isfp(A) 
integer                 strong pseudo prime ? isispprime(n,k) is 
integer                 sum as function misumf(M,A,B) modular 
integer                 sum isum(A,B) 
integer                 sum misum(M,A,B) (MACRO) modular 
integer                 to ( Heidelberg ) Integer itoI(A,h) ( SIMATH ) 
integer                 to ( Heidelberg ) Integer special version 
			itoI_sp(A,lA,h) ( SIMATH ) 
integer                 to Essen integer itoE(A,e) ( SIMATH ) 
integer                 to Essen integer with upper bound itoEb(A,e,grenze) 
			( SIMATH ) 
integer                 to Essen integer, sign and upper bound 
			itoEsb(A,e,grenze) ( SIMATH ) 
integer                 to SIMATH integer Etoi(e) Essen 
integer                 to SIMATH integer negation Etoineg(e) Essen 
integer                 to floating point itofl(A) (MACRO) 
integer                 to number field element itonf(A) (MACRO) 
integer                 to number field element, sparse representation 
			itonfs(A) 
integer                 to p-adic field element itopfel(p,d,A) 
integer                 to polynomial over integer itopi(r,A) (MACRO) 
integer                 to quadratic number field element itoqnf(D,a) 
			(MACRO) 
integer                 to rational number itor(A) 
integer                 to symmetric remainder system mitos(M,A) modular 
integer                 truncation itrunc(A,n) (MACRO) 
integer                 unit ismiunit(M,A) is modular 
integer                 using Heidelberg arithmetic functions 
			iHDfu(func,anzahlargs,arg1,arg2) 
integer                 with upper bound itoEb(A,e,grenze) ( SIMATH ) 
			integer to Essen 
integer,                difference qnfidif(D,a,b) (MACRO) quadratic number 
			field element, 
integer,                product qnfiprod(D,a,b) quadratic number field 
			element, 
integer,                quadratic number field element, difference 
			iqnfdif(D,a,b) (MACRO) 
integer,                quadratic number field element, quotient 
			iqnfquot(D,a,b) 
integer,                quotient qnfiquot(D,a,b) quadratic number field 
			element, 
integer,                sign and upper bound itoEsb(A,e,grenze) ( SIMATH ) 
			integer to Essen 
integer,                special version ecimindivs(E,P,h,ug,PL,n) elliptic 
			curve with integer coefficients, minimal model, 
			division of a point by an 
integer,                sum qnfisum(D,a,b) quadratic number field element, 
integer?                isqnfint(D,a) (MACRO) is quadratic number field 
			element 
integers                (rekursiv) pitopmi(r,P,M) polynomial over integers 
			to polynomial over modular 
integers                (rekursiv) prtopmi(r,P,M) polynomial over rationals 
			to polynomial over modular 
integers                ? (rekursiv) isdpmi(r,m,P) is dense polynomial over 
			modular 
integers                ? (rekursiv) ispi(r,P) is polynomial over 
integers                ? isimupmi(p,A) is irreducible, monic, univariate 
			polynomial over modular 
integers                ? isiupi(P) is irreducible univariate polynomial 
			over 
integers                ? isiuspi(P) is irreducible univariate squarefree 
			polynomial over 
integers                ? islisti(L) is list of 
integers                ? islistmi(M,A) is list of modular 
integers                ? ismadpi(r,M) (MACRO) is matrix of dense 
			polynomials over 
integers                ? ismai(M) (MACRO) is matrix of 
integers                ? ismami(m,M) (MACRO) is matrix of modular 
integers                ? ismapi(r,M) (MACRO) is matrix of polynomials over 
integers                ? ismapmi(r,m,M) (MACRO) is matrix of polynomials 
			over modular 
integers                ? isvecdpi(r,V) (MACRO) is vector of dense 
			polynomials over 
integers                ? isveci(V) (MACRO) is vector of 
integers                ? isvecpi(r,V) (MACRO) is vector of polynomials 
			over 
integers                Ben-Or factorization upmibofact(ip,P) univariate 
			polynomial over modular 
integers                Ben-Or factorization, special upmibofacts(ip,P) 
			univariate polynomial over modular 
integers                Berlekamp factorization, last step 
			upmibfls(ip,P,B,d) univariate polynomial over 
			modular 
integers                Bezout-matrix pibezout(r,P1,P2) polynomial over 
integers                Bezout-matrix pmibezout(r,m,P1,P2) polynomial over 
			modular 
integers                Euklid norm (rekursiv) pieuklnorm(r,P) polynomial 
			over 
integers                Euklid- Gauss- step for columns maiegsc(M,A,B) 
			matrix of 
integers                Euklid- Gauss- step for rows maiegsr(M,A,B) matrix 
			of 
integers                Galois-field with characteristic 2 element 
			evaluation first variable special version 
			(rekursiv) pigf2evalfvs(r,G,P) polynomial over 
integers                Galois-field with single characteristic element 
			evaluation first variable special version 
			(rekursiv) pigfsevalfvs(r,p,AL,P) polynomial over 
integers                Galois-field with single characteristic element 
			evaluation first variable special version 
			mapigfsevfvs(r,p,AL,M) matrix over polynomials over 
integers                Galois-field with single characteristic element 
			evaluation first variable special version 
			vecpigfsefvs(r,p,AL,V) vector over polynomials over 
integers                Gelfond-factor coefficient bound pigfcb(r,P) 
			polynomial over 
integers                Groebner basis augmentation dipigba(r,PL,P) 
			distributive polynomial over 
integers                Groebner basis augmentation dippigba(r1,r2,PL,P) 
			distributive polynomial over polynomials over 
integers                Groebner basis dipigb(r,PL) distributive polynomial 
			over 
integers                Groebner basis dippigb(r1,r2,PL) distributive 
			polynomial over polynomials over 
integers                Groebner basis recursion dipigbr(r,PL) distributive 
			polynomial over 
integers                Groebner basis recursion dippigbr(r1,r2,PL) 
			distributive polynomial over polynomials over 
integers                Groebner system 
			fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file put 
			distributive polynomial over polynomials over 
integers                Groebner system putdippigbs(r1,r2,GS,VL1,VL2,cs) 
			(MACRO) put distributive polynomial over 
			polynomials over 
integers                Groebner test dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) 
			distributive polynomial over polynomials over 
integers                Groebner test 
			fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) file 
			put distributive polynomial over polynomials over 
integers                Groebner test 
			putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) (MACRO) 
			put distributive polynomial over polynomials over 
integers                Hermite normal form ( lower triangular form with 
			negative entries ) maihermltne(A) (MACRO) matrix of 
integers                Hermite normal form ( lower triangular form with 
			positive entries ) maihermltpe(A) (MACRO) matrix of 
integers                Hermite normal form maiherm(A,ne) matrix of 
integers                Jacobi-symbol udpmijacsym(m,P1,P2) univariate dense 
			polynomial over modular 
integers                Jacobi-symbol upmijacsym(m,P1,P2) univariate 
			polynomial over modular 
integers                LLL - reduced ? isbasilllred(bas) is basis over the 
integers                Landau- Mignotte- factor coefficient bound 
			pilmfcb(r,P) polynomial over 
integers                S-polynomial dipisp(r,P1,P2) distributive 
			polynomial over 
integers                S-polynomial dippisp(r1,r2,P1,P2) distributive 
			polynomial over polynomials over 
integers                absolute value piabs(r,P) polynomial over 
integers                approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal orders 
			of the p-adic divisors of the defining polynomial 
			and p-minimal polynomials of the generators 
			ouspiapfgmic(p,P,k) order of an univariate 
			separable polynomial over the 
integers                basis from generators oibasisfgen(F,L) order over 
			the 
integers                basis of a local maximal over-order 
			ouspibaslmo(F,p,Q,pk) order of an univariate 
			separable polynomial over the 
integers                basis of a local maximal over-order with respect to 
			integer primes ouspibaslmoi(F,P,Q,pk) order of an 
			univariate separable polynomial over the 
integers                basis of the integral closure ( ORDMAX, Ordmax, 
			ordmax, integral basis ) ouspibasisic(F,pL) order 
			of an univariate separable polynomial over the 
integers                bubble sort libsort(L) list of 
integers                case distinction fgetdippicd(r1,r2,VL1,VL2,fac,pf) 
			file get distributive polynomial over polynomials 
			over 
integers                case distinction getdippicd(r1,r2,VL1,VL2,fac) 
			(MACRO) get distributive polynomial over 
			polynomials over 
integers                characteristic polynomial maichpol(M) (MACRO) 
			matrix of 
integers                characteristic polynomial mamichpol(m,M) (MACRO) 
			matrix of modular 
integers                characteristic polynomial mapichpol(r,M) (MACRO) 
			matrix of polynomials over 
integers                characteristic polynomial mapmichpol(r,m,M) (MACRO) 
			matrix of polynomials over modular 
integers                chinese remainder algorithm (rekursiv) 
			picra(r,P1,P2,M,m,a) polynomial over 
integers                choice of evaluation points picevalp(r,P,sA) 
			polynomial over 
integers                complete factorization upmicfact(ip,P) univariate 
			polynomial over modular 
integers                comprehensive Groebner basis 
			dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
integers                comprehensive Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
integers                comprehensive Groebner basis 
			putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
integers                construction 1 maicons1(n) (MACRO) matrix of 
integers                construction 1 mamicons1(m,n) (MACRO) matrix of 
			modular 
integers                construction 1 mapicons1(r,n) (MACRO) matrix of 
			polynomials over 
integers                construction 1 mapmicons1(r,m,n) (MACRO) matrix of 
			polynomials over modular 
integers                content and primitive part dipicp(r,P,pPP) 
			distributive polynomial over 
integers                content and primitive part dippicp(r1,r2,P,pPP) 
			distributive polynomial over polynomials over 
integers                content and primitive part picontpp(r,P,pPP) 
			polynomial over 
integers                content and primitive part udpicontpp(P,pPP) 
			univariate dense polynomial over 
integers                content picont(r,P) polynomial over 
integers                derivation udpmideriv(m,P) univariate dense 
			polynomial over modular 
integers                derivation, main variable pideriv(r,P) polynomial 
			over 
integers                derivation, main variable pmideriv(r,M,P) 
			polynomial over modular 
integers                derivation, specified variable (rekursiv) 
			piderivsv(r,P,n) polynomial over 
integers                derivation, specified variable (rekursiv) 
			pmiderivsv(r,m,P,n) polynomial over modular 
integers                determinant maidet(M) matrix of 
integers                determinant mamidet(m,M) matrix of modular 
integers                determinant mapidet(r,M) matrix of polynomials over 
integers                determinant mapmidet(r,m,M) matrix of polynomials 
			over modular 
integers                difference (rekursiv) dpmidif(r,m,P1,P2) dense 
			polynomial over modular 
integers                difference (rekursiv) pidif(r,P1,P2) polynomial 
			over 
integers                difference (rekursiv) pmidif(r,M,P1,P2) polynomial 
			over modular 
integers                difference dipidif(r,P1,P2) distributive polynomial 
			over 
integers                difference dippidif(r1,r2,P1,P2) distributive 
			polynomial over polynomials over 
integers                difference maidif(M,N) (MACRO) matrix of 
integers                difference mamidif(m,M,N) (MACRO) matrix of modular 
integers                difference mapidif(r,M,N) (MACRO) matrix of 
			polynomials over 
integers                difference mapmidif(r,m,M,N) (MACRO) matrix of 
			polynomials over modular 
integers                difference udpidif(P1,P2) univariate dense 
			polynomial over 
integers                difference udpmidif(m,P1,P2) univariate dense 
			polynomial over modular 
integers                difference vecidif(U,V) (MACRO) vector of 
integers                difference vecmidif(m,U,V) (MACRO) vector of 
			modular 
integers                difference vecpidif(r,U,V) (MACRO) vector of 
			polynomials over 
integers                difference vecpmidif(r,m,U,V) (MACRO) vector of 
			polynomials over modular 
integers                dimension dippidim(r1,r2,s,PL,CONDS,fac,VL1,VL2,pf) 
			distributive polynomial over polynomials over 
integers                dimension fputdippidim(r1,r2,DIML,VL1,VL2,pf) file 
			put distributive polynomial over polynomials over 
integers                dimension putdippidim(r1,r2,DIML,VL1,VL2) (MACRO) 
			put distributive polynomial over polynomials over 
integers                discriminant pidiscr(r,P,n) polynomial over 
integers                discriminant pmidiscr(r,M,P,n) polynomial over 
			modular 
integers                discriminant via Hankel matrix pmidiscrhank(r,M,P) 
			polynomial over modular 
integers                discriminant via Hankel- matrix pidiscrhank(r,P) 
			polynomial over 
integers                distinct degree factorization upmiddfact(ip,P) 
			univariate polynomial over modular 
integers                eigenvalues and irreducible factors of the 
			characteristic polynomial maievifcp(M,pL) matrix of 
integers                eigenvalues and irreducible factors of the 
			characteristic polynomial mamievifcp(p,M,pL) matrix 
			of modular 
integers                eigenvalues maiev(M) (MACRO) matrix of 
integers                eigenvalues mamiev(p,M) (MACRO) matrix of modular 
integers                element test modielemtest(B,a) module over the 
integers                elementary divisor form and cofactors 
			maiedfcf(M,pA,pB) matrix of 
integers                equal one ? ispione(r,P) is polynomial over 
integers                evaluation, main variable pieval(r,P,A) polynomial 
			over 
integers                evaluation, main variable pmieval(r,M,P,A) 
			polynomial over modular 
integers                evaluation, specified variable (rekursiv) 
			pievalsv(r,P,n,A) polynomial over 
integers                evaluation, specified variable (rekursiv) 
			pmievalsv(r,m,P,n,a) polynomial over modular 
integers                exponentiation maiexp(M,n) matrix of 
integers                exponentiation mamiexp(m,M,n) matrix of modular 
integers                exponentiation mapiexp(r,M,n) matrix of polynomials 
			over 
integers                exponentiation mapmiexp(r,m,M,n) matrix of 
			polynomials over modular 
integers                exponentiation piexp(r,P,n) polynomial over 
integers                exponentiation pmiexp(r,m,P,n) polynomial over 
			modular 
integers                extended greatest common divisor 
			udpmiegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over modular 
integers                extended greatest common divisor 
			upmiegcd(P,P1,P2,pP3,pP4) univariate polynomial 
			over modular 
integers                factor coefficient bound pifcb(L) polynomial over 
integers                factorization (rekursiv) pifact(r,P) polynomial 
			over 
integers                factorization rdiscupifact(rd,c,pL) reduced 
			discriminant and discriminant of an univariate 
			polynomial over the 
integers                factorization spifact(r,P) squarefree polynomial 
			over 
integers                factorization upifact(P) univariate polynomial over 
integers                factorization uspifact(P) univariate squarefree 
			polynomial over 
integers                factorization, Berlekamp algorithm 
			upmibfact(ip,P,d) univariate polynomial over 
			modular 
integers                fgetli(pf) file get list of 
integers                fgetmai(pf) (MACRO) file get matrix of 
integers                fgetmami(m,pf) (MACRO) file get matrix of modular 
integers                fgetmapi(r,V,pf) (MACRO) file get matrix of 
			polynomials over 
integers                fgetmapmi(r,m,V,pf) (MACRO) file get matrix of 
			polynomials over modular 
integers                fgetpi(r,V,pf) file get polynomial over 
integers                fgetpmi(r,M,V,pf) file get polynomial over modular 
integers                fgetveci(pf) (MACRO) file get vector of 
integers                fgetvecmi(m,pf) (MACRO) file get vector of modular 
integers                fgetvecpi(r,VL,pf) (MACRO) file get vector of 
			polynomials over 
integers                fgetvecpmi(r,m,VL,pf) (MACRO) file get vector of 
			polynomials over modular 
integers                fputli(L,pf) file put list of 
integers                fputlpi(r,L,V,pf) file put list of polynomials over 
integers                fputmai(M,pf) (MACRO) file put matrix of 
integers                fputmami(m,M,pf) (MACRO) file put matrix of modular 
integers                fputmapi(r,M,V,pf) (MACRO) file put matrix of 
			polynomials over 
integers                fputmapmi(r,m,M,V,pf) (MACRO) file put matrix of 
			polynomials over modular 
integers                fputpi(r,P,V,pf) file put polynomial over 
integers                fputpmi(r,M,P,V,pf) file put polynomial over 
			modular 
integers                fputveci(V,pf) (MACRO) file put vector of 
integers                fputvecmi(m,V,pf) (MACRO) file put vector of 
			modular 
integers                fputvecpi(r,V,VL,pf) (MACRO) file put vector of 
			polynomials over 
integers                fputvecpmi(r,m,V,VL,pf) (MACRO) file put vector of 
			polynomials over modular 
integers                from special coefficient list upifscl(L) univariate 
			polynomial over the 
integers                getli() (MACRO) get list of 
integers                getmai() (MACRO) get matrix of 
integers                getmami(m) (MACRO) get matrix of modular 
integers                getmapi(r,V) (MACRO) get matrix of polynomials over 
integers                getmapmi(r,m,V) (MACRO) get matrix of polynomials 
			over modular 
integers                getpi(r,V) (MACRO) get polynomial over 
integers                getpmi(r,M,V) (MACRO) get polynomial over modular 
integers                getveci() (MACRO) get vector of 
integers                getvecmi(m) (MACRO) get vector of modular 
integers                getvecpi(r,VL) (MACRO) get vector of polynomials 
			over 
integers                getvecpmi(r,m,VL) (MACRO) get vector of polynomials 
			over modular 
integers                greatest common divisor and cofactors (rekursiv) 
			pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
integers                greatest common divisor and cofactors 
			pigcdcf(r,P1,P2,pQ1,pQ2) polynomial over 
integers                greatest common divisor udpmigcd(m,P1,P2) 
			univariate dense polynomial over modular 
integers                greatest common divisor upmigcd(ip,P1,P2) 
			univariate polynomial over modular 
integers                greatest squarefree divisor (rekursiv) 
			upmigsd(ip,P) univariate polynomial over modular 
integers                half extended greatest common divisor 
			udpmihegcd(m,P1,P2,pP3) univariate dense polynomial 
			over modular 
integers                half extended greatest common divisor 
			upmihegcd(P,P1,P2,pP3) univariate polynomial over 
			modular 
integers                hermitian reduction, special maihermspec(M,r,pD) 
			matrix of 
integers                in graduated lexicographical order dipilotoglo(r,P) 
			distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over 
integers                in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over polynomials over 
integers                in lexicographical order to distributive polynomial 
			over integers in graduated lexicographical order 
			dipilotoglo(r,P) distributive polynomial over 
integers                in lexicographical order to distributive polynomial 
			over integers in lexicographical order with inverse 
			exponent vector dipilotolio(r,P) distributive 
			polynomial over 
integers                in lexicographical order to distributive polynomial 
			over integers with total degree ordering 
			dipilototdo(r,P) distributive polynomial over 
integers                in lexicographical order to distributive polynomial 
			over polynomials over integers in graduated 
			lexicographical order dippilotoglo(r1,r2,P) 
			distributive polynomial over polynomials over 
integers                in lexicographical order to distributive polynomial 
			over polynomials over integers in lexicographical 
			order with inverse exponent vector 
			dippilotolio(r1,r2,P) distributive polynomial over 
			polynomials over 
integers                in lexicographical order to distributive polynomial 
			over polynomials over integers with total degree 
			ordering dippilototdo(r1,r2,P) distributive 
			polynomial over polynomials over 
integers                in lexicographical order with inverse exponent 
			vector dipilotolio(r,P) distributive polynomial 
			over integers in lexicographical order to 
			distributive polynomial over 
integers                in lexicographical order with inverse exponent 
			vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over 
integers                integer content (rekursiv) piicont(r,P) polynomial 
			over 
integers                integer product udpiiprod(P,A) univariate dense 
			polynomial over 
integers                interpolation (rekursiv) pmiinter(r,m,P1,P2,P3,a,b) 
			polynomial over modular 
integers                inverse maiinv(M) matrix of 
integers                inverse mamiinv(m,M) matrix of modular 
integers                inverse mapiinv(r,M) matrix of polynomials over 
integers                inverse mapmiinv(r,m,M) matrix of polynomials over 
			modular 
integers                isuspi(P) is univariate squarefree polynomial over 
integers                linear combination vecilc(s1,s2,V1,V2) vector of 
integers                linear combination vecmilc(M,S1,S2,L1,L2) vector of 
			modular 
integers                linear combination vecpilc(r,P1,P2,V1,V2) vector of 
			polynomials over 
integers                linear combination vecpmilc(r,m,P1,P2,V1,V2) vector 
			of polynomials over modular 
integers                list fgetdipil(r,VL,pf) file get distributive 
			polynomial over 
integers                list fgetdippil(r1,r2,VL1,VL2,pf) file get 
			distributive polynomial over polynomials over 
integers                list fputdipil(r,PL,VL,pf) file put distributive 
			polynomial over 
integers                list fputdippil(r1,r2,PL,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
integers                list getdipil(r,VL) (MACRO) get distributive 
			polynomial over 
integers                list getdippil(r1,r2,VL1,VL2) (MACRO) get 
			distributive polynomial over polynomials over 
integers                list putdipil(r,PL,VL) (MACRO) put distributive 
			polynomial over 
integers                list putdippil(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
integers                maitomami(m,M) matrix of integers to matrix of 
			modular 
integers                maitomapi(r,M) matrix of integers to matrix of 
			polynomials over 
integers                mapitomapmi(r,M,m) matrix of polynomials over 
			integers to matrix of polynomials over modular 
integers                mapitompmpi(r,M,P) matrix of polynomials over 
			integers to matrix of polynomials modulo polynomial 
			over 
integers                mapmitomapmp(r,m,P,M) matrix of polynomials over 
			modular integers to matrix of polynomials modulo 
			polynomial over modular 
integers                maprtomapmi(r,M,m) matrix of polynomials over 
			rationals to matrix of polynomials over modular 
integers                martomami(m,M) matrix of rationals to matrix of 
			modular 
integers                maximum norm (rekursiv) pimaxnorm(r,P) polynomial 
			over 
integers                merge limerge(L1,L2) list of 
integers                modular ideal homomorphism pimidhom(r,S,P) 
			polynomial over 
integers                modular ideal product pimidprod(r,S,P1,P2) 
			polynomial over 
integers                modular ideal solution of equation 
			pmimidse(r,M,S,P1,P2,F1,F2,H,pV) polynomial over 
			modular 
integers                modular polynomial exponentiation 
			upmimpexp(ip,K,E,P) univariate polynomial over 
			modular 
integers                monic pmimonic(r,M,P) polynomial over modular 
integers                monic udpmimonic(m,P) univariate dense polynomial 
			over modular 
integers                monic, modular ideal quotient and remainder 
			pmimidqrem(r,M,S,P1,P2,pR) polynomial over modular 
integers                mudpitudpmi(M,m) matrix of univariate dense 
			polynomials over integers to matrix of univariate 
			dense polynomials over modular 
integers                negation (rekursiv) dpmineg(r,m,P) dense polynomial 
			over modular 
integers                negation (rekursiv) pineg(r,P) polynomial over 
integers                negation (rekursiv) pmineg(r,M,P) polynomial over 
			modular 
integers                negation dipineg(r,P) distributive polynomial over 
integers                negation dippineg(r1,r2,P) distributive polynomial 
			over polynomials over 
integers                negation maineg(M) (MACRO) matrix of 
integers                negation mamineg(m,M) (MACRO) matrix of modular 
integers                negation mapineg(r,M) (MACRO) matrix of polynomials 
			over 
integers                negation mapmineg(r,m,M) (MACRO) matrix of 
			polynomials over modular 
integers                negation udpineg(P) univariate dense polynomial 
			over 
integers                negation udpmineg(m,P) univariate dense polynomial 
			over modular 
integers                negation vecineg(V) (MACRO) vector of 
integers                negation vecmineg(m,V) (MACRO) vector of modular 
integers                negation vecpineg(r,V) (MACRO) vector of 
			polynomials over 
integers                negation vecpmineg(r,m,V) (MACRO) vector of 
			polynomials over modular 
integers                normelpruspi(P,a) norm of an element of the 
			polynomial ring of an univariate separable 
			polynomial over the 
integers                number field element evaluation first variable 
			special version mapinfevlfvs(r,F,M) matrix of 
			polynomials over 
integers                number field element evaluation first variable 
			special version pinfevalfvs(r,F,P) polynomial over 
integers                number field element evaluation first variable 
			special version vpinfevalfvs(r,F,V) vector of 
			polynomials over 
integers                number field element evaluation special 
			upinfeevals(F,P,a) univariate polynomial over the 
integers                number field element evaluation upinfeval(P,F,a) 
			univariate polynomial over 
integers                number field element, sparse representation, 
			evaluation upinfseval(P,F,a) univariate polynomial 
			over 
integers                of degree 4 cubic resolvent upid4cubres(P) 
			univariate polynomial over 
integers                of degree 4 real ? isupid4real(P) is univariate 
			polynomial over 
integers                one ? isdipione(r,P) is distributive polynomial 
			over 
integers                one ? isdippione(r1,r2,P) is distributive 
			polynomial over polynomials over 
integers                parametric ideal membership test 
			dippipim(r1,r2,s,PL,PTL,CONDS,OPL) distributive 
			polynomial over polynomials over 
integers                parametric ideal membership test 
			fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
integers                parametric ideal membership test 
			putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
integers                primitive part piprimpart(r,P) (MACRO) polynomial 
			over 
integers                product (rekursiv) dpmiprod(r,M,P1,P2) dense 
			polynomial over modular 
integers                product (rekursiv) piprod(r,P1,P2) polynomial over 
integers                product (rekursiv) pmimiprod(r,M,P,A) polynomial 
			over modular integers, modular 
integers                product (rekursiv) pmiprod(r,M,P1,P2) polynomial 
			over modular 
integers                product (rekursiv) pmiupmiprod(r,m,P1,P2) 
			polynomial over modular integers, univariate 
			polynomial over modular 
integers                product dipiprod(r,P1,P2) distributive polynomial 
			over 
integers                product dippipiprod(r1,r2,P,A) distributive 
			polynomial over polynomials over integers, 
			polynomial over 
integers                product dippiprod(r1,r2,P1,P2) distributive 
			polynomial over polynomials over 
integers                product liprod(L1,L2) list of 
integers                product maiprod(M,N) (MACRO) matrix of 
integers                product mamiprod(m,M,N) (MACRO) matrix of modular 
integers                product mapiprod(r,M,N) (MACRO) matrix of 
			polynomials over 
integers                product mapmiprod(r,m,M,N) (MACRO) matrix of 
			polynomials over modular 
integers                product over all entries liprodoe(L) list of 
integers                product udpiprod(P1,P2) univariate dense polynomial 
			over 
integers                product udpmiprod(m,P1,P2) univariate dense 
			polynomial over modular 
integers                pseudo remainder pipsrem(r,P1,P2) polynomial over 
integers                pseudo remainder pmipsrem(r,m,P1,P2) polynomial 
			over modular 
integers                pseudo remainder udpipsrem(P1,P2) univariate dense 
			polynomial over 
integers                putli(L) (MACRO) put list of 
integers                putmai(M) (MACRO) put matrix of 
integers                putmami(m,M) (MACRO) put matrix of modular 
integers                putmapi(r,M,V) (MACRO) put matrix of polynomials 
			over 
integers                putmapmi(r,m,M,V) (MACRO) put matrix of polynomials 
			over modular 
integers                putpi(r,P,V) (MACRO) put polynomial over 
integers                putpmi(r,m,P,V) (MACRO) put polynomial over modular 
integers                putveci(V) (MACRO) put vector of 
integers                putvecmi(m,V) (MACRO) put vector of modular 
integers                putvecpi(r,V,VL) (MACRO) put vector of polynomials 
			over 
integers                putvecpmi(r,m,V,VL) (MACRO) put vector of 
			polynomials over modular 
integers                quantifier free formula 
			dippiqff(r1,r2,s,PL,CONDS,fac) distributive 
			polynomial over polynomials over 
integers                quantifier free formula 
			fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
integers                quantifier free formula 
			putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
integers                quotient (rekursiv) pmiupmiquot(r,m,P1,P2) 
			polynomial over modular integers, univariate 
			polynomial over modular 
integers                quotient and remainder (rekursiv) 
			piqrem(r,P1,P2,pR) polynomial over 
integers                quotient and remainder (rekursiv) 
			pmiqrem(r,M,P1,P2,pR) polynomial over modular 
integers                quotient and remainder udpmiqrem(m,P1,P2,pP3) 
			univariate dense polynomial over modular 
integers                quotient piquot(r,P1,P2) (MACRO) polynomial over 
integers                quotient pmiquot(r,M,P1,P2) (MACRO) polynomial over 
			modular 
integers                quotient udpmiquot(m,P1,P2) (MACRO) univariate 
			dense polynomial over modular 
integers                randomize upmirand(ip,m) univariate polynomial over 
			modular 
integers                rational transformation 
			pirtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) polynomial over 
			the 
integers                reduced comprehensive Groebner basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
integers                reduced discriminant and content of resultant 
			equation upireddiscc(P,pc) univariate polynomial 
			over the 
integers                relative prime factorization 
			upmirelpfact(P,F,Fak,pA2) univariate polynomial 
			over modular 
integers                remainder pirem(r,P1,P2) (MACRO) polynomial over 
integers                remainder pmirem(r,M,P1,P2) (MACRO) polynomial over 
			modular 
integers                remainder udpmirem(ip,P,P2) univariate dense 
			polynomial over modular 
integers                remainder upmirem(M,P1,P2) univariate polynomial 
			over modular 
integers                resultant and cofactor of resultant equation 
			upiresulc(P1,P2,pB) univariate polynomial over the 
integers                resultant and cofactor of resultant equation 
			upmiresulc(m,P1,P2,pC) univariate polynomial over 
			modular 
integers                resultant pmires(r,m,P1,P2,n) polynomial over 
			modular 
integers                resultant upmires(m,P1,P2) univariate polynomial 
			over modular 
integers                resultant, Bezout algorithm piresbez(r,P1,P2) 
			polynomial over 
integers                resultant, Collins algorithm (rekursiv) 
			pmirescoll(r,m,P1,P2) polynomial over modular 
integers                resultant, Collins algorithm pirescoll(r,P1,P2,n) 
			polynomial over 
integers                resultant, Collins algorithm special 
			pirescspec(r,P1,P2,n) polynomial over the 
integers                resultant, Sylvester algorithm piressylv(r,P1,P2) 
			polynomial over 
integers                scalar multiplication maismul(M,el) matrix of 
integers                scalar multiplication mamismul(m,M,el) matrix of 
			modular 
integers                scalar multiplication mapismul(r,M,P) matrix of 
			polynomials over 
integers                scalar multiplication mapmismul(r,m,M,P) matrix of 
			polynomials over modular 
integers                scalar multiplication vecismul(s,V) vector of 
integers                scalar multiplication vecmismul(m,s,V) vector of 
			modular 
integers                scalar multiplication vecpismul(r,P,V) vector of 
			polynomials over 
integers                scalar multiplication vecpmismul(r,m,P,V) vector of 
			polynomials over modular 
integers                scalar product vecisprod(V,W) vector of 
integers                scalar product vecmisprod(M,V,W) vector of modular 
integers                scalar product vecpisprod(r,V,W) vector of 
			polynomials over 
integers                scalar product vecpmisprod(r,m,V,W) vector of 
			polynomials over modular 
integers                sclfupi(P,n) special coefficient list from 
			univariate polynomial over the 
integers                separate factor of equal degree upmisfed(ip,G,d) 
			univariate polynomial over modular 
integers                sign, base variable pisign(r,P) polynomial over 
integers                squarefree factorization (rekursiv) upmisfact(ip,P) 
			univariate polynomial over modular 
integers                squarefree factorization pisfact(r,P) polynomial 
			over 
integers                squarefree part upmisfp(m,P) univariate polynomial 
			over modular 
integers                substitution with respect to a cubic equation 
			bpmisubcubeq(p,P,R) bivariate polynomial over 
			modular 
integers                substitution, main variable pisubst(r,P1,P2) 
			polynomial over 
integers                substitution, main variable pmisubst(r,m,P1,P2) 
			polynomial over modular 
integers                substitution, specified variable (rekursiv) 
			pisubstsv(r,P1,n,P2) polynomial over 
integers                substitution, specified variable (rekursiv) 
			pmisubstsv(r,m,P1,n,P2) polynomial over modular 
integers                sum (rekursiv) dpmisum(r,M,P1,P2) dense polynomial 
			over modular 
integers                sum (rekursiv) pisum(r,P1,P2) polynomial over 
integers                sum (rekursiv) pmisum(r,M,P1,P2) polynomial over 
			modular 
integers                sum dipisum(r,P1,P2) distributive polynomial over 
integers                sum dippisum(r1,r2,P1,P2) distributive polynomial 
			over polynomials over 
integers                sum maisum(M,N) (MACRO) matrix of 
integers                sum mamisum(m,M,N) (MACRO) matrix of modular 
integers                sum mapisum(r,M,N) (MACRO) matrix of polynomials 
			over 
integers                sum mapmisum(r,m,M,N) (MACRO) matrix of polynomials 
			over modular 
integers                sum norm (rekursiv) pisumnorm(r,P) polynomial over 
integers                sum udpisum(P1,P2) univariate dense polynomial over 
integers                sum udpmisum(m,P1,P2) univariate dense polynomial 
			over modular 
integers                sum vecisum(U,V) (MACRO) vector of 
integers                sum vecmisum(m,U,V) (MACRO) vector of modular 
integers                sum vecpisum(r,U,V) (MACRO) vector of polynomials 
			over 
integers                sum vecpmisum(r,m,U,V) (MACRO) vector of 
			polynomials over modular 
integers                to matrix of modular integers maitomami(m,M) matrix 
			of 
integers                to matrix of modular singles maitomams(m,M) matrix 
			of 
integers                to matrix of number field elements maitomanf(M) 
			matrix of 
integers                to matrix of number field elements, sparse 
			representation maitomanfs(M) matrix of 
integers                to matrix of polynomials modulo polynomial over 
			integers mapitompmpi(r,M,P) matrix of polynomials 
			over 
integers                to matrix of polynomials modulo polynomial over 
			modular integers mapmitomapmp(r,m,P,M) matrix of 
			polynomials over modular 
integers                to matrix of polynomials over integers 
			maitomapi(r,M) matrix of 
integers                to matrix of polynomials over modular integers 
			mapitomapmi(r,M,m) matrix of polynomials over 
integers                to matrix of polynomials over modular singles 
			mapitomapms(r,M,m) matrix of polynomials over 
integers                to matrix of polynomials over number field 
			mapitomapnf(r,M) matrix of polynomials over 
integers                to matrix of rational functions over rationals 
			mapitomarfr(r,M) matrix of polynomials over 
integers                to matrix of rationals maitomar(M) matrix of 
integers                to matrix of rationals mapitomapr(r,M) matrix of 
integers                to matrix of univariate dense polynomials over 
			modular integers mudpitudpmi(M,m) matrix of 
			univariate dense polynomials over 
integers                to matrix of univariate dense polynomials over 
			rationals mudpitmudpr(M) matrix of univariate dense 
			polynomials over 
integers                to matrix over Galois-field with single 
			characteristic maitomagfs(p,M) matrix over 
integers                to polynomial over a number field (rekursiv) 
			pitopnf(r,P) polynomial over the 
integers                to polynomial over modular integers (rekursiv) 
			pitopmi(r,P,M) polynomial over 
integers                to polynomial over modular singles (rekursiv) 
			pitopms(r,P,m) polynomial over 
integers                to polynomial over p-adic field pitoppf(r,P,p,d) 
			polynomial over 
integers                to polynomial over rationals (rekursiv) pitopr(r,P) 
			polynomial over 
integers                to rational function over the rationals 
			pitorfr(r,P) polynomial over 
integers                to symmetric remainder system (rekursiv) 
			pmitos(r,M,P) polynomial over modular 
integers                to univariate dense polynomial over modular 
			integers udpitoudpmi(P,M) univariate dense 
			polynomial over 
integers                to univariate dense polynomial over p-adic field 
			udpitoudppf(P,p,d) univariate dense polynomial over 
integers                to univariate polynomial over rationals 
			udpitoudpr(P) univariate polynomial over 
integers                to vector of modular integers vecitovecmi(M,V) 
			vector of 
integers                to vector of modular singles vecitovecms(m,V) 
			vector of 
integers                to vector of number field elements vecitovecnf(V) 
			vector of 
integers                to vector of number field elements, sparse 
			representation vecitovnfs(V) vector of 
integers                to vector of polynomials modulo polynomial over 
			integers vecpitvpmpi(r,V,P) vector of polynomials 
			over 
integers                to vector of polynomials modulo polynomial over 
			modular integers vecpmitovpmp(r,m,P,V) vector of 
			polynomials over modular 
integers                to vector of polynomials over integers 
			vecitovecpi(r,V) vector of 
integers                to vector of polynomials over modular integers 
			vecpitovpmi(r,V,m) vector of polynomials over 
integers                to vector of polynomials over modular singles 
			vecpitovpms(r,V,m) vector of polynomials over 
integers                to vector of polynomials over number field 
			vecpitovpnf(r,V) vector of polynomials over 
integers                to vector of polynomials over rationals 
			vecpitovpr(V) vector of polynomials over 
integers                to vector of rational functions over rationals 
			vecpitovrfr(r,V) vector of polynomials over 
integers                to vector of rationals vecitovecr(V) vector of 
integers                to vector of univariate dense polynomials over 
			modular integers vudpitudpmi(V,M) vector of 
			univariate dense polynomials over 
integers                to vector of univariate dense polynomials over 
			rationals vudpitvudpr(V) vector of univariate dense 
			polynomials over 
integers                to vector over Galois-field with single 
			characteristic vecitovecgfs(p,V) vector over 
integers                trace maitrace(M) matrix of 
integers                transformation mapitransf(r1,M1,V1,r2,P2,V2,Vn,pV3) 
			matrix of polynomials over the 
integers                transformation 
			mapmitransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over modular 
integers                transformation pitransf(r1,P1,V1,r2,P2,V2,Vn,pV3) 
			polynomial over the 
integers                transformation 
			pmitransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over modular 
integers                transformation upmitransf(M,P,r,P1) univariate 
			polynomial over modular 
integers                transformation 
			vecpitransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over the 
integers                transformation version2 upmitransf2(M,P,r,P1) 
			univariate polynomial over modular 
integers                transformation 
			vpmitransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over modular 
integers                translation, all variables (rekursiv) 
			pitransav(r,P,LI) polynomial over 
integers                translation, all variables (rekursiv) 
			pmitransav(r,m,P,Lmi) polynomial over modular 
integers                translation, main variable pitrans(r,P,A) 
			polynomial over 
integers                translation, main variable pmitrans(r,m,P,a) 
			polynomial over modular 
integers                truncation (rekursiv) pitrunc(r,S,P) polynomial 
			over 
integers                truncation product (rekursiv) pitrprod(r,S,P1,P2) 
			polynomial over 
integers                udpitoudpmi(P,M) univariate dense polynomial over 
			integers to univariate dense polynomial over 
			modular 
integers                unimodular transformation veciunimtr(V,W,i,pV1,pW1) 
			vector of 
integers                unit? ispmiunit(r,m,P) is polynomial over modular 
integers                univariate content (rekursiv) pmiucont(r,m,P) 
			polynomial over modular 
integers                vecitovecmi(M,V) vector of integers to vector of 
			modular 
integers                vecitovecpi(r,V) vector of integers to vector of 
			polynomials over 
integers                vecpitovpmi(r,V,m) vector of polynomials over 
			integers to vector of polynomials over modular 
integers                vecpitvpmpi(r,V,P) vector of polynomials over 
			integers to vector of polynomials modulo polynomial 
			over 
integers                vecpmitovpmp(r,m,P,V) vector of polynomials over 
			modular integers to vector of polynomials modulo 
			polynomial over modular 
integers                vecprtovpmi(r,V,m) vector of polynomials over 
			rationals to vector of polynomials over modular 
integers                vecrtovecmi(m,V) vector of rationals to vector of 
			modular 
integers                vector multiplication maivecmul(A,x) (MACRO) matrix 
			of 
integers                vector multiplication mamivecmul(m,A,x) (MACRO) 
			matrix of modular 
integers                vector multiplication mapivecmul(r,A,x) (MACRO) 
			matrix of polynomials over 
integers                vector multiplication mapmivecmul(r,m,A,x) (MACRO) 
			matrix of polynomials over modular 
integers                vepvelpruspi(F,a,p,k,v) values of the extensions of 
			the p-adic valuation of an element of the 
			polynomial ring of an univariate separable 
			polynomial over the 
integers                vudpitudpmi(V,M) vector of univariate dense 
			polynomials over integers to vector of univariate 
			dense polynomials over modular 
integers                with total degree ordering dipilototdo(r,P) 
			distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over 
integers                with total degree ordering dippilototdo(r1,r2,P) 
			distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
			polynomial over polynomials over 
integers,               Berlekamp Q polynomials construction upmibqp(ip,P) 
			univariate polynomial over modular 
integers,               Berlekamp factorization, Zassenhaus method 
			upmibfzm(ip,s,P,G) univariate polynomial over 
			modular 
integers,               Dedekind maximality test oupidedekmt(M,P) order of 
			an univariate polynomial over the 
integers,               Hensel lemma factorization approximation 
			pihlfa(r,p,L,M,S,P) polynomial over 
integers,               Hensel lemma factorization approximation 
			upihlfa(p,P,L,k) univariate polynomial over the 
integers,               Hensel lemma factorization approximation with 
			respect to integer prime upihlfaip(p,P,L,k) 
			univariate polynomial over 
integers,               Hensel lemma initialization upihli(p,P,L) 
			univariate polynomial over 
integers,               Hensel lemma initialization with respect to integer 
			prime upihliip(P,F,L) univariate polynomial over 
integers,               Hensel lemma quadratic step 
			upihlqs(p,p_k,p_l,P,L1,L2,A) univariate polynomial 
			over 
integers,               Hensel lemma quadratic step with respect to integer 
			prime upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over 
integers,               LLL reduction modilllred(bas) module over the 
integers,               approximation of p-adic factorization 
			uspiapf(p,P,k) univariate separable polynomial over 
			the 
integers,               complete factorization special upmicfacts(P,F) 
			univariate polynomial over modular 
integers,               integer product (rekursiv) piiprod(r,P,A) 
			polynomial over 
integers,               integer product dipiiprod(r,P,A) distributive 
			polynomial over 
integers,               integer quotient (rekursiv) piiquot(r,P,A) 
			polynomial over 
integers,               modular ideal product pmimidprod(r,M,S,P1,P2) 
			polynomial over modular 
integers,               modular ideal, Hensel lemma quadratic step on a 
			single variable pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) 
			polynomial over modular 
integers,               modular ideal, Hensel lemma quadratic step 
			pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial over 
integers,               modular ideal, Hensel lemma quadratic step 
			pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial 
			over modular 
integers,               modular integer product udpmimiprod(m,P,a) 
			univariate dense polynomial over modular 
integers,               modular integer quotient (rekursiv) 
			pmimiquot(r,m,P,a) polynomial over modular 
integers,               modular integers product (rekursiv) 
			pmimiprod(r,M,P,A) polynomial over modular 
integers,               monomial, polynomial, remainder upmimprem(ip,K,E,P) 
			univariate polynomial over modular 
integers,               null space basis maminsb(P,M) matrix of modular 
integers,               number of irreducible factors upminif(m,P) 
			univariate polynomial over modular 
integers,               orthogonalized basis modiorthobas(bas) module over 
			the 
integers,               polynomial over integers product 
			dippipiprod(r1,r2,P,A) distributive polynomial over 
			polynomials over 
integers,               root finding (rekursiv) upmirf(ip,P) univariate 
			polynomial over modular 
integers,               root finding, special (rekursiv) upmirfspec(ip,P) 
			univariate polynomial over modular 
integers,               trace function, special upmitfsp(ip,G,d,M) 
			univariate polynomial over modular 
integers,               univariate polynomial over modular integers product 
			(rekursiv) pmiupmiprod(r,m,P1,P2) polynomial over 
			modular 
integers,               univariate polynomial over modular integers 
			quotient (rekursiv) pmiupmiquot(r,m,P1,P2) 
			polynomial over modular 
integers?               (rekursiv) isdpi(r,P) is dense polynomial over 
integral                P-primary number field element, core algorithm with 
			respect to integer primes ippnfecalip(F,P,Q,mp) 
integral                algebraic function over modular single prime, 
			transcendence degree 1, P-star valuation 
			iafmsp1psval(p,P,A) 
integral                algebraic function over modular single primes, 
			transcendence degree 1, minimal polynomial 
			iafmsp1mpol(p,F,a,Q) 
integral                algebraic function over modular single primes, 
			transcendence degree 1, minimal polynomial modulo 
			power of an univariate prime polynomial over 
			modular single primes iafmsp1mpmpp(p,F,a,P,e,Q) 
integral                basis ) ouspibasisic(F,pL) order of an univariate 
			separable polynomial over the integers basis of the 
			integral closure ( ORDMAX, Ordmax, ordmax, 
integral                basis ouspprmsp1ib(p,F,pL) order of an univariate 
			separable polynomial over the polynomial ring over 
			modular single prime, transcendence degree 1, 
integral                basis qnfintbas(D) quadratic number field 
integral                closure ( ORDMAX, Ordmax, ordmax, integral basis ) 
			ouspibasisic(F,pL) order of an univariate separable 
			polynomial over the integers basis of the 
integral                coefficients ecqnftoeci(D,L) elliptic curve over 
			quadratic number field to elliptic curve with 
integral                element prime ideal factorization, special version 
			qnfielpifacts(D,a,L) quadratic number field 
integral                element, prime ideal order qnfielpiord(D,P,pi,z,a) 
			quadratic number field, 
integral                element? isqnfiel(D,a) is quadratic number field 
			element 
integral                number field element minimal polynomial modulo 
			p-power infeminpmpp(F,a,p,e,Q) 
integral                number field element minimal polynomial modulo 
			p-power with respect to integer primes 
			infempmppip(F,a,p,e,Q) 
integral                number field element p-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial infepptfact(F,p,Q,ppot,a0,z) 
integral                number field element p-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial with respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) 
integral                number field element p-star valuation 
			infepstarval(p,A) 
integral                number field element p-star valuation with respect 
			to integer primes infepstarvip(P,A) 
integral                p-primary number field element regulation with 
			respect to integer primes 
			ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) 
integral                p-primary number field element regulation, version1 
			ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) 
integral                p-primary number field element regulation, version2 
			ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) 
integral                p-primary number field element, core algorithm 
			ippnfecoreal(F,p,Q,mp) 
integral                p-primary number field element, increasing the 
			denominator of the p-star value 
			ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) 
integral                p-primary number field element, increasing the 
			denominator of the p-star value with respect to 
			integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) 
integration,            main variable printegr(r,P) polynomial over 
			rationals 
interpolation           (rekursiv) pmiinter(r,m,P1,P2,P3,a,b) polynomial 
			over modular integers 
interpolation           (rekursiv) pmsinter(r,m,P1,P2,P3,a,b) polynomial 
			over modular singles 
intersection            csetinter(S,T) characteristic set 
intersection            sinter(L1,L2) set 
intersection            usinter(L1,L2) unordered set 
into                    pseudoprimes (rekursiv) ifactpp(N) integer 
			factorization 
intpp(p,m)              integer p-part 
intppint(P,A)           integer P-part with respect to an integer 
invariant               j cmodinv(q,ln_q) complex modular 
invariants              fputecrinv(E,pf) file put elliptic curve over the 
			rational numbers, 
invariants              putecrinv(E) (MACRO) put elliptic curve over the 
			rational numbers, 
inverse                 cdprfmsp1inv(p,F,A) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, 
inverse                 cdprinv(F,A) common denominator polynomial over the 
			rationals 
inverse                 element qnfinv(D,a) quadratic number field element 
inverse                 exponent vector dipgfslotlio(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
inverse                 exponent vector dipilotolio(r,P) distributive 
			polynomial over integers in lexicographical order 
			to distributive polynomial over integers in 
			lexicographical order with 
inverse                 exponent vector dipmiplotlio(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular integer primes in lexicographical 
			order with 
inverse                 exponent vector dipmsplotlio(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular single primes in lexicographical order 
			with 
inverse                 exponent vector dipnflotolio(r,F,P) distributive 
			polynomial over number field in lexicographical 
			order to distributive polynomial over number field 
			in lexicographical order with 
inverse                 exponent vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers in lexicographical 
			order with 
inverse                 exponent vector diprfrlotlio(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order with 
inverse                 exponent vector diprlotolio(r,P) distributive 
			polynomial over rationals in lexicographical order 
			to distributive polynomial over rationals in 
			lexicographical order with 
inverse                 gf2inv(G,a) Galois-field with characteristic 2 
inverse                 gfsinv(p,AL,a) Galois-field with single 
			characteristic 
inverse                 lcinv(L) list constructive 
inverse                 linv(L) list 
inverse                 magfsinv(p,AL,M) matrix of Galois-field with single 
			characteristic elements 
inverse                 maiinv(M) matrix of integers 
inverse                 mamiinv(m,M) matrix of modular integers 
inverse                 mamsinv(m,M) matrix of modular singles 
inverse                 manfinv(F,M) matrix of number field elements 
inverse                 manfsinv(F,M) matrix of number field elements, 
			sparse representation, 
inverse                 mapgfsinv(r,p,AL,M) matrix of polynomials over 
			Galois-field with single characteristic 
inverse                 mapiinv(r,M) matrix of polynomials over integers 
inverse                 mapmiinv(r,m,M) matrix of polynomials over modular 
			integers 
inverse                 mapmsinv(r,m,M) matrix of polynomials over modular 
			singles 
inverse                 mapnfinv(r,F,M) matrix of polynomials over number 
			field 
inverse                 maprinv(r,M) matrix of polynomials over rationals 
inverse                 marfmsp1inv(p,M) matrix of rational functions over 
			modular single primes, transcendence degree 1, 
inverse                 marfrinv(r,M) matrix of rational functions over 
			rationals 
inverse                 marinv(M) matrix of rationals 
inverse                 miinv(M,A) modular integer 
inverse                 msinv(m,a) modular single 
inverse                 nfinv(F,a) number field 
inverse                 nfsinv(F,a) number field, sparse representation, 
inverse                 pfinv(p,a) p-adic field element 
inverse                 rfmsp1inv(p,R) rational function over modular 
			single primes, transcendence degree 1, 
inverse                 rfrinv(r,R) rational function over the rationals 
inverse                 rinv(R) rational number 
inverse                 transformation ecrbtinv(BT) elliptic curve over 
			rational numbers, birational transformation, 
inverse,                lists only miinv_lo(M,A) modular integer 
iodd(A)                 (MACRO) integer odd 
ip2prod(A,n)            integer power of 2 product 
ip2quot(A,n)            integer power of 2 quotient 
ipgen(u,o)              integer prime generator 
iphi(N)                 integer eulerian phi-value 
ipjacsym(a,p)           integer prime Jacobi-symbol ( Legendre-symbol ) 
ippnfecalip(F,P,Q,mp)   integral P-primary number field element, core 
			algorithm with respect to integer primes 
ippnfecoreal(F,p,Q,mp)  integral p-primary number field element, core 
			algorithm 
ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral p-primary number field 
			element, increasing the denominator of the p-star 
			value 
ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral p-primary number field 
			element, increasing the denominator of the p-star 
			value with respect to integer primes 
ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral p-primary number field element 
			regulation with respect to integer primes 
ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) integral p-primary number field element 
			regulation, version1 
ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) integral p-primary number field element 
			regulation, version2 
iprimeconstr(bits,f,pL,n) integer prime construction 
iprniqf(p,D)            integer prime representation as a norm in an 
			imaginary quadratic field 
iprod(A,B)              integer product 
iprod_lo(A,B)           integer product, lists only 
iprpdbqf(D,h1,h2)       integer primitive reduced positive definite binary 
			quadratic forms 
iqnfdif(D,a,b)          (MACRO) integer, quadratic number field element, 
			difference 
iqnfquot(D,a,b)         integer, quadratic number field element, quotient 
iqrem(A,B,pQ,pR)        integer quotient and remainder 
iqrem_2(A,B,pQ,pR)      integer quotient and remainder, old version 
iqrem_3(A,B,pQ,pR)      integer quotient and remainder special version 3 
iqrem_lo(A,B,pQ,pR)     integer quotient and remainder, lists only 
iquot(A,B)              (MACRO) integer quotient 
irand(G)                integer randomize 
irand_2(u)              integer randomize, alternative version 
irandprime(a1,a2,n)     integer random prime 
irds(n,G,p)             integer random divisor search (rekursiv) 
irem(A,B)               (MACRO) integer remainder 
iroot(A,n,ps)           integer root 
irrational              qffmsrqired(m,D,d,Q,P,pPr) quadratic function field 
			over modular singles reduction of a real quadratic 
irrational              qffmssrqired(m,D,d,Q,P,pPr) quadratic function 
			field over modular singles, sparse representation, 
			reduction of a real quadratic 
irreducible             and monic polynomial in special bit-representation 
			? isgf2impsb(G) is Galois-field with characteristic 
			2 
irreducible             and monic polynomial in special bit-representation 
			generator gf2impsbgen(n,H) Galois-field with 
			characteristic 2 
irreducible             and monic trinomial, generator upm2imtgen(n) 
			univariate polynomial over modular 2, 
irreducible             and monic trinomial, generator upmsimtgen(p,n) 
			univariate polynomial over modular singles, 
irreducible             and monic, generator upm2imgen(n) univariate 
			polynomial over modular 2, 
irreducible             and monic, generator upmsimgen(p,n) univariate 
			polynomial over modular singles, 
irreducible             factors of the characteristic polynomial 
			magfsevifcp(p,AL,M,pL) matrix over Galois-field 
			with single characteristic eigenvalues and 
irreducible             factors of the characteristic polynomial 
			maievifcp(M,pL) matrix of integers eigenvalues and 
irreducible             factors of the characteristic polynomial 
			mamievifcp(p,M,pL) matrix of modular integers 
			eigenvalues and 
irreducible             factors of the characteristic polynomial 
			mamsevifcp(p,M,pL) matrix of modular singles 
			eigenvalues and 
irreducible             factors of the characteristic polynomial 
			marevifcp(M,*pL) matrix of rationals eigenvalues 
			and 
irreducible             factors upgfsnif(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic number of 
irreducible             factors upminif(m,P) univariate polynomial over 
			modular integers, number of 
irreducible             factors upmsnif(m,P) univariate polynomial over 
			modular singles, number of 
irreducible             univariate polynomial over integers ? isiupi(P) is 
irreducible             univariate polynomial over rationals ? isiupr(P) is 
irreducible             univariate squarefree polynomial over integers ? 
			isiuspi(P) is 
irreducible,            monic, univariate polynomial over modular integers 
			? isimupmi(p,A) is 
irreducible,            monic, univariate polynomial over modular singles ? 
			isimupms(p,A) is 
irshift(A)              integer right shift 
is                      Galois-field with characteristic 2 element ? 
			isgf2el(G,a) (MACRO) 
is                      Galois-field with characteristic 2 irreducible and 
			monic polynomial in special bit-representation ? 
			isgf2impsb(G) 
is                      Galois-field with single characteristic arithmetic 
			list ? isgfsal(p,AL) 
is                      Galois-field with single characteristic element ? 
			isgfsel(p,AL,a) 
is                      Galois-field with single characteristic element one 
			? isgfsone(p,AL,a) 
is                      atom ? isatom(a) (MACRO) 
is                      basis over the integers LLL - reduced ? 
			isbasilllred(bas) 
is                      bound in STACK ? isbound(pL) 
is                      complex number in ball ? iscinball(z,r,eps) 
is                      dense polynomial ? (rekursiv) isdpol(r,P) 
is                      dense polynomial over integers? (rekursiv) 
			isdpi(r,P) 
is                      dense polynomial over modular integers ? (rekursiv) 
			isdpmi(r,m,P) 
is                      dense polynomial over modular singles ? (rekursiv) 
			isdpms(r,m,P) 
is                      dense polynomial over p-adic field ? isdppf(r,p,P) 
is                      dense polynomial over rationals? (rekursiv) 
			isdpr(r,P) 
is                      distributive polynomial ? isdipol(r,P) 
is                      distributive polynomial over integers one ? 
			isdipione(r,P) 
is                      distributive polynomial over polynomials over 
			integers one ? isdippione(r1,r2,P) 
is                      distributive polynomial over rational functions 
			over the rationals one ? isdiprfrone(r1,r2,P) 
is                      distributive polynomial over rationals one ? 
			isdiprone(r,P) 
is                      element of an elliptic curve over Galois-field with 
			characteristic 2 ? iselecgf2(G,a1,a2,a3,a4,a6,P) 
is                      element of an elliptic curve over modular primes ? 
			iselecmp(p,a1,a2,a3,a4,a6,P) 
is                      element of an elliptic curve over modular primes, 
			short normal form ? iselecmpsnf(p,a,b,P) 
is                      element of an elliptic curve over number field ? 
			iselecnf(F,a1,a2,a3,a4,a6,P) 
is                      element of an elliptic curve over number field, 
			short normal form ? iselecnfsnf(F,a,b,P) 
is                      element of an ideal class qffmsiselic(m,D,L,Q,P) 
			quadratic function field over modular singles 
is                      equal ideal special qffmsiseqids(m,D,Q1,P1,Q2,P2) 
			quadratic function field over modular singles 
is                      floating point ? isfloat(A) 
is                      in list of points on elliptic curve with integer 
			coefficients, minimal model isineciminpl(E,P,h,PL) 
is                      integer ? isint(A) 
is                      integer prime ? isiprime(n) 
is                      integer prime, printing messages isiprimemsg(n) 
			(MACRO) 
is                      integer pseudo prime ? isipprime(n,a) 
is                      integer square ? isisqr(A) 
is                      integer strong pseudo prime ? isispprime(n,k) 
is                      irreducible univariate polynomial over integers ? 
			isiupi(P) 
is                      irreducible univariate polynomial over rationals ? 
			isiupr(P) 
is                      irreducible univariate squarefree polynomial over 
			integers ? isiuspi(P) 
is                      irreducible, monic, univariate polynomial over 
			modular integers ? isimupmi(p,A) 
is                      irreducible, monic, univariate polynomial over 
			modular singles ? isimupms(p,A) 
is                      list ? (rekursiv) islist(L) 
is                      list element ? islelt(L,a) 
is                      list of Galois-field with characteristic 2 elements 
			? islistgf2(G,L) 
is                      list of Galois-field with single characteristic 
			elements ? islistgfs(p,AL,L) 
is                      list of integers ? islisti(L) 
is                      list of modular integers ? islistmi(M,A) 
is                      list of modular singles ? islistms(m,A) 
is                      list of non negative singles ? islistnns(A) 
is                      list of singles ? islists(A) 
is                      matrix ? isma(M) 
is                      matrix of Galois-field with single characteristic 
			elements ? ismagfs(p,AL,M) (MACRO) 
is                      matrix of ____ ? isma_(M,is,anzahlargs,arg1,arg2) 
is                      matrix of ____, special ? 
			ismaspec_(M,is,anzahlargs,arg1,...,arg5) 
is                      matrix of dense polynomials ? ismadp(r,M) (MACRO) 
is                      matrix of dense polynomials over integers ? 
			ismadpi(r,M) (MACRO) 
is                      matrix of dense polynomials over modular singles ? 
			ismadpms(r,m,M) (MACRO) 
is                      matrix of dense polynomials over rationals ? 
			ismadpr(r,M) (MACRO) 
is                      matrix of equal elements ismaeqel(M,el) 
is                      matrix of integers ? ismai(M) (MACRO) 
is                      matrix of modular integers ? ismami(m,M) (MACRO) 
is                      matrix of modular singles ? ismams(m,M) (MACRO) 
is                      matrix of number field elements ? ismanf(F,M) 
			(MACRO) 
is                      matrix of number field elements, sparse 
			representation ? ismanfs(F,M) (MACRO) 
is                      matrix of polynomials ? ismap(r,M) (MACRO) 
is                      matrix of polynomials over Galois-field with single 
			characteristic ? ismapgfs(r,p,AL,M) (MACRO) 
is                      matrix of polynomials over integers ? ismapi(r,M) 
			(MACRO) 
is                      matrix of polynomials over modular integers ? 
			ismapmi(r,m,M) (MACRO) 
is                      matrix of polynomials over modular singles ? 
			ismapms(r,m,M) (MACRO) 
is                      matrix of polynomials over rationals ? ismapr(r,M) 
			(MACRO) 
is                      matrix of rational functions over modular single 
			primes, transcendence degree 1 ? ismarfmsp1(p,M) 
			(MACRO) 
is                      matrix of rational functions over rationals ? 
			ismarfr(r,M) (MACRO) 
is                      matrix of rationals ? ismar(M) (MACRO) 
is                      matrix of singles ? ismas(M) 
is                      modular integer ? ismi(m,a) 
is                      modular integer Fermat residue ? ismifr(M,A,B) 
is                      modular integer square ? ismisquare(M,A) 
is                      modular integer unit ismiunit(M,A) 
is                      modular single ? isms(m,a) 
is                      null-matrix isnullma(M) (MACRO) 
is                      null-vector isnullvec(V) 
is                      number field element one isnfone(F,A) 
is                      number field element, sparse representation ? 
			isnfels(F,a) 
is                      number field element? isnfel(F,a) 
is                      number field of degree 3 equal to number field of 
			degree 3 isnf3eqnf3(F,P,pFD,pPD,pQ) 
is                      object ? isobj(a) (MACRO) 
is                      p-adic field element? ispfel(p,a) 
is                      point of an elliptic curve over the rationals point 
			at infinity ? ispecrpai(P) (MACRO) 
is                      point on elliptic curve over rational numbers, 
			actual model isponecrac(E,P) 
is                      point on elliptic curve with integer coefficients, 
			minimal model isponecimin(E,P) 
is                      point on elliptic curve with integer coefficients, 
			model in short normal form isponecisnf(E,P) 
is                      polynomial ? (rekursiv) ispol(r,P) 
is                      polynomial constant ? ispconst(r,P,pC) 
is                      polynomial monomial ? ispmonom(r,P) 
is                      polynomial over Galois-field with single 
			characteristic ? (rekursiv) ispgfs(r,p,AL,P) 
is                      polynomial over integers ? (rekursiv) ispi(r,P) 
is                      polynomial over integers equal one ? ispione(r,P) 
is                      polynomial over modular integer ? (rekursiv) 
			ispmi(r,m,P) 
is                      polynomial over modular integers unit? 
			ispmiunit(r,m,P) 
is                      polynomial over modular singles ? (rekursiv) 
			ispms(r,m,P) 
is                      polynomial over modular singles unit? 
			ispmsunit(r,m,P) 
is                      polynomial over rationals ? (rekursiv) ispr(r,P) 
is                      projective point of an elliptic curve over 
			Galois-field with characteristic 2 equal ? 
			isppecgf2eq(p,P1,P2) 
is                      projective point of an elliptic curve over 
			Galois-field with characteristic 2 point at 
			infinity ? isppecgf2pai(G,P) 
is                      projective point of an elliptic curve over modular 
			primes equal ? isppecmpeq(p,P1,P2) 
is                      projective point of an elliptic curve over modular 
			primes point at infinity ? isppecmppai(p,P) 
is                      projective point of an elliptic curve over number 
			field equal? isppecnfeq(F,P1,P2) 
is                      projective point of an elliptic curve over number 
			field point at infinity ? isppecnfpai(P) 
is                      quadratic number field element integer? 
			isqnfint(D,a) (MACRO) 
is                      quadratic number field element integral element? 
			isqnfiel(D,a) 
is                      quadratic number field element one? isqnfone(D,a) 
			(MACRO) 
is                      quadratic number field element power of prime ideal 
			homomorphism zero? isqnfppihom0(D,P,k,pi,z,a) 
is                      quadratic number field element rational 
			isqnfrat(D,a) (MACRO) 
is                      quadratic number field ideal one? isqnfidone(D,A) 
is                      rational function over modular single prime, 
			transcendence degree 1 ? isrfmsp1(p,R) 
is                      rational function over rationals one isrfrone(r,A) 
is                      rational function over the rationals ? isrfr(r,R) 
is                      rational number ? israt(R) 
is                      rational number one ? isrone(A) 
is                      rational number square ? isrsqr(R) 
is                      single ? issingle(a) (MACRO) 
is                      single power of a prime ? isspprime(a,pc) 
is                      single prime ? issprime(a,pc) 
is                      sorted list of singles ? issortls(A) 
is                      torsion point on elliptic curve with integer 
			coefficients, minimal model isecimintorp(E,P) 
is                      univariate dense polynomial over modular 2 in 
			special bit-representation ? isudpm2sb(A) 
is                      univariate polynomial over integers of degree 4 
			real ? isupid4real(P) 
is                      univariate squarefree polynomial over integers 
			isuspi(P) 
is                      variable list ? isvarl(r,V) 
is                      vector ? isvec(V) (MACRO) 
is                      vector of Galois-field with single characteristic 
			elements ? isvecgfs(p,AL,A) (MACRO) 
is                      vector of ____ ? isvec_(V,is,anzahlargs,arg1,arg2) 
is                      vector of ____, special ? 
			isvecspec_(V,is,anzahlargs,arg1,...,arg5) 
is                      vector of dense polynomials ? isvecdp(r,V) (MACRO) 
is                      vector of dense polynomials over integers ? 
			isvecdpi(r,V) (MACRO) 
is                      vector of dense polynomials over modular singles ? 
			isvecdpms(r,m,V) (MACRO) 
is                      vector of dense polynomials over rationals ? 
			isvecdpr(r,V) (MACRO) 
is                      vector of integers ? isveci(V) (MACRO) 
is                      vector of modular singles ? isvecms(m,A) (MACRO) 
is                      vector of number field elements ? isvecnf(F,V) 
			(MACRO) 
is                      vector of number field elements, sparse 
			representation ? isvecnfs(F,V) (MACRO) 
is                      vector of polynomials ? isvecp(r,V) (MACRO) 
is                      vector of polynomials over Galois-field with single 
			characteristic ? isvecpgfs(r,p,AL,V) (MACRO) 
is                      vector of polynomials over integers ? isvecpi(r,V) 
			(MACRO) 
is                      vector of polynomials over modular singles ? 
			isvecpms(r,m,V) (MACRO) 
is                      vector of polynomials over rationals ? isvecpr(r,V) 
			(MACRO) 
is                      vector of rational functions over modular single 
			primes, transcendence degree 1 ? isvecrfmsp1(p,V) 
			(MACRO) 
is                      vector of rational functions over rationals ? 
			isvecrfr(r,V) (MACRO) 
is                      vector of rationals ? isvecr(V) (MACRO) 
isatom(a)               (MACRO) is atom ? 
isbasilllred(bas)       is basis over the integers LLL - reduced ? 
isbound(pL)             is bound in STACK ? 
iscinball(z,r,eps)      is complex number in ball ? 
isdipione(r,P)          is distributive polynomial over integers one ? 
isdipol(r,P)            is distributive polynomial ? 
isdippione(r1,r2,P)     is distributive polynomial over polynomials over 
			integers one ? 
isdiprfrone(r1,r2,P)    is distributive polynomial over rational functions 
			over the rationals one ? 
isdiprone(r,P)          is distributive polynomial over rationals one ? 
isdpi(r,P)              is dense polynomial over integers? (rekursiv) 
isdpmi(r,m,P)           is dense polynomial over modular integers ? 
			(rekursiv) 
isdpms(r,m,P)           is dense polynomial over modular singles ? 
			(rekursiv) 
isdpol(r,P)             is dense polynomial ? (rekursiv) 
isdppf(r,p,P)           is dense polynomial over p-adic field ? 
isdpr(r,P)              is dense polynomial over rationals? (rekursiv) 
isecimintorp(E,P)       is torsion point on elliptic curve with integer 
			coefficients, minimal model 
iselecgf2(G,a1,a2,a3,a4,a6,P) is element of an elliptic curve over 
			Galois-field with characteristic 2 ? 
iselecmp(p,a1,a2,a3,a4,a6,P) is element of an elliptic curve over modular 
			primes ? 
iselecmpsnf(p,a,b,P)    is element of an elliptic curve over modular 
			primes, short normal form ? 
iselecnf(F,a1,a2,a3,a4,a6,P) is element of an elliptic curve over number 
			field ? 
iselecnfsnf(F,a,b,P)    is element of an elliptic curve over number field, 
			short normal form ? 
isfloat(A)              is floating point ? 
isfp(A)                 integer squarefree part 
isgf2el(G,a)            (MACRO) is Galois-field with characteristic 2 
			element ? 
isgf2impsb(G)           is Galois-field with characteristic 2 irreducible 
			and monic polynomial in special bit-representation 
			? 
isgfsal(p,AL)           is Galois-field with single characteristic 
			arithmetic list ? 
isgfsel(p,AL,a)         is Galois-field with single characteristic element 
			? 
isgfsone(p,AL,a)        is Galois-field with single characteristic element 
			one ? 
isign(A)                integer sign 
isimupmi(p,A)           is irreducible, monic, univariate polynomial over 
			modular integers ? 
isimupms(p,A)           is irreducible, monic, univariate polynomial over 
			modular singles ? 
isineciminpl(E,P,h,PL)  is in list of points on elliptic curve with integer 
			coefficients, minimal model 
isint(A)                is integer ? 
isipprime(n,a)          is integer pseudo prime ? 
isiprime(n)             is integer prime ? 
isiprimemsg(n)          (MACRO) is integer prime, printing messages 
isispprime(n,k)         is integer strong pseudo prime ? 
isisqr(A)               is integer square ? 
isiupi(P)               is irreducible univariate polynomial over integers 
			? 
isiupr(P)               is irreducible univariate polynomial over rationals 
			? 
isiuspi(P)              is irreducible univariate squarefree polynomial 
			over integers ? 
islelt(L,a)             is list element ? 
islist(L)               is list ? (rekursiv) 
islistgf2(G,L)          is list of Galois-field with characteristic 2 
			elements ? 
islistgfs(p,AL,L)       is list of Galois-field with single characteristic 
			elements ? 
islisti(L)              is list of integers ? 
islistmi(M,A)           is list of modular integers ? 
islistms(m,A)           is list of modular singles ? 
islistnns(A)            is list of non negative singles ? 
islists(A)              is list of singles ? 
isma(M)                 is matrix ? 
isma_(M,is,anzahlargs,arg1,arg2) is matrix of ____ ? 
ismadp(r,M)             (MACRO) is matrix of dense polynomials ? 
ismadpi(r,M)            (MACRO) is matrix of dense polynomials over 
			integers ? 
ismadpms(r,m,M)         (MACRO) is matrix of dense polynomials over modular 
			singles ? 
ismadpr(r,M)            (MACRO) is matrix of dense polynomials over 
			rationals ? 
ismaeqel(M,el)          is matrix of equal elements 
ismagfs(p,AL,M)         (MACRO) is matrix of Galois-field with single 
			characteristic elements ? 
ismai(M)                (MACRO) is matrix of integers ? 
ismami(m,M)             (MACRO) is matrix of modular integers ? 
ismams(m,M)             (MACRO) is matrix of modular singles ? 
ismanf(F,M)             (MACRO) is matrix of number field elements ? 
ismanfs(F,M)            (MACRO) is matrix of number field elements, sparse 
			representation ? 
ismap(r,M)              (MACRO) is matrix of polynomials ? 
ismapgfs(r,p,AL,M)      (MACRO) is matrix of polynomials over Galois-field 
			with single characteristic ? 
ismapi(r,M)             (MACRO) is matrix of polynomials over integers ? 
ismapmi(r,m,M)          (MACRO) is matrix of polynomials over modular 
			integers ? 
ismapms(r,m,M)          (MACRO) is matrix of polynomials over modular 
			singles ? 
ismapr(r,M)             (MACRO) is matrix of polynomials over rationals ? 
ismar(M)                (MACRO) is matrix of rationals ? 
ismarfmsp1(p,M)         (MACRO) is matrix of rational functions over 
			modular single primes, transcendence degree 1 ? 
ismarfr(r,M)            (MACRO) is matrix of rational functions over 
			rationals ? 
ismas(M)                is matrix of singles ? 
ismaspec_(M,is,anzahlargs,arg1,...,arg5) is matrix of ____, special ? 
ismi(m,a)               is modular integer ? 
ismifr(M,A,B)           is modular integer Fermat residue ? 
ismisquare(M,A)         is modular integer square ? 
ismiunit(M,A)           is modular integer unit 
isms(m,a)               is modular single ? 
isnf3eqnf3(F,P,pFD,pPD,pQ) is number field of degree 3 equal to number field 
			of degree 3 
isnfel(F,a)             is number field element? 
isnfels(F,a)            is number field element, sparse representation ? 
isnfone(F,A)            is number field element one 
isnullma(M)             (MACRO) is null-matrix 
isnullvec(V)            is null-vector 
isobj(a)                (MACRO) is object ? 
isomorphic              embedding of subfield gf2ies(Gm,Gn,n) Galois field 
			with characteristic 2 
isomorphic              embedding of subfield gfsalgenies(p,m,n,ALn) 
			Galois-field with single characteristic arithmetic 
			list generator 
isomorphy               type, imaginary case qffmsicggii(m,D,H,L,pIT) 
			quadratic function field over modular singles ideal 
			class group generators and 
isomorphy               type, imaginary case qffmszcgiti(m,D,LG,IT) 
			quadratic function field over modular singles zero 
			class group 
isomorphy               type, real case qffmsicggir(m,D,d,H,L,pIT) 
			quadratic function field over modular singles ideal 
			class group generators and 
isomorphy               type, real case qffmszcgitr(m,D,d,H,LG,R,IT) 
			quadratic function field over modular singles zero 
			class group 
ispconst(r,P,pC)        is polynomial constant ? 
ispd(N,pM)              integer small prime divisors search 
ispd_lo(N,pM)           integer small prime divisors ( lists only ) 
ispecrpai(P)            (MACRO) is point of an elliptic curve over the 
			rationals point at infinity ? 
ispfel(p,a)             is p-adic field element? 
ispgfs(r,p,AL,P)        is polynomial over Galois-field with single 
			characteristic ? (rekursiv) 
ispi(r,P)               is polynomial over integers ? (rekursiv) 
ispione(r,P)            is polynomial over integers equal one ? 
ispmi(r,m,P)            is polynomial over modular integer ? (rekursiv) 
ispmiunit(r,m,P)        is polynomial over modular integers unit? 
ispmonom(r,P)           is polynomial monomial ? 
ispms(r,m,P)            is polynomial over modular singles ? (rekursiv) 
ispmsunit(r,m,P)        is polynomial over modular singles unit? 
ispol(r,P)              is polynomial ? (rekursiv) 
isponecimin(E,P)        is point on elliptic curve with integer 
			coefficients, minimal model 
isponecisnf(E,P)        is point on elliptic curve with integer 
			coefficients, model in short normal form 
isponecrac(E,P)         is point on elliptic curve over rational numbers, 
			actual model 
isppecgf2eq(p,P1,P2)    is projective point of an elliptic curve over 
			Galois-field with characteristic 2 equal ? 
isppecgf2pai(G,P)       is projective point of an elliptic curve over 
			Galois-field with characteristic 2 point at 
			infinity ? 
isppecmpeq(p,P1,P2)     is projective point of an elliptic curve over 
			modular primes equal ? 
isppecmppai(p,P)        is projective point of an elliptic curve over 
			modular primes point at infinity ? 
isppecnfeq(F,P1,P2)     is projective point of an elliptic curve over 
			number field equal? 
isppecnfpai(P)          is projective point of an elliptic curve over 
			number field point at infinity ? 
ispr(r,P)               is polynomial over rationals ? (rekursiv) 
isprod(A,b)             integer single-precision product 
ispt(M,M1,F)            integer Selfridge primality test 
isqnfidone(D,A)         is quadratic number field ideal one? 
isqnfiel(D,a)           is quadratic number field element integral element? 
isqnfint(D,a)           (MACRO) is quadratic number field element integer? 
isqnfone(D,a)           (MACRO) is quadratic number field element one? 
isqnfppihom0(D,P,k,pi,z,a) is quadratic number field element power of prime 
			ideal homomorphism zero? 
isqnfrat(D,a)           (MACRO) is quadratic number field element rational 
isqrem(A,b,pQ,pr)       integer single-precision quotient and remainder 
isqrt(A)                integer square root 
isqrt_lo(A)             integer square root ( lists only ) 
isquot(A,b)             (MACRO) integer single-precision quotient 
israt(R)                is rational number ? 
isrem(A,b)              (MACRO) integer single-precision remainder 
isrfmsp1(p,R)           is rational function over modular single prime, 
			transcendence degree 1 ? 
isrfr(r,R)              is rational function over the rationals ? 
isrfrone(r,A)           is rational function over rationals one 
isrone(A)               is rational number one ? 
isrsqr(R)               is rational number square ? 
issingle(a)             (MACRO) is single ? 
issortls(A)             is sorted list of singles ? 
isspprime(a,pc)         is single power of a prime ? 
issprime(a,pc)          is single prime ? 
isudpm2sb(A)            is univariate dense polynomial over modular 2 in 
			special bit-representation ? 
isum(A,B)               integer sum 
isupid4real(P)          is univariate polynomial over integers of degree 4 
			real ? 
isuspi(P)               is univariate squarefree polynomial over integers 
isvarl(r,V)             is variable list ? 
isvec(V)                (MACRO) is vector ? 
isvec_(V,is,anzahlargs,arg1,arg2) is vector of ____ ? 
isvecdp(r,V)            (MACRO) is vector of dense polynomials ? 
isvecdpi(r,V)           (MACRO) is vector of dense polynomials over 
			integers ? 
isvecdpms(r,m,V)        (MACRO) is vector of dense polynomials over modular 
			singles ? 
isvecdpr(r,V)           (MACRO) is vector of dense polynomials over 
			rationals ? 
isvecgfs(p,AL,A)        (MACRO) is vector of Galois-field with single 
			characteristic elements ? 
isveci(V)               (MACRO) is vector of integers ? 
isvecms(m,A)            (MACRO) is vector of modular singles ? 
isvecnf(F,V)            (MACRO) is vector of number field elements ? 
isvecnfs(F,V)           (MACRO) is vector of number field elements, sparse 
			representation ? 
isvecp(r,V)             (MACRO) is vector of polynomials ? 
isvecpgfs(r,p,AL,V)     (MACRO) is vector of polynomials over Galois-field 
			with single characteristic ? 
isvecpi(r,V)            (MACRO) is vector of polynomials over integers ? 
isvecpms(r,m,V)         (MACRO) is vector of polynomials over modular 
			singles ? 
isvecpr(r,V)            (MACRO) is vector of polynomials over rationals ? 
isvecr(V)               (MACRO) is vector of rationals ? 
isvecrfmsp1(p,V)        (MACRO) is vector of rational functions over 
			modular single primes, transcendence degree 1 ? 
isvecrfr(r,V)           (MACRO) is vector of rational functions over 
			rationals ? 
isvecspec_(V,is,anzahlargs,arg1,...,arg5) is vector of ____, special ? 
itoE(A,e)               ( SIMATH ) integer to Essen integer 
itoEb(A,e,grenze)       ( SIMATH ) integer to Essen integer with upper 
			bound 
itoEsb(A,e,grenze)      ( SIMATH ) integer to Essen integer, sign and upper 
			bound 
itoI(A,h)               ( SIMATH ) integer to ( Heidelberg ) Integer 
itoI_sp(A,lA,h)         ( SIMATH ) integer to ( Heidelberg ) Integer 
			special version 
itofl(A)                (MACRO) integer to floating point 
itonf(A)                (MACRO) integer to number field element 
itonfs(A)               integer to number field element, sparse 
			representation 
itopfel(p,d,A)          integer to p-adic field element 
itopi(r,A)              (MACRO) integer to polynomial over integer 
itoqnf(D,a)             (MACRO) integer to quadratic number field element 
itor(A)                 integer to rational number 
itrunc(A,n)             (MACRO) integer truncation 
j                       cmodinv(q,ln_q) complex modular invariant 
j-invariant             ecgf2jinv(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with characteristic 2, 
j-invariant             ecmpjinv(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular primes, 
j-invariant             ecmpsnfjinv(p,a4,a6) elliptic curve over modular 
			primes, short normal form, 
j-invariant             ecnfjinv(F,a1,a2,a3,a4,a6) elliptic curve over 
			number field 
j-invariant             ecnfsnfjinv(F,a,b) elliptic curve over number 
			field, short normal form, 
j-invariant             ecqnfjinv(E) elliptic curve over quadratic number 
			field, 
j-invariant             ecrfdenjinv(E) elliptic curve over the rationals, 
			factorization of the denominator of the 
j-invariant             ecrjinv(E) elliptic curve over rational numbers, 
j-invariant             iecgnpj(p,m,h1,h2,D) integer elliptic curve of 
			given number of points, 
j-invariant             to equation iecjtoeq(p,j) integer elliptic curve 
j-invariant             to equation special version iecjtoeqsv(p,j,pi) 
			integer elliptic curve 
known                   prime ilkprime() integer largest 
large                   conductor ecrlserhdlc(E,A,s,result) elliptic curve 
			over the rationals, L-series, higher derivative, 
large                   factor ifactlf(n,G,p,quot) integer factorization 
large                   prime divisor search ilpds(N,A,B,pP,pN1) integer 
largest                 known prime ilkprime() integer 
last                    object llast(L) list 
last                    step upgfsbfls(p,AL,P,B,d) univariate polynomial 
			over Galois-field with single characteristic 
			Berlekamp factorization, 
last                    step upmibfls(ip,P,B,d) univariate polynomial over 
			modular integers Berlekamp factorization, 
last                    step upmsbfls(m,P,B,d) univariate polynomial over 
			modular singles Berlekamp factorization, 
law                     affmsp1decl(p,F,P) algebraic function field over 
			modular single prime, transcendence degree 1, 
			decomposition 
law                     nfipdeclaw(F,P) number field, integer prime 
			decomposition 
law                     nfspdeclaw(F,p) number field, single prime 
			decomposition 
law                     ouspprmsp1dl(p,F,P,k) order of a univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			decomposition 
lblength(L,b)           list bounded length 
lcconc(L1,L2)           list constructive concatenation 
lcinv(L)                list constructive inverse 
lcomp(a,L)              list composition 
lcomp2(a,b,L)           (MACRO) list composition, 2 objects 
lcomp3(a,b,c,L)         (MACRO) list composition, 3 objects 
lcomp4(a,b,c,d,L)       (MACRO) list composition, 4 objects 
lcomp5(a,b,c,d,e,L)     (MACRO) list composition, 5 objects 
lcomp6(a,b,c,d,e,f,L)   (MACRO) list composition, 6 objects 
lconc(L1,L2)            list concatenation 
lcopy(L)                list copy (rekursiv) 
leading                 base coefficient diplbc(r,P) (MACRO) distributive 
			polynomial 
leading                 base coefficient, main variable plbc(r,P) 
			polynomial 
leading                 coefficient, main variable plc(r,P) (MACRO) 
			polynomial 
leading                 monomial dipevl(r,P) distributive polynomial 
			exponent vector of the 
least                   common multiple dipevlcm(r,EV1,EV2) distributive 
			polynomial exponent vector 
least                   common multiple ilcm(A,B) integer 
lecdel(L,n)             list element constructive delete 
lecins(L,k,a)           list element constructive insert 
ledel(pL,n)             list element delete 
leins(L,k,a)            list element insert 
leins2(a,L)             list element insert, 2nd position 
lelt(L,k)               list element 
lemma                   factorization approximation pihlfa(r,p,L,M,S,P) 
			polynomial over integers, Hensel 
lemma                   factorization approximation upihlfa(p,P,L,k) 
			univariate polynomial over the integers, Hensel 
lemma                   factorization approximation with respect to integer 
			prime upihlfaip(p,P,L,k) univariate polynomial over 
			integers, Hensel 
lemma                   initialization upihli(p,P,L) univariate polynomial 
			over integers, Hensel 
lemma                   initialization upprmsp1hli(p,F,P,L) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Hensel 
lemma                   initialization with respect to integer prime 
			upihliip(P,F,L) univariate polynomial over 
			integers, Hensel 
lemma                   quadratic step on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
			modular integers, modular ideal, Hensel 
lemma                   quadratic step pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) 
			polynomial over integers, modular ideal, Hensel 
lemma                   quadratic step 
			pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial 
			over modular integers, modular ideal, Hensel 
lemma                   quadratic step upihlqs(p,p_k,p_l,P,L1,L2,A) 
			univariate polynomial over integers, Hensel 
lemma                   quadratic step with respect to integer prime 
			upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over integers, Hensel 
length                  lblength(L,b) list bounded 
length                  llength(L) list 
length                  veclength(V) (MACRO) vector 
lepermg(L)              list element permutations generator 
lerot(L,k,l)            list element rotation 
leset(L,k,a)            list element set 
lexicographical         order dipgfslotglo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in graduated 
lexicographical         order dipilotoglo(r,P) distributive polynomial over 
			integers in lexicographical order to distributive 
			polynomial over integers in graduated 
lexicographical         order dipmiplotglo(r,p,P) distributive polynomial 
			over modular integer primes in lexicographical 
			order to distributive polynomial over modular 
			integer primes in graduated 
lexicographical         order dipmsplotglo(r,p,P) distributive polynomial 
			over modular single primes in lexicographical order 
			to distributive polynomial over modular single 
			primes in graduated 
lexicographical         order dipnflotoglo(r,F,P) distributive polynomial 
			over number field in lexicographical order to 
			distributive polynomial over number field in 
			graduated 
lexicographical         order dippilotoglo(r1,r2,P) distributive polynomial 
			over polynomials over integers in lexicographical 
			order to distributive polynomial over polynomials 
			over integers in graduated 
lexicographical         order diprfrlotglo(r1,r2,P) distributive polynomial 
			over rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			graduated 
lexicographical         order diprlotoglo(r,P) distributive polynomial over 
			rationals in lexicographical order to distributive 
			polynomial over rationals in graduated 
lexicographical         order lscomp(L1,L2) list of singles comparison, 
lexicographical         order to distributive polynomial over Galois-field 
			with single characteristic in graduated 
			lexicographical order dipgfslotglo(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in 
lexicographical         order to distributive polynomial over Galois-field 
			with single characteristic in lexicographical order 
			with inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in 
lexicographical         order to distributive polynomial over Galois-field 
			with single characteristic with total degree 
			ordering dipgfslottdo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in 
lexicographical         order to distributive polynomial over integers in 
			graduated lexicographical order dipilotoglo(r,P) 
			distributive polynomial over integers in 
lexicographical         order to distributive polynomial over integers in 
			lexicographical order with inverse exponent vector 
			dipilotolio(r,P) distributive polynomial over 
			integers in 
lexicographical         order to distributive polynomial over integers with 
			total degree ordering dipilototdo(r,P) distributive 
			polynomial over integers in 
lexicographical         order to distributive polynomial over modular 
			integer primes in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in 
lexicographical         order to distributive polynomial over modular 
			integer primes in lexicographical order with 
			inverse exponent vector dipmiplotlio(r,p,P) 
			distributive polynomial over modular integer primes 
			in 
lexicographical         order to distributive polynomial over modular 
			integer primes with total degree ordering 
			dipmiplottdo(r,p,P) distributive polynomial over 
			modular integer primes in 
lexicographical         order to distributive polynomial over modular 
			single primes in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in 
lexicographical         order to distributive polynomial over modular 
			single primes in lexicographical order with inverse 
			exponent vector dipmsplotlio(r,p,P) distributive 
			polynomial over modular single primes in 
lexicographical         order to distributive polynomial over modular 
			single primes with total degree ordering 
			dipmsplottdo(r,p,P) distributive polynomial over 
			modular single primes in 
lexicographical         order to distributive polynomial over number field 
			in graduated lexicographical order 
			dipnflotoglo(r,F,P) distributive polynomial over 
			number field in 
lexicographical         order to distributive polynomial over number field 
			in lexicographical order with inverse exponent 
			vector dipnflotolio(r,F,P) distributive polynomial 
			over number field in 
lexicographical         order to distributive polynomial over number field 
			with total degree ordering dipnflototdo(r,F,P) 
			distributive polynomial over number field in 
lexicographical         order to distributive polynomial over polynomials 
			over integers in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in 
lexicographical         order to distributive polynomial over polynomials 
			over integers in lexicographical order with inverse 
			exponent vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
lexicographical         order to distributive polynomial over polynomials 
			over integers with total degree ordering 
			dippilototdo(r1,r2,P) distributive polynomial over 
			polynomials over integers in 
lexicographical         order to distributive polynomial over rational 
			functions over the rationals in graduated 
			lexicographical order diprfrlotglo(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in 
lexicographical         order to distributive polynomial over rational 
			functions over the rationals in lexicographical 
			order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
lexicographical         order to distributive polynomial over rational 
			functions over the rationals with total degree 
			ordering diprfrlottdo(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in 
lexicographical         order to distributive polynomial over rationals in 
			graduated lexicographical order diprlotoglo(r,P) 
			distributive polynomial over rationals in 
lexicographical         order to distributive polynomial over rationals in 
			lexicographical order with inverse exponent vector 
			diprlotolio(r,P) distributive polynomial over 
			rationals in 
lexicographical         order to distributive polynomial over rationals 
			with total degree ordering diprlototdo(r,P) 
			distributive polynomial over rationals in 
lexicographical         order with inverse exponent vector 
			dipgfslotlio(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
lexicographical         order with inverse exponent vector dipilotolio(r,P) 
			distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over integers in 
lexicographical         order with inverse exponent vector 
			dipmiplotlio(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			in 
lexicographical         order with inverse exponent vector 
			dipmsplotlio(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			in 
lexicographical         order with inverse exponent vector 
			dipnflotolio(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over number field in 
lexicographical         order with inverse exponent vector 
			dippilotolio(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over polynomials over 
			integers in 
lexicographical         order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
lexicographical         order with inverse exponent vector diprlotolio(r,P) 
			distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over rationals in 
lfifth(L)               (MACRO) list fifth 
lfirst(L)               (MACRO) list first 
lfourth(L)              (MACRO) list fourth 
libsort(L)              list of integers bubble sort 
limerge(L1,L2)          list of integers merge 
line                    nfeltomaln(n,a) number field element to matrix 
line                    through points ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over Galois-field with 
			characteristic 2, 
line                    through points ecmplp(p,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over modular primes, 
line                    through points ecmpsnflp(p,a4,a6,P1,P2) elliptic 
			curve over modular primes, short normal form, 
line                    through points ecnflp(F,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over number field 
line                    through points ecnfsnflp(F,a,b,P1,P2) elliptic 
			curve over number field short normal form 
linear                  combination ilcomb(A,B,m,n) integer 
linear                  combination vecgfslc(p,AL,s1,s2,L1,L2) vector of 
			Galois-field with single characteristic elements 
linear                  combination vecilc(s1,s2,V1,V2) vector of integers 
linear                  combination vecmilc(M,S1,S2,L1,L2) vector of 
			modular integers 
linear                  combination vecmslc(m,s1,s2,L1,L2) vector of 
			modular singles 
linear                  combination vecnflc(F,s1,s2,L1,L2) vector of number 
			field elements 
linear                  combination vecnfslc(F,s1,s2,L1,L2) vector of 
			number field elements, sparse representation, 
linear                  combination vecpgfslc(r,p,AL,s1,s2,L1,L2) vector of 
			polynomials over Galois-field with single 
			characteristic 
linear                  combination vecpilc(r,P1,P2,V1,V2) vector of 
			polynomials over integers 
linear                  combination vecpmilc(r,m,P1,P2,V1,V2) vector of 
			polynomials over modular integers 
linear                  combination vecpmslc(r,m,P1,P2,V1,V2) vector of 
			polynomials over modular singles 
linear                  combination vecpnflc(r,F,s1,s2,L1,L2) vector of 
			polynomials over number field 
linear                  combination vecprlc(r,P1,P2,V1,V2) vector of 
			polynomials over rationals 
linear                  combination vecrfmsp1lc(p,F1,F2,V1,V2) vector of 
			rational functions over modular single primes, 
			transcendence degree 1, 
linear                  combination vecrfrlc(r,F1,F2,V1,V2) vector of 
			rational functions over rationals 
linear                  combination vecrlc(s1,s2,V1,V2) vector of rationals 
linear                  equations magfsssle(p,AL,A,b,pX,pN) matrix of 
			Galois-field with single characteristic elements 
			solution of a system of 
linear                  equations mamsssle(p,A,b,pX,pN) matrix of modular 
			singles solution of a system of 
linear                  equations manfssle(F,A,b,pX,pN) matrix of number 
			field elements solution of a system of 
linear                  equations manfsssle(F,A,b,pX,pN) matrix of number 
			field elements, sparse representation, solution of 
			a system of 
linear                  equations marfmsp1ssle(p,A,b,pX,pN) matrix of 
			rational functions over modular single primes, 
			transcendence degree 1, solution of a system of 
linear                  equations marfrssle(r,A,b,pX,pN) matrix of rational 
			functions over rationals solution of a system of 
linear                  equations marssle(A,b,pX,pN) matrix of rationals 
			solution of a system of 
lines                   flines(k,pf) file 
lines                   lines(k) (MACRO) 
lines(k)                (MACRO) lines 
linv(L)                 list inverse 
lipairspmax(L)          list of integer pairs power maximum 
liprod(L1,L2)           list of integers product 
liprodoe(L)             list of integers product over all entries 
list                    (rekursiv) fgetl(pf) file get 
list                    (rekursiv) fputl(L,pf) file put 
list                    (rekursiv) sgetl(ps) string get 
list                    ? (rekursiv) islist(L) is 
list                    ? isgfsal(p,AL) is Galois-field with single 
			characteristic arithmetic 
list                    ? isvarl(r,V) is variable 
list                    bounded length lblength(L,b) 
list                    cdprfcl(L) common denominator polynomial over the 
			rationals from coefficient 
list                    cdprfmsp1fcl(L,p) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from coefficient 
list                    chinese remainder algorithm milcra(m1,m2,L1,L2) 
			modular integer 
list                    chinese remainder algorithm mslcra(m1,m2,L1,L2) 
			modular single 
list                    composition lcomp(a,L) 
list                    composition, 2 objects lcomp2(a,b,L) (MACRO) 
list                    composition, 3 objects lcomp3(a,b,c,L) (MACRO) 
list                    composition, 4 objects lcomp4(a,b,c,d,L) (MACRO) 
list                    composition, 5 objects lcomp5(a,b,c,d,e,L) (MACRO) 
list                    composition, 6 objects lcomp6(a,b,c,d,e,f,L) 
			(MACRO) 
list                    concatenation lconc(L1,L2) 
list                    constructive concatenation lcconc(L1,L2) 
list                    constructive inverse lcinv(L) 
list                    copy (rekursiv) lcopy(L) 
list                    ecrrl(E) elliptic curve over rational numbers 
			reduction 
list                    element ? islelt(L,a) is 
list                    element constructive delete lecdel(L,n) 
list                    element constructive insert lecins(L,k,a) 
list                    element delete ledel(pL,n) 
list                    element insert leins(L,k,a) 
list                    element insert, 2nd position leins2(a,L) 
list                    element lelt(L,k) 
list                    element permutations generator lepermg(L) 
list                    element rotation lerot(L,k,l) 
list                    element set leset(L,k,a) 
list                    extension pvext(r,P,V,VN) polynomial variable 
list                    fgetdipgfsl(r,p,AL,VL,Vgfs,pf) file get 
			distributive polynomial over Galois-field with 
			single characteristic 
list                    fgetdipil(r,VL,pf) file get distributive polynomial 
			over integers 
list                    fgetdipmipl(r,p,VL,pf) file get distributive 
			polynomial over modular integer primes 
list                    fgetdipmspl(r,p,VL,pf) file get distributive 
			polynomial over modular single primes 
list                    fgetdipnfl(r,F,VL,Vnf,pf) file get distributive 
			polynomial over number field 
list                    fgetdippil(r1,r2,VL1,VL2,pf) file get distributive 
			polynomial over polynomials over integers 
list                    fgetdiprfrl(r1,r2,VL1,VL2,pf) file get distributive 
			polynomial over rational functions over the 
			rationals 
list                    fgetdiprl(r,VL,pf) file get distributive polynomial 
			over rationals 
list                    fgetvl(pf) file get variable 
list                    fifth lfifth(L) (MACRO) 
list                    first lfirst(L) (MACRO) 
list                    fourth lfourth(L) (MACRO) 
list                    fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put 
			distributive polynomial over Galois-field with 
			single characteristic 
list                    fputdipil(r,PL,VL,pf) file put distributive 
			polynomial over integers 
list                    fputdipmipl(r,p,PL,VL,pf) file put distributive 
			polynomial over modular integer primes 
list                    fputdipmspl(r,p,PL,VL,pf) file put distributive 
			polynomial over modular single primes 
list                    fputdipnfl(r,F,PL,VL,Vnf,pf) file put distributive 
			polynomial over number field 
list                    fputdippil(r1,r2,PL,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers 
list                    fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file put 
			distributive polynomial over rational functions 
			over the rationals 
list                    fputdiprl(r,PL,VL,pf) file put distributive 
			polynomial over rationals 
list                    fputfactl(L,pf) file put factor 
list                    fputifel(L,pf) file put integer factor exponent 
list                    fputqnffel(D,L,pf) file put quadratic number field 
			element factor exponent 
list                    from common denominator matrix of rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1lfm(M,p) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, 
list                    from common denominator matrix of rationals 
			cdprlfcdmar(M) common denominator polynomial over 
			the rationals 
list                    from common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 clfcdprfmsp1(P,n) coefficient 
list                    from common denominator polynomial over the 
			rationals clfcdpr(P,n) coefficient 
list                    from univariate polynomial over rational functions 
			over modular single prime, transcendence degree 1 
			sclfuprfmsp1(P,n) special coefficient 
list                    from univariate polynomial over the integers 
			sclfupi(P,n) special coefficient 
list                    generator gf2algen(n,H) Galois-field with 
			characteristic 2 arithmetic 
list                    generator gfsalgen(p,n,G) Galois-field with single 
			characteristic arithmetic 
list                    generator isomorphic embedding of subfield 
			gfsalgenies(p,m,n,ALn) Galois-field with single 
			characteristic arithmetic 
list                    getdipgfsl(r,p,AL,VL,Vgfs) (MACRO) get distributive 
			polynomial over Galois-field with single 
			characteristic 
list                    getdipil(r,VL) (MACRO) get distributive polynomial 
			over integers 
list                    getdipmipl(r,p,VL) (MACRO) get distributive 
			polynomial over modular integer primes 
list                    getdipmspl(r,p,VL) (MACRO) get distributive 
			polynomial over modular single primes 
list                    getdipnfl(r,F,VL,Vnf) (MACRO) get distributive 
			polynomial over number field 
list                    getdippil(r1,r2,VL1,VL2) (MACRO) get distributive 
			polynomial over polynomials over integers 
list                    getdiprfrl(r1,r2,VL1,VL2) (MACRO) get distributive 
			polynomial over rational functions over the 
			rationals 
list                    getdiprl(r,VL) (MACRO) get distributive polynomial 
			over rationals 
list                    getl() (MACRO) get 
list                    getvl() (MACRO) get variable 
list                    gf2prodAL(AL,a,b) Galois-field with characteristic 
			2 product with arithmetic 
list                    gf2squAL(AL,a) Galois-field with characteristic 2 
			square with arithmetic 
list                    ifel(LP) integer factor exponent 
list                    ifrl(N,pm) integer Fermat residue 
list                    inverse linv(L) 
list                    last object llast(L) 
list                    length llength(L) 
list                    member lmemb(a,L) 
list                    merge pvmerge(LV,LP,pLP) polynomial variable 
list                    msfrl(m,a) modular single Fermat residue 
list                    of 2 objects list2(a,b) (MACRO) 
list                    of 3 objects list3(a,b,c) (MACRO) 
list                    of 4 objects list4(a,b,c,d) (MACRO) 
list                    of 5 objects list5(a,b,c,d,e) (MACRO) 
list                    of 6 objects list6(a,b,c,d,e,f) (MACRO) 
list                    of Galois-field with characteristic 2 elements ? 
			islistgf2(G,L) is 
list                    of Galois-field with single characteristic elements 
			? islistgfs(p,AL,L) is 
list                    of integer pairs power maximum lipairspmax(L) 
list                    of integers ? islisti(L) is 
list                    of integers bubble sort libsort(L) 
list                    of integers fgetli(pf) file get 
list                    of integers fputli(L,pf) file put 
list                    of integers getli() (MACRO) get 
list                    of integers merge limerge(L1,L2) 
list                    of integers product liprod(L1,L2) 
list                    of integers product over all entries liprodoe(L) 
list                    of integers putli(L) (MACRO) put 
list                    of lists concatenation llconc(L) 
list                    of modular integers ? islistmi(M,A) is 
list                    of modular singles ? islistms(m,A) is 
list                    of non negative singles ? islistnns(A) is 
list                    of one object list1(a) (MACRO) 
list                    of points ecrbtlistp(LP,BT,modus) elliptic curve 
			over rational numbers, birational transformation of 
list                    of points fputecrlistp(P,modus,pf) file put 
			elliptic curve over the rational numbers, 
list                    of points on elliptic curve with integer 
			coefficients, minimal model isineciminpl(E,P,h,PL) 
			is in 
list                    of points putecrlistp(P,modus) (MACRO) put elliptic 
			curve over rational numbers, 
list                    of polynomials bubble sort, special lpbsorts(r,L) 
list                    of polynomials over integers fputlpi(r,L,V,pf) file 
			put 
list                    of polynomials over rationals fputlpr(r,L,V,pf) 
			file put 
list                    of rational numbers fgetlr(pf) file get 
list                    of rational numbers getlr() (MACRO) get 
list                    of rationals fputlr(L,pf) file put 
list                    of reductants next lrednext(L) 
list                    of single precision bubble sort lsbsort(L) 
list                    of single precisions bubble merge sort lsbmsort(L) 
list                    of single precisions insert lsins(n,L) 
list                    of single precisions merge lsmerge(L1,L2) 
list                    of singles ? islists(A) is 
list                    of singles ? issortls(A) is sorted 
list                    of singles comparison special version 
			lscomps(L1,L2) 
list                    of singles comparison, lexicographical order 
			lscomp(L1,L2) 
list                    of singles maximum special version lsmaxs(L1,L2) 
list                    of singles minimum special version lsmins(L1,L2) 
list                    of singles random permutation lsrandperm(n) 
list                    of variables pmakevl(s) polynomial make 
list                    pair lpair(L1,L2) 
list                    permutation lpermut(L,PI) 
list                    product ifelprod(a,b) integer factor exponent 
list                    ptol(pc) (MACRO) pointer to 
list                    putdipgfsl(r,p,AL,PL,VL,Vgfs) (MACRO) put 
			distributive polynomial over Galois-field with 
			single characteristic 
list                    putdipil(r,PL,VL) (MACRO) put distributive 
			polynomial over integers 
list                    putdipmipl(r,p,PL,VL) (MACRO) put distributive 
			polynomial over modular integer primes 
list                    putdipmspl(r,p,PL,VL) (MACRO) put distributive 
			polynomial over modular single primes 
list                    putdipnfl(r,F,PL,VL,Vnf) (MACRO) put distributive 
			polynomial over number field 
list                    putdippil(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers 
list                    putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive polynomial over rational functions 
			over the rationals 
list                    putdiprl(r,PL,VL) (MACRO) put distributive 
			polynomial over rationals 
list                    putfactl(L) (MACRO) put factor 
list                    putifel(L) (MACRO) put integer factor exponent 
list                    putl(L) (MACRO) put 
list                    putqnffel(D,L) (MACRO) put quadratic number field 
			element factor exponent 
list                    reductum lred(L) (MACRO) 
list                    reductum, 2 objects lred2(L) (MACRO) 
list                    reductum, 3 objects lred3(L) (MACRO) 
list                    reductum, 4 objects lred4(L) (MACRO) 
list                    reductum, 5 objects lred5(L) (MACRO) 
list                    reductum, 6 objects lred6(L) 
list                    reductum, general lreduct(L,k) 
list                    search lsrch(a,L) 
list                    second lsecond(L) (MACRO) 
list                    set first lsfirst(L,a) (MACRO) 
list                    set reductum lsred(L1,L2) (MACRO) 
list                    sfel(n) single factor exponent 
list                    sixth lsixth(L) 
list                    size lsize(l) (MACRO) 
list                    size recursive part (rekursiv) lsizerec(l,n) 
list                    sort vlsort(V,pPI) variable 
list                    sputl(l,str) string put 
list                    structure (rekursiv) fputlstruct(L,pf) file put 
list                    structure putlstruct(L) (MACRO) put 
list                    suffix lsuffix(L,a) (MACRO) 
list                    third lthird(L) (MACRO) 
list                    to pointer ltop(L) (MACRO) 
list                    union eciminplunion(E,L1,L2,modus) elliptic curve 
			with integer coefficients, minimal model, point 
list                    upifscl(L) univariate polynomial over the integers 
			from special coefficient 
list                    uprfmsp1fscl(L) univariate polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, from special coefficient 
list,                   insert point eciminplinsp(P,h,PL) elliptic curve 
			with integer coefficients, minimal model, point 
list1(a)                (MACRO) list of one object 
list2(a,b)              (MACRO) list of 2 objects 
list3(a,b,c)            (MACRO) list of 3 objects 
list4(a,b,c,d)          (MACRO) list of 4 objects 
list5(a,b,c,d,e)        (MACRO) list of 5 objects 
list6(a,b,c,d,e,f)      (MACRO) list of 6 objects 
lists                   concatenation llconc(L) list of 
lists                   only ) ijacsym_lo(A,B) integer Jacobi-symbol ( 
lists                   only ) ispd_lo(N,pM) integer small prime divisors ( 
lists                   only ) isqrt_lo(A) integer square root ( 
lists                   only ) miexp_lo(M,A,E) modular integer 
			exponentiation ( 
lists                   only ) rhopds_lo(N,b,z) rho- method by Pollard 
			divisor search ( 
lists                   only igcd_lo(A,B) integer greatest common divisor, 
lists                   only iprod_lo(A,B) integer product, 
lists                   only iqrem_lo(A,B,pQ,pR) integer quotient and 
			remainder, 
lists                   only miinv_lo(M,A) modular integer inverse, 
llast(L)                list last object 
llconc(L)               list of lists concatenation 
llength(L)              list length 
lmemb(a,L)              list member 
local                   height at the archimedean absolute value 
			eciminlhaav(E,P) elliptic curve with integer 
			coefficients, minimal model, 
local                   heights at all non archimedean absolute values 
			eciminlhnaav(E,P) elliptic curve with integer 
			coefficients, minimal model, 
local                   maximal over-order ouspibaslmo(F,p,Q,pk) order of 
			an univariate separable polynomial over the 
			integers basis of a 
local                   maximal over-order ouspprmsp1bl(p,F,P,Q,pk) order 
			of an univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, basis of a 
local                   maximal over-order with respect to integer primes 
			ouspibaslmoi(F,P,Q,pk) order of an univariate 
			separable polynomial over the integers basis of a 
logarithm               (rekursiv) fllog(f) floating point natural 
logarithm               of point ecisnfelogp(E,P,n) elliptic curve with 
			integer coefficients, short normal form, elliptic 
logarithm,              base 10 ilog10(n) integer 
logarithm,              base 2 ilog2(A) integer 
logarithm,              base 2 rlog2(R) rational number 
logarithm,              base 2 slog2(a) single-precision 
lower                   triangular form with negative entries ) 
			maihermltne(A) (MACRO) matrix of integers Hermite 
			normal form ( 
lower                   triangular form with positive entries ) 
			maihermltpe(A) (MACRO) matrix of integers Hermite 
			normal form ( 
lpair(L1,L2)            list pair 
lpbsorts(r,L)           list of polynomials bubble sort, special 
lpermut(L,PI)           list permutation 
lred(L)                 (MACRO) list reductum 
lred2(L)                (MACRO) list reductum, 2 objects 
lred3(L)                (MACRO) list reductum, 3 objects 
lred4(L)                (MACRO) list reductum, 4 objects 
lred5(L)                (MACRO) list reductum, 5 objects 
lred6(L)                list reductum, 6 objects 
lrednext(L)             list of reductants next 
lreduct(L,k)            list reductum, general 
lsbmsort(L)             list of single precisions bubble merge sort 
lsbsort(L)              list of single precision bubble sort 
lscomp(L1,L2)           list of singles comparison, lexicographical order 
lscomps(L1,L2)          list of singles comparison special version 
lsecond(L)              (MACRO) list second 
lsfirst(L,a)            (MACRO) list set first 
lsins(n,L)              list of single precisions insert 
lsixth(L)               list sixth 
lsize(l)                (MACRO) list size 
lsizerec(l,n)           list size recursive part (rekursiv) 
lsmaxs(L1,L2)           list of singles maximum special version 
lsmerge(L1,L2)          list of single precisions merge 
lsmins(L1,L2)           list of singles minimum special version 
lsrandperm(n)           list of singles random permutation 
lsrch(a,L)              list search 
lsred(L1,L2)            (MACRO) list set reductum 
lsuffix(L,a)            (MACRO) list suffix 
lthird(L)               (MACRO) list third 
ltop(L)                 (MACRO) list to pointer 
m-adic                  value iaval(m,A) integer additive 
m-adic                  value raval(m,R) rational additive 
m4hom(a)                (MACRO) modular 4 homomorphism 
maam(M,el)              matrix adjoin matrix 
macconc(M,N)            matrix constructive concatenation 
machpol(M,det,minusEins,anzahlargs,arg1,arg2) matrix characteristic 
			polynomial 
machpolspec(M,det,minusEins,anzahlargs,arg1,...,arg5) matrix characteristic 
			polynomial special 
maconc(M,N)             matrix concatenation 
maconsdiag(n,el)        matrix construction diagonal-matrix 
maconszero(m,n)         matrix construction zero 
macopy(M)               matrix copy 
mactransp(M)            matrix constructive transpose 
macup(n,L)              matrix of coefficients of univariate polynomials 
madel1rc(pM,i,j)        matrix delete 1 row and 1 column 
madelsc(pM,I)           matrix delete several columns 
madelsr(pM,I)           matrix delete several rows 
madelsrc(pM,I,J)        (MACRO) matrix delete several rows and columns 
madptomap(r,M)          matrix of dense polynomials to matrix of 
			polynomials 
mafldet(M)              matrix of floatings determinant 
magfschpol(p,AL,M)      (MACRO) matrix of Galois-field with single 
			characteristic elements characteristic polynomial 
magfscons1(p,AL,n)      (MACRO) matrix of Galois-field with single 
			characteristic elements construction 1 
magfsdet(p,AL,M)        matrix of Galois-field with single characteristic 
			elements determinant 
magfsdif(p,AL,M,N)      (MACRO) matrix of Galois-field with single 
			characteristic elements difference 
magfsefe(p,ALm,M,g)     matrix over Galois-field with single characteristic 
			embedding in field extension 
magfsevifcp(p,AL,M,pL)  matrix over Galois-field with single characteristic 
			eigenvalues and irreducible factors of the 
			characteristic polynomial 
magfsexp(p,AL,M,n)      matrix of Galois-field with single characteristic 
			elements exponentiation 
magfsinv(p,AL,M)        matrix of Galois-field with single characteristic 
			elements inverse 
magfsneg(p,AL,M)        (MACRO) matrix of Galois-field with single 
			characteristic elements negation 
magfsnsb(p,AL,M)        matrix of Galois-field with single characteristic 
			elements, null space basis 
magfsprod(p,AL,M,N)     (MACRO) matrix of Galois-field with single 
			characteristic elements product 
magfsrk(p,AL,M)         matrix of Galois-field with single characteristic 
			elements rank 
magfssmul(p,AL,M,el)    matrix of Galois-field with single characteristic 
			elements scalar multiplication 
magfsssle(p,AL,A,b,pX,pN) matrix of Galois-field with single characteristic 
			elements solution of a system of linear equations 
magfssum(p,AL,M,N)      (MACRO) matrix of Galois-field with single 
			characteristic elements sum 
magfsvecmul(p,AL,A,x)   (MACRO) matrix of Galois-field with single 
			characteristic elements vector multiplication 
maichpol(M)             (MACRO) matrix of integers characteristic 
			polynomial 
maicons1(n)             (MACRO) matrix of integers construction 1 
maidet(M)               matrix of integers determinant 
maidif(M,N)             (MACRO) matrix of integers difference 
maiedfcf(M,pA,pB)       matrix of integers elementary divisor form and 
			cofactors 
maiegsc(M,A,B)          matrix of integers Euklid- Gauss- step for columns 
maiegsr(M,A,B)          matrix of integers Euklid- Gauss- step for rows 
maiev(M)                (MACRO) matrix of integers eigenvalues 
maievifcp(M,pL)         matrix of integers eigenvalues and irreducible 
			factors of the characteristic polynomial 
maiexp(M,n)             matrix of integers exponentiation 
maiherm(A,ne)           matrix of integers Hermite normal form 
maihermltne(A)          (MACRO) matrix of integers Hermite normal form ( 
			lower triangular form with negative entries ) 
maihermltpe(A)          (MACRO) matrix of integers Hermite normal form ( 
			lower triangular form with positive entries ) 
maihermspec(M,r,pD)     matrix of integers hermitian reduction, special 
maiinv(M)               matrix of integers inverse 
main                    variable (rekursiv) ppfderiv(r,p,P) polynomial over 
			p-adic field derivation, 
main                    variable dipnmv(r,P,n) distributive polynomial new 
main                    variable pdegree(r,P) (MACRO) polynomial degree, 
main                    variable pgf2deriv(r,G,P) polynomial over 
			Galois-field with characteristic 2 derivation, 
main                    variable pgf2eval(r,G,P,a) polynomial over 
			Galois-field with characteristic 2 evaluation, 
main                    variable pgfsderiv(r,p,AL,P) polynomial over 
			Galois-field with single characteristic derivation, 
main                    variable pgfseval(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic evaluation, 
main                    variable pideriv(r,P) polynomial over integers 
			derivation, 
main                    variable pieval(r,P,A) polynomial over integers 
			evaluation, 
main                    variable pisubst(r,P1,P2) polynomial over integers 
			substitution, 
main                    variable pitrans(r,P,A) polynomial over integers 
			translation, 
main                    variable plbc(r,P) polynomial leading base 
			coefficient, 
main                    variable plc(r,P) (MACRO) polynomial leading 
			coefficient, 
main                    variable pmideriv(r,M,P) polynomial over modular 
			integers derivation, 
main                    variable pmieval(r,M,P,A) polynomial over modular 
			integers evaluation, 
main                    variable pmisubst(r,m,P1,P2) polynomial over 
			modular integers substitution, 
main                    variable pmitrans(r,m,P,a) polynomial over modular 
			integers translation, 
main                    variable pmsderiv(r,m,P) polynomial over modular 
			singles derivation, 
main                    variable pmseval(r,m,P,a) polynomial over modular 
			singles evaluation, 
main                    variable pmssubst(r,m,P1,P2) polynomial over 
			modular singles substitution, 
main                    variable pmstrans(r,m,P,a) polynomial over modular 
			singles translation, 
main                    variable pnfderiv(r,F,P) polynomial over number 
			field derivation, 
main                    variable pnfeval(r,F,P,a) polynomial over number 
			field evaluation, 
main                    variable ppfeval(r,p,P,A) polynomial over p-adic 
			field evaluation, 
main                    variable ppfsubst(r,p,P1,P2) polynomial over p-adic 
			field substitution, 
main                    variable ppftrans(r,p,P,A) polynomial over p-adic 
			field translation, 
main                    variable ppmvprod(r,P,n) polynomial product by 
			power of 
main                    variable ppmvquot(r,P,n) polynomial quotient by 
			power of 
main                    variable prderiv(r,P) polynomial over rationals 
			derivation, 
main                    variable preval(r,P,A) polynomial over rationals 
			evaluation, 
main                    variable prfmsp1deriv(r,p,P) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, derivation, 
main                    variable printegr(r,P) polynomial over rationals 
			integration, 
main                    variable prsubst(r,P1,P2) polynomial over rationals 
			substitution, 
main                    variable prtrans(r,P,A) polynomial over rationals 
			translation, 
maineg(M)               (MACRO) matrix of integers negation 
maiprod(M,N)            (MACRO) matrix of integers product 
maismul(M,el)           matrix of integers scalar multiplication 
maisum(M,N)             (MACRO) matrix of integers sum 
maitomagfs(p,M)         matrix over integers to matrix over Galois-field 
			with single characteristic 
maitomami(m,M)          matrix of integers to matrix of modular integers 
maitomams(m,M)          matrix of integers to matrix of modular singles 
maitomanf(M)            matrix of integers to matrix of number field 
			elements 
maitomanfs(M)           matrix of integers to matrix of number field 
			elements, sparse representation 
maitomapi(r,M)          matrix of integers to matrix of polynomials over 
			integers 
maitomar(M)             matrix of integers to matrix of rationals 
maitrace(M)             matrix of integers trace 
maivecmul(A,x)          (MACRO) matrix of integers vector multiplication 
make                    list of variables pmakevl(s) polynomial 
mamichpol(m,M)          (MACRO) matrix of modular integers characteristic 
			polynomial 
mamicons1(m,n)          (MACRO) matrix of modular integers construction 1 
mamidet(m,M)            matrix of modular integers determinant 
mamidif(m,M,N)          (MACRO) matrix of modular integers difference 
mamiev(p,M)             (MACRO) matrix of modular integers eigenvalues 
mamievifcp(p,M,pL)      matrix of modular integers eigenvalues and 
			irreducible factors of the characteristic 
			polynomial 
mamiexp(m,M,n)          matrix of modular integers exponentiation 
mamiinv(m,M)            matrix of modular integers inverse 
mamineg(m,M)            (MACRO) matrix of modular integers negation 
maminsb(P,M)            matrix of modular integers, null space basis 
mamiprod(m,M,N)         (MACRO) matrix of modular integers product 
mamismul(m,M,el)        matrix of modular integers scalar multiplication 
mamisum(m,M,N)          (MACRO) matrix of modular integers sum 
mamivecmul(m,A,x)       (MACRO) matrix of modular integers vector 
			multiplication 
mamschpol(m,M)          (MACRO) matrix of modular singles characteristic 
			polynomial 
mamscons1(m,n)          (MACRO) matrix of modular singles construction 1 
mamsdet(m,M)            matrix of modular singles determinant 
mamsdif(m,M,N)          (MACRO) matrix of modular singles difference 
mamsev(p,M)             (MACRO) matrix of modular singles eigenvalues 
mamsevifcp(p,M,pL)      matrix of modular singles eigenvalues and 
			irreducible factors of the characteristic 
			polynomial 
mamsexp(m,M,n)          matrix of modular singles exponentiation 
mamsinv(m,M)            matrix of modular singles inverse 
mamsneg(m,M)            (MACRO) matrix of modular singles negation 
mamsnsb(p,A)            (MACRO) matrix of modular singles null space basis 
mamsprod(m,M,N)         (MACRO) matrix of modular singles product 
mamssmul(m,M,el)        matrix of modular singles scalar multiplication 
mamsssle(p,A,b,pX,pN)   matrix of modular singles solution of a system of 
			linear equations 
mamssum(m,M,N)          (MACRO) matrix of modular singles sum 
mamsvecmul(m,A,x)       (MACRO) matrix of modular singles vector 
			multiplication 
management              HDimem() Heidelberg arithmetic package: memory 
maneg(M,neg,anzahlargs,arg1,arg2) matrix negation 
manegspec(M,neg,anzahlargs,arg1,...,arg5) matrix negation special 
manfchpol(F,M)          (MACRO) matrix of number field elements 
			characteristic polynomial 
manfcons1(F,n)          (MACRO) matrix of number field elements 
			construction 1 
manfdet(F,M)            matrix of number field elements determinant 
manfdif(F,M,N)          (MACRO) matrix of number field elements difference 
manfexp(F,M,n)          matrix of number field elements exponentiation 
manfinv(F,M)            matrix of number field elements inverse 
manfneg(F,M)            (MACRO) matrix of number field elements negation 
manfnsb(F,M)            matrix of number field elements null space basis 
manfprod(F,M,N)         (MACRO) matrix of number field elements product 
manfrk(F,M)             matrix of number field elements rank 
manfscons1(F,n)         (MACRO) matrix of number field elements, sparse 
			representation, construction 1 
manfsdet(F,M)           matrix of number field elements, sparse 
			representation, determinant 
manfsdif(F,M,N)         (MACRO) matrix of number field elements, sparse 
			representation, difference 
manfsexp(F,M,n)         matrix of number field elements, sparse 
			representation, exponentiation 
manfsinv(F,M)           matrix of number field elements, sparse 
			representation, inverse 
manfsmul(F,M,el)        matrix of number field elements scalar 
			multiplication 
manfsneg(F,M)           (MACRO) matrix of number field elements, sparse 
			representation, negation 
manfsnsb(F,M)           matrix of number field elements, sparse 
			representation, null space basis 
manfsprod(F,M,N)        (MACRO) matrix of number field elements, sparse 
			representation, product 
manfsrk(F,M)            matrix of number field elements, sparse 
			representation, rank 
manfssle(F,A,b,pX,pN)   matrix of number field elements solution of a 
			system of linear equations 
manfssmul(F,M,el)       matrix of number field elements, sparse 
			representation, scalar multiplication 
manfsssle(F,A,b,pX,pN)  matrix of number field elements, sparse 
			representation, solution of a system of linear 
			equations 
manfssum(F,M,N)         (MACRO) matrix of number field elements, sparse 
			representation, sum 
manfsum(F,M,N)          (MACRO) matrix of number field elements sum 
manfsvecmul(F,A,x)      (MACRO) matrix of number field elements, sparse 
			representation, vector multiplication 
manftomudpr(F,M)        matrix of number field elements to matrix of 
			univariate dense polynomials over rationals 
manfvecmul(F,A,x)       (MACRO) matrix of number field elements vector 
			multiplication 
manrcol(M)              (MACRO) matrix number of columns 
manrrow(M)              (MACRO) matrix number of rows 
mantissa                flmant(f) (MACRO) floating point 
mapgfschpol(r,p,AL,M)   (MACRO) matrix of polynomials over Galois-field 
			with single characteristic characteristic 
			polynomial 
mapgfscons1(r,p,AL,n)   (MACRO) matrix of polynomials over Galois-field 
			with single characteristic construction 1 
mapgfsdet(r,p,AL,M)     matrix of polynomials over Galois-field with single 
			characteristic determinant 
mapgfsdif(r,p,AL,M,N)   (MACRO) matrix of polynomials over Galois-field 
			with single characteristic difference 
mapgfsefe(r,p,ALm,M,g)  matrix over polynomials over Galois-field with 
			single characteristic embedding in field extension 
mapgfsexp(r,p,AL,M,n)   matrix of polynomials over Galois-field with single 
			characteristic exponentiation 
mapgfsinv(r,p,AL,M)     matrix of polynomials over Galois-field with single 
			characteristic inverse 
mapgfsneg(r,p,AL,M)     (MACRO) matrix of polynomials over Galois-field 
			with single characteristic negation 
mapgfsprod(r,p,AL,M,N)  (MACRO) matrix of polynomials over Galois-field 
			with single characteristic product 
mapgfssmul(r,p,AL,M,el) matrix of polynomials over Galois-field with single 
			characteristic scalar multiplication 
mapgfssum(r,p,AL,M,N)   (MACRO) matrix of polynomials over Galois-field 
			with single characteristic sum 
mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) matrix of polynomials over 
			Galois-field with single characteristic 
			transformation 
mapgfsvmul(r,p,AL,A,x)  (MACRO) matrix of polynomials over Galois-field 
			with single characteristic vector multiplication 
mapichpol(r,M)          (MACRO) matrix of polynomials over integers 
			characteristic polynomial 
mapicons1(r,n)          (MACRO) matrix of polynomials over integers 
			construction 1 
mapidet(r,M)            matrix of polynomials over integers determinant 
mapidif(r,M,N)          (MACRO) matrix of polynomials over integers 
			difference 
mapiexp(r,M,n)          matrix of polynomials over integers exponentiation 
mapigfsevfvs(r,p,AL,M)  matrix over polynomials over integers Galois-field 
			with single characteristic element evaluation first 
			variable special version 
mapiinv(r,M)            matrix of polynomials over integers inverse 
mapineg(r,M)            (MACRO) matrix of polynomials over integers 
			negation 
mapinfevlfvs(r,F,M)     matrix of polynomials over integers number field 
			element evaluation first variable special version 
mapiprod(r,M,N)         (MACRO) matrix of polynomials over integers product 
mapismul(r,M,P)         matrix of polynomials over integers scalar 
			multiplication 
mapisum(r,M,N)          (MACRO) matrix of polynomials over integers sum 
mapitomapmi(r,M,m)      matrix of polynomials over integers to matrix of 
			polynomials over modular integers 
mapitomapms(r,M,m)      matrix of polynomials over integers to matrix of 
			polynomials over modular singles 
mapitomapnf(r,M)        matrix of polynomials over integers to matrix of 
			polynomials over number field 
mapitomapr(r,M)         matrix of integers to matrix of rationals 
mapitomarfr(r,M)        matrix of polynomials over integers to matrix of 
			rational functions over rationals 
mapitompmpi(r,M,P)      matrix of polynomials over integers to matrix of 
			polynomials modulo polynomial over integers 
mapitransf(r1,M1,V1,r2,P2,V2,Vn,pV3) matrix of polynomials over the integers 
			transformation 
mapivecmul(r,A,x)       (MACRO) matrix of polynomials over integers vector 
			multiplication 
mapmichpol(r,m,M)       (MACRO) matrix of polynomials over modular integers 
			characteristic polynomial 
mapmicons1(r,m,n)       (MACRO) matrix of polynomials over modular integers 
			construction 1 
mapmidet(r,m,M)         matrix of polynomials over modular integers 
			determinant 
mapmidif(r,m,M,N)       (MACRO) matrix of polynomials over modular integers 
			difference 
mapmiexp(r,m,M,n)       matrix of polynomials over modular integers 
			exponentiation 
mapmiinv(r,m,M)         matrix of polynomials over modular integers inverse 
mapmineg(r,m,M)         (MACRO) matrix of polynomials over modular integers 
			negation 
mapmiprod(r,m,M,N)      (MACRO) matrix of polynomials over modular integers 
			product 
mapmismul(r,m,M,P)      matrix of polynomials over modular integers scalar 
			multiplication 
mapmisum(r,m,M,N)       (MACRO) matrix of polynomials over modular integers 
			sum 
mapmitomapmp(r,m,P,M)   matrix of polynomials over modular integers to 
			matrix of polynomials modulo polynomial over 
			modular integers 
mapmitransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of polynomials over modular 
			integers transformation 
mapmivecmul(r,m,A,x)    (MACRO) matrix of polynomials over modular integers 
			vector multiplication 
mapmschpol(r,m,M)       (MACRO) matrix of polynomials over modular singles 
			characteristic polynomial 
mapmscons1(r,m,n)       (MACRO) matrix of polynomials over modular singles 
			construction 1 
mapmsdet(r,m,M)         matrix of polynomials over modular singles 
			determinant 
mapmsdif(r,m,M,N)       (MACRO) matrix of polynomials over modular singles 
			difference 
mapmsexp(r,m,M,n)       matrix of polynomials over modular singles 
			exponentiation 
mapmsinv(r,m,M)         matrix of polynomials over modular singles inverse 
mapmsneg(r,m,M)         (MACRO) matrix of polynomials over modular singles 
			negation 
mapmsprod(r,m,M,N)      (MACRO) matrix of polynomials over modular singles 
			product 
mapmssmul(r,m,M,P)      matrix of polynomials over modular singles scalar 
			multiplication 
mapmssum(r,m,M,N)       (MACRO) matrix of polynomials over modular singles 
			sum 
mapmstomapmp(r,m,P,M)   matrix of polynomials over modular singles to 
			matrix of polynomials modulo polynomial over 
			modular singles 
mapmstransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of polynomials over modular 
			singles transformation 
mapmsvecmul(r,m,A,x)    (MACRO) matrix of polynomials over modular singles 
			vector multiplication 
mapnfchpol(r,F,M)       (MACRO) matrix of polynomials over number field 
			characteristic polynomial 
mapnfcons1(r,F,n)       (MACRO) matrix of polynomials over number field 
			construction 1 
mapnfdet(r,F,M)         matrix of polynomials over number field determinant 
mapnfdif(r,F,M,N)       (MACRO) matrix of polynomials over number field 
			difference 
mapnfexp(r,F,M,n)       matrix of polynomials over number field 
			exponentiation 
mapnfinv(r,F,M)         matrix of polynomials over number field inverse 
mapnfneg(r,F,M)         (MACRO) matrix of polynomials over number field 
			negation 
mapnfprod(r,F,M,N)      (MACRO) matrix of polynomials over number field 
			product 
mapnfsmul(r,F,M,el)     matrix of polynomials over number field scalar 
			multiplication 
mapnfsum(r,F,M,N)       (MACRO) matrix of polynomials over number field sum 
mapnftomapmp(r,F,P,M)   matrix of polynomials over number field to matrix 
			of polynomials modulo polynomial over number field 
mapnftomapr(r,M)        matrix of polynomials over number field to matrix 
			of polynomials over rationals 
mapnftransf(r1,F,M1,V1,r2,P2,V2,Vn,pV3) matrix of polynomials over number 
			field transformation 
mapnfvecmul(r,F,A,x)    (MACRO) matrix of polynomials over number field 
			vector multiplication 
maprchpol(r,M)          (MACRO) matrix of polynomials over rationals 
			characteristic polynomial 
maprcons1(r,n)          (MACRO) matrix of polynomials over rationals 
			construction 1 
maprdet(r,M)            matrix of polynomials over rationals determinant 
maprdif(r,M,N)          (MACRO) matrix of polynomials over rationals 
			difference 
maprexp(r,M,n)          matrix of polynomials over rationals exponentiation 
maprinv(r,M)            matrix of polynomials over rationals inverse 
maprneg(r,M)            (MACRO) matrix of polynomials over rationals 
			negation 
maprnfevlfvs(r,F,M)     matrix of polynomials over rationals number field 
			element evaluation first variable special version 
maprod(M,N,prod,sum,anzahlargs,arg1,arg2) matrix product 
maprodspec(M,N,prod,sum,anzahlargs,arg1,...,arg5) matrix product special 
maprprod(r,M,N)         (MACRO) matrix of polynomials over rationals 
			product 
maprsmul(r,M,P)         matrix of polynomials over rationals scalar 
			multiplication 
maprsum(r,M,N)          (MACRO) matrix of polynomials over rationals sum 
maprtomapmi(r,M,m)      matrix of polynomials over rationals to matrix of 
			polynomials over modular integers 
maprtomapnf(r,M)        matrix of polynomials over rationals to matrix of 
			polynomials over number field 
maprtomarfr(r,M)        matrix of polynomials over rationals to matrix of 
			rational functions over rationals 
maprtompmpr(r,M,P)      matrix of polynomials over rationals to matrix of 
			polynomials modulo polynomial over rationals 
maprtransf(r1,M1,V1,r2,P2,V2,Vn,pV3) matrix of polynomials over the 
			rationals transformation 
maprvecmul(r,A,x)       (MACRO) matrix of polynomials over rationals vector 
			multiplication 
maptomadp(r,M)          matrix of polynomials to matrix of dense 
			polynomials 
maptomaup(r,M)          matrix of polynomials to matrix of univariate 
			polynomials 
marchpol(M)             (MACRO) matrix of rationals characteristic 
			polynomial 
marcons1(n)             (MACRO) matrix of rationals construction 1 
mardet(M)               matrix of rationals determinant 
mardif(M,N)             (MACRO) matrix of rationals difference 
marev(M)                (MACRO) matrix of rationals eigenvalues 
marevifcp(M,*pL)        matrix of rationals eigenvalues and irreducible 
			factors of the characteristic polynomial 
marexp(M,n)             matrix of rationals exponentiation 
marfmsp1c1(p,n)         (MACRO) matrix of rational functions over modular 
			single primes, transcendence degree 1, construction 
			1 
marfmsp1det(p,M)        matrix of rational functions over modular single 
			primes transcendence degree 1, determinant 
marfmsp1dif(p,M,N)      (MACRO) matrix of rational functions over modular 
			single primes transcendence degree 1, difference 
marfmsp1exp(p,M,n)      matrix of rational functions over modular single 
			primes, transcendence degree 1, exponentiation 
marfmsp1inv(p,M)        matrix of rational functions over modular single 
			primes, transcendence degree 1, inverse 
marfmsp1neg(p,M)        (MACRO) matrix of rational functions over modular 
			single primes, transcendence degree 1, negation 
marfmsp1nsb(p,M)        matrix of rational functions over modular single 
			primes, transcendence degree 1, null space basis 
marfmsp1prod(p,M,N)     (MACRO) matrix of rational functions over modular 
			single primes, transcendence degree 1, product 
marfmsp1rk(p,M)         matrix of rational functions over modular single 
			primes, transcendence degree 1, rank 
marfmsp1smul(p,M,F)     matrix of rational functions over modular single 
			primes, transcendence degree 1, scalar 
			multiplication 
marfmsp1ssle(p,A,b,pX,pN) matrix of rational functions over modular single 
			primes, transcendence degree 1, solution of a 
			system of linear equations 
marfmsp1sum(p,M,N)      (MACRO) matrix of rational functions over modular 
			single primes, transcendence degree 1, sum 
marfmsp1vmul(p,A,x)     (MACRO) matrix of rational functions over modular 
			single primes, transcendence degree 1, vector 
			multiplication 
marfrchpol(r,M)         matrix of rational functions over rationals 
			characteristic polynomial 
marfrcons1(r,n)         (MACRO) matrix of rational functions over rationals 
			construction 1 
marfrdet(r,M)           matrix of rational functions over rationals 
			determinant 
marfrdif(r,M,N)         (MACRO) matrix of rational functions over rationals 
			difference 
marfrexp(r,M,n)         matrix of rational functions over rationals 
			exponentiation 
marfrinv(r,M)           matrix of rational functions over rationals inverse 
marfrneg(r,M)           (MACRO) matrix of rational functions over rationals 
			negation 
marfrnsb(r,M)           matrix of rational functions over rationals, null 
			space basis 
marfrprod(r,M,N)        (MACRO) matrix of rational functions over rationals 
			product 
marfrrk(r,M)            matrix of rational functions over rationals rank 
marfrsmul(r,M,F)        matrix of rational functions over rationals scalar 
			multiplication 
marfrssle(r,A,b,pX,pN)  matrix of rational functions over rationals 
			solution of a system of linear equations 
marfrsum(r,M,N)         (MACRO) matrix of rational functions over rationals 
			sum 
marfrtransf(r1,M1,V1,r2,R2,V2,Vn,pV3) matrix of rational functions over the 
			rationals transformation 
marfrvecmul(r,A,x)      (MACRO) matrix of rational functions over rationals 
			vector multiplication 
marinv(M)               matrix of rationals inverse 
marlllred(bas)          matrix of rationals, LLL reduction 
marneg(M)               (MACRO) matrix of rationals negation 
marnsb(M)               matrix of rationals null space basis 
marprod(M,N)            (MACRO) matrix of rationals product 
marrk(M)                matrix of rationals rank 
marsmul(M,el)           matrix of rationals scalar multiplication 
marssle(A,b,pX,pN)      matrix of rationals solution of a system of linear 
			equations 
marsum(M,N)             (MACRO) matrix of rationals sum 
martomami(m,M)          matrix of rationals to matrix of modular integers 
martomanf(M)            matrix of rationals to matrix of number field 
			elements 
martomanfs(M)           matrix of rationals to matrix of number field 
			elements, sparse representation 
martomapr(r,M)          matrix of rationals to matrix of polynomials over 
			rationals 
marvecmul(A,x)          (MACRO) matrix of rationals vector multiplication 
maselel(M,m,n)          (MACRO) matrix select element 
masetel(M,m,n,el)       (MACRO) matrix set element 
masrand(m,n,grenze)     matrix of singles randomize 
masum(M,N,sum,anzahlargs,arg1,arg2) matrix sum 
masumspec(M,N,sum,anzahlargs,arg1,...,arg5) matrix sum special 
matransp(M)             matrix transpose 
matrix                  ? isma(M) is 
matrix                  adjoin matrix maam(M,el) 
matrix                  characteristic polynomial 
			machpol(M,det,minusEins,anzahlargs,arg1,arg2) 
matrix                  characteristic polynomial special 
			machpolspec(M,det,minusEins,anzahlargs,arg1,...,arg5) 
matrix                  concatenation maconc(M,N) 
matrix                  construction diagonal-matrix maconsdiag(n,el) 
matrix                  construction zero maconszero(m,n) 
matrix                  constructive concatenation macconc(M,N) 
matrix                  constructive transpose mactransp(M) 
matrix                  copy macopy(M) 
matrix                  delete 1 row and 1 column madel1rc(pM,i,j) 
matrix                  delete several columns madelsc(pM,I) 
matrix                  delete several rows and columns madelsrc(pM,I,J) 
			(MACRO) 
matrix                  delete several rows madelsr(pM,I) 
matrix                  fgetma(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) file 
			get 
matrix                  fputma(M,pf,fputfkt,anzahlargs,arg1,arg2,arg3) file 
			put 
matrix                  line nfeltomaln(n,a) number field element to 
matrix                  maam(M,el) matrix adjoin 
matrix                  negation maneg(M,neg,anzahlargs,arg1,arg2) 
matrix                  negation special 
			manegspec(M,neg,anzahlargs,arg1,...,arg5) 
matrix                  number of columns manrcol(M) (MACRO) 
matrix                  number of rows manrrow(M) (MACRO) 
matrix                  of Galois-field with single characteristic elements 
			? ismagfs(p,AL,M) (MACRO) is 
matrix                  of Galois-field with single characteristic elements 
			characteristic polynomial magfschpol(p,AL,M) 
			(MACRO) 
matrix                  of Galois-field with single characteristic elements 
			construction 1 magfscons1(p,AL,n) (MACRO) 
matrix                  of Galois-field with single characteristic elements 
			determinant magfsdet(p,AL,M) 
matrix                  of Galois-field with single characteristic elements 
			difference magfsdif(p,AL,M,N) (MACRO) 
matrix                  of Galois-field with single characteristic elements 
			exponentiation magfsexp(p,AL,M,n) 
matrix                  of Galois-field with single characteristic elements 
			fgetmagfs(p,AL,V,pf) (MACRO) file get 
matrix                  of Galois-field with single characteristic elements 
			fputmagfs(p,AL,M,V,pf) (MACRO) file put 
matrix                  of Galois-field with single characteristic elements 
			getmagfs(p,AL,V) (MACRO) get 
matrix                  of Galois-field with single characteristic elements 
			inverse magfsinv(p,AL,M) 
matrix                  of Galois-field with single characteristic elements 
			negation magfsneg(p,AL,M) (MACRO) 
matrix                  of Galois-field with single characteristic elements 
			product magfsprod(p,AL,M,N) (MACRO) 
matrix                  of Galois-field with single characteristic elements 
			putmagfs(p,AL,M,V) (MACRO) put 
matrix                  of Galois-field with single characteristic elements 
			rank magfsrk(p,AL,M) 
matrix                  of Galois-field with single characteristic elements 
			scalar multiplication magfssmul(p,AL,M,el) 
matrix                  of Galois-field with single characteristic elements 
			solution of a system of linear equations 
			magfsssle(p,AL,A,b,pX,pN) 
matrix                  of Galois-field with single characteristic elements 
			sum magfssum(p,AL,M,N) (MACRO) 
matrix                  of Galois-field with single characteristic elements 
			vector multiplication magfsvecmul(p,AL,A,x) (MACRO) 
matrix                  of Galois-field with single characteristic 
			elements, null space basis magfsnsb(p,AL,M) 
matrix                  of ____ ? isma_(M,is,anzahlargs,arg1,arg2) is 
matrix                  of ____, special ? 
			ismaspec_(M,is,anzahlargs,arg1,...,arg5) is 
matrix                  of coefficients of univariate polynomials 
			macup(n,L) 
matrix                  of dense polynomials ? ismadp(r,M) (MACRO) is 
matrix                  of dense polynomials maptomadp(r,M) matrix of 
			polynomials to 
matrix                  of dense polynomials over integers ? ismadpi(r,M) 
			(MACRO) is 
matrix                  of dense polynomials over modular singles ? 
			ismadpms(r,m,M) (MACRO) is 
matrix                  of dense polynomials over rationals ? ismadpr(r,M) 
			(MACRO) is 
matrix                  of dense polynomials to matrix of polynomials 
			madptomap(r,M) 
matrix                  of equal elements ismaeqel(M,el) is 
matrix                  of floatings by fix point fputmaflfx(M,v,n,pf) file 
			put 
matrix                  of floatings by fix point putmaflfx(M,v,n) (MACRO) 
			put 
matrix                  of floatings determinant mafldet(M) 
matrix                  of integers ? ismai(M) (MACRO) is 
matrix                  of integers Euklid- Gauss- step for columns 
			maiegsc(M,A,B) 
matrix                  of integers Euklid- Gauss- step for rows 
			maiegsr(M,A,B) 
matrix                  of integers Hermite normal form ( lower triangular 
			form with negative entries ) maihermltne(A) (MACRO) 
matrix                  of integers Hermite normal form ( lower triangular 
			form with positive entries ) maihermltpe(A) (MACRO) 
matrix                  of integers Hermite normal form maiherm(A,ne) 
matrix                  of integers characteristic polynomial maichpol(M) 
			(MACRO) 
matrix                  of integers construction 1 maicons1(n) (MACRO) 
matrix                  of integers determinant maidet(M) 
matrix                  of integers difference maidif(M,N) (MACRO) 
matrix                  of integers eigenvalues and irreducible factors of 
			the characteristic polynomial maievifcp(M,pL) 
matrix                  of integers eigenvalues maiev(M) (MACRO) 
matrix                  of integers elementary divisor form and cofactors 
			maiedfcf(M,pA,pB) 
matrix                  of integers exponentiation maiexp(M,n) 
matrix                  of integers fgetmai(pf) (MACRO) file get 
matrix                  of integers fputmai(M,pf) (MACRO) file put 
matrix                  of integers getmai() (MACRO) get 
matrix                  of integers hermitian reduction, special 
			maihermspec(M,r,pD) 
matrix                  of integers inverse maiinv(M) 
matrix                  of integers negation maineg(M) (MACRO) 
matrix                  of integers product maiprod(M,N) (MACRO) 
matrix                  of integers putmai(M) (MACRO) put 
matrix                  of integers scalar multiplication maismul(M,el) 
matrix                  of integers sum maisum(M,N) (MACRO) 
matrix                  of integers to matrix of modular integers 
			maitomami(m,M) 
matrix                  of integers to matrix of modular singles 
			maitomams(m,M) 
matrix                  of integers to matrix of number field elements 
			maitomanf(M) 
matrix                  of integers to matrix of number field elements, 
			sparse representation maitomanfs(M) 
matrix                  of integers to matrix of polynomials over integers 
			maitomapi(r,M) 
matrix                  of integers to matrix of rationals maitomar(M) 
matrix                  of integers to matrix of rationals mapitomapr(r,M) 
matrix                  of integers trace maitrace(M) 
matrix                  of integers vector multiplication maivecmul(A,x) 
			(MACRO) 
matrix                  of modular integers ? ismami(m,M) (MACRO) is 
matrix                  of modular integers characteristic polynomial 
			mamichpol(m,M) (MACRO) 
matrix                  of modular integers construction 1 mamicons1(m,n) 
			(MACRO) 
matrix                  of modular integers determinant mamidet(m,M) 
matrix                  of modular integers difference mamidif(m,M,N) 
			(MACRO) 
matrix                  of modular integers eigenvalues and irreducible 
			factors of the characteristic polynomial 
			mamievifcp(p,M,pL) 
matrix                  of modular integers eigenvalues mamiev(p,M) (MACRO) 
matrix                  of modular integers exponentiation mamiexp(m,M,n) 
matrix                  of modular integers fgetmami(m,pf) (MACRO) file get 
matrix                  of modular integers fputmami(m,M,pf) (MACRO) file 
			put 
matrix                  of modular integers getmami(m) (MACRO) get 
matrix                  of modular integers inverse mamiinv(m,M) 
matrix                  of modular integers maitomami(m,M) matrix of 
			integers to 
matrix                  of modular integers martomami(m,M) matrix of 
			rationals to 
matrix                  of modular integers negation mamineg(m,M) (MACRO) 
matrix                  of modular integers product mamiprod(m,M,N) (MACRO) 
matrix                  of modular integers putmami(m,M) (MACRO) put 
matrix                  of modular integers scalar multiplication 
			mamismul(m,M,el) 
matrix                  of modular integers sum mamisum(m,M,N) (MACRO) 
matrix                  of modular integers vector multiplication 
			mamivecmul(m,A,x) (MACRO) 
matrix                  of modular integers, null space basis maminsb(P,M) 
matrix                  of modular singles ? ismams(m,M) (MACRO) is 
matrix                  of modular singles characteristic polynomial 
			mamschpol(m,M) (MACRO) 
matrix                  of modular singles construction 1 mamscons1(m,n) 
			(MACRO) 
matrix                  of modular singles determinant mamsdet(m,M) 
matrix                  of modular singles difference mamsdif(m,M,N) 
			(MACRO) 
matrix                  of modular singles eigenvalues and irreducible 
			factors of the characteristic polynomial 
			mamsevifcp(p,M,pL) 
matrix                  of modular singles eigenvalues mamsev(p,M) (MACRO) 
matrix                  of modular singles exponentiation mamsexp(m,M,n) 
matrix                  of modular singles fgetmams(m,pf) (MACRO) file get 
matrix                  of modular singles fputmams(m,M,pf) (MACRO) file 
			put 
matrix                  of modular singles getmams(m) (MACRO) get 
matrix                  of modular singles inverse mamsinv(m,M) 
matrix                  of modular singles maitomams(m,M) matrix of 
			integers to 
matrix                  of modular singles negation mamsneg(m,M) (MACRO) 
matrix                  of modular singles null space basis mamsnsb(p,A) 
			(MACRO) 
matrix                  of modular singles product mamsprod(m,M,N) (MACRO) 
matrix                  of modular singles putmams(m,M) (MACRO) put 
matrix                  of modular singles scalar multiplication 
			mamssmul(m,M,el) 
matrix                  of modular singles solution of a system of linear 
			equations mamsssle(p,A,b,pX,pN) 
matrix                  of modular singles sum mamssum(m,M,N) (MACRO) 
matrix                  of modular singles vector multiplication 
			mamsvecmul(m,A,x) (MACRO) 
matrix                  of number field elements ? ismanf(F,M) (MACRO) is 
matrix                  of number field elements characteristic polynomial 
			manfchpol(F,M) (MACRO) 
matrix                  of number field elements construction 1 
			manfcons1(F,n) (MACRO) 
matrix                  of number field elements determinant manfdet(F,M) 
matrix                  of number field elements difference manfdif(F,M,N) 
			(MACRO) 
matrix                  of number field elements exponentiation 
			manfexp(F,M,n) 
matrix                  of number field elements fgetmanf(F,VL,pf) (MACRO) 
			file get 
matrix                  of number field elements fputmanf(F,M,VL,pf) 
			(MACRO) file put 
matrix                  of number field elements getmanf(F,VL) (MACRO) get 
matrix                  of number field elements inverse manfinv(F,M) 
matrix                  of number field elements maitomanf(M) matrix of 
			integers to 
matrix                  of number field elements martomanf(M) matrix of 
			rationals to 
matrix                  of number field elements maudprtomnf(M) matrix of 
			univariate dense polynomials over rationals to 
matrix                  of number field elements negation manfneg(F,M) 
			(MACRO) 
matrix                  of number field elements null space basis 
			manfnsb(F,M) 
matrix                  of number field elements product manfprod(F,M,N) 
			(MACRO) 
matrix                  of number field elements putmanf(F,M,VL) (MACRO) 
			put 
matrix                  of number field elements rank manfrk(F,M) 
matrix                  of number field elements scalar multiplication 
			manfsmul(F,M,el) 
matrix                  of number field elements solution of a system of 
			linear equations manfssle(F,A,b,pX,pN) 
matrix                  of number field elements sum manfsum(F,M,N) (MACRO) 
matrix                  of number field elements to matrix of univariate 
			dense polynomials over rationals manftomudpr(F,M) 
matrix                  of number field elements vector multiplication 
			manfvecmul(F,A,x) (MACRO) 
matrix                  of number field elements, sparse representation ? 
			ismanfs(F,M) (MACRO) is 
matrix                  of number field elements, sparse representation 
			fgetmanfs(F,VL,pf) (MACRO) file get 
matrix                  of number field elements, sparse representation 
			fputmanfs(F,M,VL,pf) (MACRO) file put 
matrix                  of number field elements, sparse representation 
			getmanfs(F,VL) (MACRO) get 
matrix                  of number field elements, sparse representation 
			maitomanfs(M) matrix of integers to 
matrix                  of number field elements, sparse representation 
			martomanfs(M) matrix of rationals to 
matrix                  of number field elements, sparse representation 
			putmanfs(F,M,VL) (MACRO) put 
matrix                  of number field elements, sparse representation, 
			construction 1 manfscons1(F,n) (MACRO) 
matrix                  of number field elements, sparse representation, 
			determinant manfsdet(F,M) 
matrix                  of number field elements, sparse representation, 
			difference manfsdif(F,M,N) (MACRO) 
matrix                  of number field elements, sparse representation, 
			exponentiation manfsexp(F,M,n) 
matrix                  of number field elements, sparse representation, 
			inverse manfsinv(F,M) 
matrix                  of number field elements, sparse representation, 
			negation manfsneg(F,M) (MACRO) 
matrix                  of number field elements, sparse representation, 
			null space basis manfsnsb(F,M) 
matrix                  of number field elements, sparse representation, 
			product manfsprod(F,M,N) (MACRO) 
matrix                  of number field elements, sparse representation, 
			rank manfsrk(F,M) 
matrix                  of number field elements, sparse representation, 
			scalar multiplication manfssmul(F,M,el) 
matrix                  of number field elements, sparse representation, 
			solution of a system of linear equations 
			manfsssle(F,A,b,pX,pN) 
matrix                  of number field elements, sparse representation, 
			sum manfssum(F,M,N) (MACRO) 
matrix                  of number field elements, sparse representation, 
			vector multiplication manfsvecmul(F,A,x) (MACRO) 
matrix                  of polynomials ? ismap(r,M) (MACRO) is 
matrix                  of polynomials madptomap(r,M) matrix of dense 
			polynomials to 
matrix                  of polynomials modulo polynomial over Galois-field 
			with single characteristic mpgfstompmp(r,p,AL,P,M) 
			matrix of polynomials over Galois-field with single 
			characteristic to 
matrix                  of polynomials modulo polynomial over integers 
			mapitompmpi(r,M,P) matrix of polynomials over 
			integers to 
matrix                  of polynomials modulo polynomial over modular 
			integers mapmitomapmp(r,m,P,M) matrix of 
			polynomials over modular integers to 
matrix                  of polynomials modulo polynomial over modular 
			singles mapmstomapmp(r,m,P,M) matrix of polynomials 
			over modular singles to 
matrix                  of polynomials modulo polynomial over number field 
			mapnftomapmp(r,F,P,M) matrix of polynomials over 
			number field to 
matrix                  of polynomials modulo polynomial over rationals 
			maprtompmpr(r,M,P) matrix of polynomials over 
			rationals to 
matrix                  of polynomials over Galois-field with single 
			characteristic ? ismapgfs(r,p,AL,M) (MACRO) is 
matrix                  of polynomials over Galois-field with single 
			characteristic characteristic polynomial 
			mapgfschpol(r,p,AL,M) (MACRO) 
matrix                  of polynomials over Galois-field with single 
			characteristic construction 1 mapgfscons1(r,p,AL,n) 
			(MACRO) 
matrix                  of polynomials over Galois-field with single 
			characteristic determinant mapgfsdet(r,p,AL,M) 
matrix                  of polynomials over Galois-field with single 
			characteristic difference mapgfsdif(r,p,AL,M,N) 
			(MACRO) 
matrix                  of polynomials over Galois-field with single 
			characteristic exponentiation mapgfsexp(r,p,AL,M,n) 
matrix                  of polynomials over Galois-field with single 
			characteristic fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) 
			file get 
matrix                  of polynomials over Galois-field with single 
			characteristic fputmapgfs(r,p,AL,M,V,Vgfs,pf) 
			(MACRO) file put 
matrix                  of polynomials over Galois-field with single 
			characteristic getmapgfs(r,p,AL,V,Vgfs) (MACRO) get 
matrix                  of polynomials over Galois-field with single 
			characteristic inverse mapgfsinv(r,p,AL,M) 
matrix                  of polynomials over Galois-field with single 
			characteristic mpmstompgfs(r,p,M) matrix of 
			polynomials over modular singles to 
matrix                  of polynomials over Galois-field with single 
			characteristic negation mapgfsneg(r,p,AL,M) (MACRO) 
matrix                  of polynomials over Galois-field with single 
			characteristic product mapgfsprod(r,p,AL,M,N) 
			(MACRO) 
matrix                  of polynomials over Galois-field with single 
			characteristic putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) 
			put 
matrix                  of polynomials over Galois-field with single 
			characteristic scalar multiplication 
			mapgfssmul(r,p,AL,M,el) 
matrix                  of polynomials over Galois-field with single 
			characteristic sum mapgfssum(r,p,AL,M,N) (MACRO) 
matrix                  of polynomials over Galois-field with single 
			characteristic to matrix of polynomials modulo 
			polynomial over Galois-field with single 
			characteristic mpgfstompmp(r,p,AL,P,M) 
matrix                  of polynomials over Galois-field with single 
			characteristic transformation 
			mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) 
matrix                  of polynomials over Galois-field with single 
			characteristic vector multiplication 
			mapgfsvmul(r,p,AL,A,x) (MACRO) 
matrix                  of polynomials over integers ? ismapi(r,M) (MACRO) 
			is 
matrix                  of polynomials over integers characteristic 
			polynomial mapichpol(r,M) (MACRO) 
matrix                  of polynomials over integers construction 1 
			mapicons1(r,n) (MACRO) 
matrix                  of polynomials over integers determinant 
			mapidet(r,M) 
matrix                  of polynomials over integers difference 
			mapidif(r,M,N) (MACRO) 
matrix                  of polynomials over integers exponentiation 
			mapiexp(r,M,n) 
matrix                  of polynomials over integers fgetmapi(r,V,pf) 
			(MACRO) file get 
matrix                  of polynomials over integers fputmapi(r,M,V,pf) 
			(MACRO) file put 
matrix                  of polynomials over integers getmapi(r,V) (MACRO) 
			get 
matrix                  of polynomials over integers inverse mapiinv(r,M) 
matrix                  of polynomials over integers maitomapi(r,M) matrix 
			of integers to 
matrix                  of polynomials over integers negation mapineg(r,M) 
			(MACRO) 
matrix                  of polynomials over integers number field element 
			evaluation first variable special version 
			mapinfevlfvs(r,F,M) 
matrix                  of polynomials over integers product 
			mapiprod(r,M,N) (MACRO) 
matrix                  of polynomials over integers putmapi(r,M,V) (MACRO) 
			put 
matrix                  of polynomials over integers scalar multiplication 
			mapismul(r,M,P) 
matrix                  of polynomials over integers sum mapisum(r,M,N) 
			(MACRO) 
matrix                  of polynomials over integers to matrix of 
			polynomials modulo polynomial over integers 
			mapitompmpi(r,M,P) 
matrix                  of polynomials over integers to matrix of 
			polynomials over modular integers 
			mapitomapmi(r,M,m) 
matrix                  of polynomials over integers to matrix of 
			polynomials over modular singles mapitomapms(r,M,m) 
matrix                  of polynomials over integers to matrix of 
			polynomials over number field mapitomapnf(r,M) 
matrix                  of polynomials over integers to matrix of rational 
			functions over rationals mapitomarfr(r,M) 
matrix                  of polynomials over integers vector multiplication 
			mapivecmul(r,A,x) (MACRO) 
matrix                  of polynomials over modular integers ? 
			ismapmi(r,m,M) (MACRO) is 
matrix                  of polynomials over modular integers characteristic 
			polynomial mapmichpol(r,m,M) (MACRO) 
matrix                  of polynomials over modular integers construction 1 
			mapmicons1(r,m,n) (MACRO) 
matrix                  of polynomials over modular integers determinant 
			mapmidet(r,m,M) 
matrix                  of polynomials over modular integers difference 
			mapmidif(r,m,M,N) (MACRO) 
matrix                  of polynomials over modular integers exponentiation 
			mapmiexp(r,m,M,n) 
matrix                  of polynomials over modular integers 
			fgetmapmi(r,m,V,pf) (MACRO) file get 
matrix                  of polynomials over modular integers 
			fputmapmi(r,m,M,V,pf) (MACRO) file put 
matrix                  of polynomials over modular integers 
			getmapmi(r,m,V) (MACRO) get 
matrix                  of polynomials over modular integers inverse 
			mapmiinv(r,m,M) 
matrix                  of polynomials over modular integers 
			mapitomapmi(r,M,m) matrix of polynomials over 
			integers to 
matrix                  of polynomials over modular integers 
			maprtomapmi(r,M,m) matrix of polynomials over 
			rationals to 
matrix                  of polynomials over modular integers negation 
			mapmineg(r,m,M) (MACRO) 
matrix                  of polynomials over modular integers product 
			mapmiprod(r,m,M,N) (MACRO) 
matrix                  of polynomials over modular integers 
			putmapmi(r,m,M,V) (MACRO) put 
matrix                  of polynomials over modular integers scalar 
			multiplication mapmismul(r,m,M,P) 
matrix                  of polynomials over modular integers sum 
			mapmisum(r,m,M,N) (MACRO) 
matrix                  of polynomials over modular integers to matrix of 
			polynomials modulo polynomial over modular integers 
			mapmitomapmp(r,m,P,M) 
matrix                  of polynomials over modular integers transformation 
			mapmitransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) 
matrix                  of polynomials over modular integers vector 
			multiplication mapmivecmul(r,m,A,x) (MACRO) 
matrix                  of polynomials over modular singles ? 
			ismapms(r,m,M) (MACRO) is 
matrix                  of polynomials over modular singles characteristic 
			polynomial mapmschpol(r,m,M) (MACRO) 
matrix                  of polynomials over modular singles construction 1 
			mapmscons1(r,m,n) (MACRO) 
matrix                  of polynomials over modular singles determinant 
			mapmsdet(r,m,M) 
matrix                  of polynomials over modular singles difference 
			mapmsdif(r,m,M,N) (MACRO) 
matrix                  of polynomials over modular singles exponentiation 
			mapmsexp(r,m,M,n) 
matrix                  of polynomials over modular singles 
			fgetmapms(r,m,V,pf) (MACRO) file get 
matrix                  of polynomials over modular singles 
			fputmapms(r,m,M,V,pf) (MACRO) file put 
matrix                  of polynomials over modular singles getmapms(r,m,V) 
			(MACRO) get 
matrix                  of polynomials over modular singles inverse 
			mapmsinv(r,m,M) 
matrix                  of polynomials over modular singles 
			mapitomapms(r,M,m) matrix of polynomials over 
			integers to 
matrix                  of polynomials over modular singles negation 
			mapmsneg(r,m,M) (MACRO) 
matrix                  of polynomials over modular singles product 
			mapmsprod(r,m,M,N) (MACRO) 
matrix                  of polynomials over modular singles 
			putmapms(r,m,M,V) (MACRO) put 
matrix                  of polynomials over modular singles scalar 
			multiplication mapmssmul(r,m,M,P) 
matrix                  of polynomials over modular singles sum 
			mapmssum(r,m,M,N) (MACRO) 
matrix                  of polynomials over modular singles to matrix of 
			polynomials modulo polynomial over modular singles 
			mapmstomapmp(r,m,P,M) 
matrix                  of polynomials over modular singles to matrix of 
			polynomials over Galois-field with single 
			characteristic mpmstompgfs(r,p,M) 
matrix                  of polynomials over modular singles to matrix of 
			rational functions over modular single primes, 
			transcendence degree 1 mpmstmrfmsp1(p,M) 
matrix                  of polynomials over modular singles transformation 
			mapmstransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) 
matrix                  of polynomials over modular singles vector 
			multiplication mapmsvecmul(r,m,A,x) (MACRO) 
matrix                  of polynomials over number field characteristic 
			polynomial mapnfchpol(r,F,M) (MACRO) 
matrix                  of polynomials over number field construction 1 
			mapnfcons1(r,F,n) (MACRO) 
matrix                  of polynomials over number field determinant 
			mapnfdet(r,F,M) 
matrix                  of polynomials over number field difference 
			mapnfdif(r,F,M,N) (MACRO) 
matrix                  of polynomials over number field exponentiation 
			mapnfexp(r,F,M,n) 
matrix                  of polynomials over number field 
			fgetmapnf(r,F,V,Vnf,pf) (MACRO) file get 
matrix                  of polynomials over number field 
			fputmapnf(r,F,M,V,Vnf,pf) (MACRO) file put 
matrix                  of polynomials over number field 
			getmapnf(r,F,V,Vnf) (MACRO) get 
matrix                  of polynomials over number field inverse 
			mapnfinv(r,F,M) 
matrix                  of polynomials over number field mapitomapnf(r,M) 
			matrix of polynomials over integers to 
matrix                  of polynomials over number field maprtomapnf(r,M) 
			matrix of polynomials over rationals to 
matrix                  of polynomials over number field negation 
			mapnfneg(r,F,M) (MACRO) 
matrix                  of polynomials over number field product 
			mapnfprod(r,F,M,N) (MACRO) 
matrix                  of polynomials over number field 
			putmapnf(r,F,M,V,Vnf) (MACRO) put 
matrix                  of polynomials over number field scalar 
			multiplication mapnfsmul(r,F,M,el) 
matrix                  of polynomials over number field sum 
			mapnfsum(r,F,M,N) (MACRO) 
matrix                  of polynomials over number field to matrix of 
			polynomials modulo polynomial over number field 
			mapnftomapmp(r,F,P,M) 
matrix                  of polynomials over number field to matrix of 
			polynomials over rationals mapnftomapr(r,M) 
matrix                  of polynomials over number field transformation 
			mapnftransf(r1,F,M1,V1,r2,P2,V2,Vn,pV3) 
matrix                  of polynomials over number field vector 
			multiplication mapnfvecmul(r,F,A,x) (MACRO) 
matrix                  of polynomials over rationals ? ismapr(r,M) (MACRO) 
			is 
matrix                  of polynomials over rationals characteristic 
			polynomial maprchpol(r,M) (MACRO) 
matrix                  of polynomials over rationals construction 1 
			maprcons1(r,n) (MACRO) 
matrix                  of polynomials over rationals determinant 
			maprdet(r,M) 
matrix                  of polynomials over rationals difference 
			maprdif(r,M,N) (MACRO) 
matrix                  of polynomials over rationals exponentiation 
			maprexp(r,M,n) 
matrix                  of polynomials over rationals fgetmapr(r,V,pf) 
			(MACRO) file get 
matrix                  of polynomials over rationals fputmapr(r,M,V,pf) 
			(MACRO) file put 
matrix                  of polynomials over rationals getmapr(r,V) (MACRO) 
			get 
matrix                  of polynomials over rationals inverse maprinv(r,M) 
matrix                  of polynomials over rationals mapnftomapr(r,M) 
			matrix of polynomials over number field to 
matrix                  of polynomials over rationals martomapr(r,M) matrix 
			of rationals to 
matrix                  of polynomials over rationals negation maprneg(r,M) 
			(MACRO) 
matrix                  of polynomials over rationals number field element 
			evaluation first variable special version 
			maprnfevlfvs(r,F,M) 
matrix                  of polynomials over rationals product 
			maprprod(r,M,N) (MACRO) 
matrix                  of polynomials over rationals putmapr(r,M,V) 
			(MACRO) put 
matrix                  of polynomials over rationals scalar multiplication 
			maprsmul(r,M,P) 
matrix                  of polynomials over rationals sum maprsum(r,M,N) 
			(MACRO) 
matrix                  of polynomials over rationals to matrix of 
			polynomials modulo polynomial over rationals 
			maprtompmpr(r,M,P) 
matrix                  of polynomials over rationals to matrix of 
			polynomials over modular integers 
			maprtomapmi(r,M,m) 
matrix                  of polynomials over rationals to matrix of 
			polynomials over number field maprtomapnf(r,M) 
matrix                  of polynomials over rationals to matrix of rational 
			functions over rationals maprtomarfr(r,M) 
matrix                  of polynomials over rationals vector multiplication 
			maprvecmul(r,A,x) (MACRO) 
matrix                  of polynomials over the integers transformation 
			mapitransf(r1,M1,V1,r2,P2,V2,Vn,pV3) 
matrix                  of polynomials over the rationals transformation 
			maprtransf(r1,M1,V1,r2,P2,V2,Vn,pV3) 
matrix                  of polynomials to matrix of dense polynomials 
			maptomadp(r,M) 
matrix                  of polynomials to matrix of univariate polynomials 
			maptomaup(r,M) 
matrix                  of polynomials variable permutation 
			mavpermut(r,M,PI) 
matrix                  of rational functions over modular single prime, 
			transcendence degree 1 cdprfmsp1lfm(M,p) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, list 
			from common denominator 
matrix                  of rational functions over modular single prime, 
			transcendence degree 1, hermitian reduction 
			cdmarfmsp1hr(p,M) common denominator 
matrix                  of rational functions over modular single prime, 
			transcendence degree 1, identity construction 
			cdmarfmsp1id(n) common denominator 
matrix                  of rational functions over modular single primes 
			transcendence degree 1, determinant 
			marfmsp1det(p,M) 
matrix                  of rational functions over modular single primes 
			transcendence degree 1, difference 
			marfmsp1dif(p,M,N) (MACRO) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1 ? ismarfmsp1(p,M) (MACRO) is 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1 fgetmarfmsp1(p,V,pf) (MACRO) 
			file get 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1 fputmarfmsp1(p,M,V,pf) 
			(MACRO) file put 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1 getmarfmsp1(p,V) (MACRO) get 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1 mpmstmrfmsp1(p,M) matrix of 
			polynomials over modular singles to 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1 putmarfmsp1(p,M,V) (MACRO) 
			put 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, construction 1 
			marfmsp1c1(p,n) (MACRO) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, exponentiation 
			marfmsp1exp(p,M,n) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, inverse marfmsp1inv(p,M) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, negation marfmsp1neg(p,M) 
			(MACRO) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, null space basis 
			marfmsp1nsb(p,M) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, product marfmsp1prod(p,M,N) 
			(MACRO) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, rank marfmsp1rk(p,M) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, scalar multiplication 
			marfmsp1smul(p,M,F) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, solution of a system of 
			linear equations marfmsp1ssle(p,A,b,pX,pN) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, sum marfmsp1sum(p,M,N) 
			(MACRO) 
matrix                  of rational functions over modular single primes, 
			transcendence degree 1, vector multiplication 
			marfmsp1vmul(p,A,x) (MACRO) 
matrix                  of rational functions over rationals ? ismarfr(r,M) 
			(MACRO) is 
matrix                  of rational functions over rationals characteristic 
			polynomial marfrchpol(r,M) 
matrix                  of rational functions over rationals construction 1 
			marfrcons1(r,n) (MACRO) 
matrix                  of rational functions over rationals determinant 
			marfrdet(r,M) 
matrix                  of rational functions over rationals difference 
			marfrdif(r,M,N) (MACRO) 
matrix                  of rational functions over rationals exponentiation 
			marfrexp(r,M,n) 
matrix                  of rational functions over rationals 
			fgetmarfr(r,V,pf) (MACRO) file get 
matrix                  of rational functions over rationals 
			fputmarfr(r,M,V,pf) (MACRO) file put 
matrix                  of rational functions over rationals getmarfr(r,V) 
			(MACRO) get 
matrix                  of rational functions over rationals inverse 
			marfrinv(r,M) 
matrix                  of rational functions over rationals 
			mapitomarfr(r,M) matrix of polynomials over 
			integers to 
matrix                  of rational functions over rationals 
			maprtomarfr(r,M) matrix of polynomials over 
			rationals to 
matrix                  of rational functions over rationals negation 
			marfrneg(r,M) (MACRO) 
matrix                  of rational functions over rationals product 
			marfrprod(r,M,N) (MACRO) 
matrix                  of rational functions over rationals 
			putmarfr(r,M,V) (MACRO) put 
matrix                  of rational functions over rationals rank 
			marfrrk(r,M) 
matrix                  of rational functions over rationals scalar 
			multiplication marfrsmul(r,M,F) 
matrix                  of rational functions over rationals solution of a 
			system of linear equations marfrssle(r,A,b,pX,pN) 
matrix                  of rational functions over rationals sum 
			marfrsum(r,M,N) (MACRO) 
matrix                  of rational functions over rationals vector 
			multiplication marfrvecmul(r,A,x) (MACRO) 
matrix                  of rational functions over rationals, null space 
			basis marfrnsb(r,M) 
matrix                  of rational functions over the rationals 
			transformation 
			marfrtransf(r1,M1,V1,r2,R2,V2,Vn,pV3) 
matrix                  of rationals ? ismar(M) (MACRO) is 
matrix                  of rationals cdprlfcdmar(M) common denominator 
			polynomial over the rationals list from common 
			denominator 
matrix                  of rationals characteristic polynomial marchpol(M) 
			(MACRO) 
matrix                  of rationals construction 1 marcons1(n) (MACRO) 
matrix                  of rationals determinant mardet(M) 
matrix                  of rationals difference mardif(M,N) (MACRO) 
matrix                  of rationals eigenvalues and irreducible factors of 
			the characteristic polynomial marevifcp(M,*pL) 
matrix                  of rationals eigenvalues marev(M) (MACRO) 
matrix                  of rationals exponentiation marexp(M,n) 
matrix                  of rationals fgetmar(pf) (MACRO) file get 
matrix                  of rationals fputmar(M,pf) (MACRO) file put 
matrix                  of rationals getmar() (MACRO) get 
matrix                  of rationals inverse marinv(M) 
matrix                  of rationals maitomar(M) matrix of integers to 
matrix                  of rationals mapitomapr(r,M) matrix of integers to 
matrix                  of rationals negation marneg(M) (MACRO) 
matrix                  of rationals null space basis marnsb(M) 
matrix                  of rationals product marprod(M,N) (MACRO) 
matrix                  of rationals putmar(M) (MACRO) put 
matrix                  of rationals rank marrk(M) 
matrix                  of rationals scalar multiplication marsmul(M,el) 
matrix                  of rationals solution of a system of linear 
			equations marssle(A,b,pX,pN) 
matrix                  of rationals sum marsum(M,N) (MACRO) 
matrix                  of rationals to matrix of modular integers 
			martomami(m,M) 
matrix                  of rationals to matrix of number field elements 
			martomanf(M) 
matrix                  of rationals to matrix of number field elements, 
			sparse representation martomanfs(M) 
matrix                  of rationals to matrix of polynomials over 
			rationals martomapr(r,M) 
matrix                  of rationals vector multiplication marvecmul(A,x) 
			(MACRO) 
matrix                  of rationals, LLL reduction marlllred(bas) 
matrix                  of rationals, hermitian reduction cdmarhermred(M) 
			common denominator 
matrix                  of rationals, identity construction cdmarid(n) 
			common denominator 
matrix                  of singles ? ismas(M) is 
matrix                  of singles fputmas(M) file put 
matrix                  of singles randomize masrand(m,n,grenze) 
matrix                  of univariate dense polynomials over integers to 
			matrix of univariate dense polynomials over modular 
			integers mudpitudpmi(M,m) 
matrix                  of univariate dense polynomials over integers to 
			matrix of univariate dense polynomials over 
			rationals mudpitmudpr(M) 
matrix                  of univariate dense polynomials over modular 
			integers mudpitudpmi(M,m) matrix of univariate 
			dense polynomials over integers to 
matrix                  of univariate dense polynomials over rationals 
			manftomudpr(F,M) matrix of number field elements to 
matrix                  of univariate dense polynomials over rationals 
			mudpitmudpr(M) matrix of univariate dense 
			polynomials over integers to 
matrix                  of univariate dense polynomials over rationals to 
			matrix of number field elements maudprtomnf(M) 
matrix                  of univariate polynomials maptomaup(r,M) matrix of 
			polynomials to 
matrix                  of univariate polynomials over modular integer 
			primes Euklid- Gauss- step for columns 
			maupmipegsc(p,M,A,B) 
matrix                  of univariate polynomials over modular integer 
			primes Euklid- Gauss- step for rows 
			maupmipegsr(p,M,A,B) 
matrix                  of univariate polynomials over modular integer 
			primes elementary divisor form and cofactors 
			maupmipedfcf(p,M,pA,pB) 
matrix                  of univariate polynomials over modular single 
			primes Euklid- Gauss- step for columns 
			maupmspegsc(p,M,A,B) 
matrix                  of univariate polynomials over modular single 
			primes Euklid- Gauss- step for rows 
			maupmspegsr(p,M,A,B) 
matrix                  of univariate polynomials over modular single 
			primes elementary divisor form and cofactors 
			maupmspedfcf(p,M,pA,pB) 
matrix                  of univariate polynomials over modular single 
			primes hermitian reduction, special 
			maupmshermsp(p,M,r,pD) 
matrix                  of univariate polynomials over rationals Euklid- 
			Gauss- step for columns maupregsc(M,A,B) 
matrix                  of univariate polynomials over rationals Euklid- 
			Gauss- step for rows maupregsr(M,A,B) 
matrix                  of univariate polynomials over rationals elementary 
			divisor form and cofactors maupredfcf(M,pA,pB) 
matrix                  over Galois-field with single characteristic 
			eigenvalues and irreducible factors of the 
			characteristic polynomial magfsevifcp(p,AL,M,pL) 
matrix                  over Galois-field with single characteristic 
			embedding in field extension magfsefe(p,ALm,M,g) 
matrix                  over Galois-field with single characteristic 
			maitomagfs(p,M) matrix over integers to 
matrix                  over integers to matrix over Galois-field with 
			single characteristic maitomagfs(p,M) 
matrix                  over polynomials over Galois-field with single 
			characteristic embedding in field extension 
			mapgfsefe(r,p,ALm,M,g) 
matrix                  over polynomials over integers Galois-field with 
			single characteristic element evaluation first 
			variable special version mapigfsevfvs(r,p,AL,M) 
matrix                  pidiscrhank(r,P) polynomial over integers 
			discriminant via Hankel- 
matrix                  pmidiscrhank(r,M,P) polynomial over modular 
			integers discriminant via Hankel 
matrix                  product maprod(M,N,prod,sum,anzahlargs,arg1,arg2) 
matrix                  product special 
			maprodspec(M,N,prod,sum,anzahlargs,arg1,...,arg5) 
matrix                  psylvester(r,P1,P2) polynomial Sylvester 
matrix                  select element maselel(M,m,n) (MACRO) 
matrix                  set element masetel(M,m,n,el) (MACRO) 
matrix                  special 
			fgetmaspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
			file get 
matrix                  special 
			fputmaspec(M,pf,fputfkt,anzahlargs,arg1,...,arg8) 
			file put 
matrix                  sum masum(M,N,sum,anzahlargs,arg1,arg2) 
matrix                  sum special 
			masumspec(M,N,sum,anzahlargs,arg1,...,arg5) 
matrix                  transpose matransp(M) 
matrix                  vector multiplication 
			mavecmul(A,x,prod,sum,anzahlargs,arg1,arg2) 
matrix                  vector multiplication special 
			mavmulspec(A,x,prod,sum,anzahlargs,arg1,...,arg5) 
maudprtomnf(M)          matrix of univariate dense polynomials over 
			rationals to matrix of number field elements 
maupmipedfcf(p,M,pA,pB) matrix of univariate polynomials over modular 
			integer primes elementary divisor form and 
			cofactors 
maupmipegsc(p,M,A,B)    matrix of univariate polynomials over modular 
			integer primes Euklid- Gauss- step for columns 
maupmipegsr(p,M,A,B)    matrix of univariate polynomials over modular 
			integer primes Euklid- Gauss- step for rows 
maupmshermsp(p,M,r,pD)  matrix of univariate polynomials over modular 
			single primes hermitian reduction, special 
maupmspedfcf(p,M,pA,pB) matrix of univariate polynomials over modular 
			single primes elementary divisor form and cofactors 
maupmspegsc(p,M,A,B)    matrix of univariate polynomials over modular 
			single primes Euklid- Gauss- step for columns 
maupmspegsr(p,M,A,B)    matrix of univariate polynomials over modular 
			single primes Euklid- Gauss- step for rows 
maupredfcf(M,pA,pB)     matrix of univariate polynomials over rationals 
			elementary divisor form and cofactors 
maupregsc(M,A,B)        matrix of univariate polynomials over rationals 
			Euklid- Gauss- step for columns 
maupregsr(M,A,B)        matrix of univariate polynomials over rationals 
			Euklid- Gauss- step for rows 
mavecmul(A,x,prod,sum,anzahlargs,arg1,arg2) matrix vector multiplication 
mavmulspec(A,x,prod,sum,anzahlargs,arg1,...,arg5) matrix vector 
			multiplication special 
mavpermut(r,M,PI)       matrix of polynomials variable permutation 
maximal                 over-order ouspibaslmo(F,p,Q,pk) order of an 
			univariate separable polynomial over the integers 
			basis of a local 
maximal                 over-order ouspprmsp1bl(p,F,P,Q,pk) order of an 
			univariate separable polynomial over polynomial 
			ring over modular single prime, transcendence 
			degree 1, basis of a local 
maximal                 over-order with respect to integer primes 
			ouspibaslmoi(F,P,Q,pk) order of an univariate 
			separable polynomial over the integers basis of a 
			local 
maximal                 power of 2 divisibility imp2d(A) integer 
maximality              test oupidedekmt(M,P) order of an univariate 
			polynomial over the integers, Dedekind 
maximality              test ouspprmsp1dm(p,P,F) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			Dedekind 
maximum                 imax(A,B) (MACRO) integer 
maximum                 lipairspmax(L) list of integer pairs power 
maximum                 norm (rekursiv) pimaxnorm(r,P) polynomial over 
			integers 
maximum                 rmax(R,S) (MACRO) rational number 
maximum                 smax(a,b) (MACRO) single-precision 
maximum                 special version lsmaxs(L1,L2) list of singles 
mean                    cagm(a,b) complex aritho-geometric 
mean                    flagm(a,b) floating point aritho-geometric 
medium                  prime divisor search impds(N,A,B,pP,pQ) integer 
medium                  single prime divisor search imspds(N,a,b) integer 
member                  lmemb(a,L) list 
membership              test dippipim(r1,r2,s,PL,PTL,CONDS,OPL) 
			distributive polynomial over polynomials over 
			integers parametric ideal 
membership              test fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers parametric ideal 
membership              test putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers parametric ideal 
memory                  management HDimem() Heidelberg arithmetic package: 
merge                   limerge(L1,L2) list of integers 
merge                   lsmerge(L1,L2) list of single precisions 
merge                   pvmerge(LV,LP,pLP) polynomial variable list 
merge                   sort lsbmsort(L) list of single precisions bubble 
message,                I/O-operations errmsgio(name,errno) error 
messages                isiprimemsg(n) (MACRO) is integer prime, printing 
method                  ( fast reduction ) by Pollard divisor search 
			rhofrpds(N,b,z) rho- 
method                  by Pollard divisor search ( lists only ) 
			rhopds_lo(N,b,z) rho- 
method                  by Pollard divisor search rhopds(N,b,z) rho- 
method                  ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) elliptic curve 
			over Galois-field with characteristic 2, finding a 
			multiple of the order of a point with the Pollard 
			Lambda 
method                  ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
			modular primes, short normal form, finding a 
			multiple of the order of a point with the Pollard 
			Lambda 
method                  ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular primes, short normal form, finding a 
			multiple of the order of a point with the Pollard 
			Rho 
method                  upgfsbfzm(p,AL,s,P,G) univariate polynomial over 
			Galois-field with single characteristic Berlekamp 
			factorization, Zassenhaus 
method                  upmibfzm(ip,s,P,G) univariate polynomial over 
			modular integers, Berlekamp factorization, 
			Zassenhaus 
method                  upmsbfzm(m,s,P,G) univariate polynomial over 
			modular singles, Berlekamp factorization, 
			Zassenhaus 
micra(M1,M2,N1,A1,A2)   modular integer chinese remainder algorithm 
micran(n,LM,LA)         modular integer chinese remainder algorithm, n 
			arguments (rekursiv) 
midif(M,A,B)            modular integer difference 
miexp(M,A,E)            modular integer exponentiation 
miexp_lo(M,A,E)         modular integer exponentiation ( lists only ) 
mihom(M,A)              modular integer homomorphism 
mihoms(M,A)             modular integer homomorphism, symmetric remainder 
			system 
miinv(M,A)              modular integer inverse 
miinv_lo(M,A)           modular integer inverse, lists only 
milcra(m1,m2,L1,L2)     modular integer list chinese remainder algorithm 
mineg(M,A)              (MACRO) modular integer negation 
minegf(M,A)             modular integer negation as function 
minimal                 model ( Laska's algorithm ) ecractoecimin(E) 
			elliptic curve over rational numbers, actual curve 
			to global 
minimal                 model ecisnfbtmin(E) elliptic curve with integer 
			coefficients, short normal form, birational 
			transformation to 
minimal                 model ecracbtmin(E) elliptic curve over the 
			rationals, actual curve, birational transformation 
			to 
minimal                 model fputecimin(E,pf) file put elliptic curve with 
			integer coefficients, 
minimal                 model isecimintorp(E,P) is torsion point on 
			elliptic curve with integer coefficients, 
minimal                 model isineciminpl(E,P,h,PL) is in list of points 
			on elliptic curve with integer coefficients, 
minimal                 model isponecimin(E,P) is point on elliptic curve 
			with integer coefficients, 
minimal                 model putecimin(E) (MACRO) put elliptic curve with 
			integer coefficients, 
minimal                 model to short normal form ecimintosnf(E) elliptic 
			curve with integer coefficients, 
minimal                 model, Mordell-Weil-group, base eciminmwgbase(E) 
			elliptic curve with integer coefficients, 
minimal                 model, Neron-Tate height eciminnetahe(E,P) elliptic 
			curve with integer coefficients, 
minimal                 model, Neron-Tate pairing eciminnetapa(E,P,Q) 
			elliptic curve with integer coefficients, 
minimal                 model, Tate's algorithm ecimintatealg(E,p,n) 
			elliptic curve with integer coefficients, 
minimal                 model, Tate's values c4, c6 
			ecitavalc(a1,a2,a3,a4,a6) elliptic curve with 
			integer coefficients, 
minimal                 model, a1 ecimina1(E) elliptic curve with integer 
			coefficients, 
minimal                 model, a2 ecimina2(E) elliptic curve with integer 
			coefficients, 
minimal                 model, a3 ecimina3(E) elliptic curve with integer 
			coefficients, 
minimal                 model, a4 ecimina4(E) elliptic curve with integer 
			coefficients, 
minimal                 model, a6 ecimina6(E) elliptic curve with integer 
			coefficients, 
minimal                 model, b2 eciminb2(E) elliptic curve with integer 
			coefficients, 
minimal                 model, b4 eciminb4(E) elliptic curve with integer 
			coefficients, 
minimal                 model, b6 eciminb6(E) elliptic curve with integer 
			coefficients, 
minimal                 model, b8 eciminb8(E) elliptic curve with integer 
			coefficients, 
minimal                 model, bad reduction type modulo prime 
			eciminbrtmp(E,p,n) elliptic curve with integer 
			coefficients, 
minimal                 model, birational transformation of coefficients 
			eciminbtco(E,BT) elliptic curve with integer 
			coefficients, 
minimal                 model, birational transformation to actual ( 
			rational ) model eciminbtac(E) elliptic curve with 
			integer coefficients, 
minimal                 model, birational transformation to short normal 
			form eciminbtsnf(E) elliptic curve with integer 
			coefficients, 
minimal                 model, c4 eciminc4(E) elliptic curve with integer 
			coefficients, 
minimal                 model, c6 eciminc6(E) elliptic curve with integer 
			coefficients, 
minimal                 model, difference between Weil height and 
			Neron-Tate height ecimindwhnth(E) elliptic curve 
			with integer coefficients, 
minimal                 model, difference of points ecimindif(E,P,Q) 
			elliptic curve with integer coefficients, 
minimal                 model, difference of points ecisnfdif(E,P,Q) 
			elliptic curve with integer coefficients, 
minimal                 model, discriminant ecimindisc(E) elliptic curve 
			with integer coefficients, 
minimal                 model, division by 2 of a point 
			ecimindivby2(E,P,h,PL,H) elliptic curve with 
			integer coefficients, 
minimal                 model, division of a point by an integer 
			ecimindiv(E,P,n) elliptic curve with integer 
			coefficients, 
minimal                 model, division of a point by an integer, special 
			version ecimindivs(E,P,h,ug,PL,n) elliptic curve 
			with integer coefficients, 
minimal                 model, double of a point ecimindouble(E,P) elliptic 
			curve with integer coefficients, 
minimal                 model, double of point ecracdouble(E,P) elliptic 
			curve over the rational numbers, 
minimal                 model, factorization of discriminant eciminfdisc(E) 
			elliptic curve with integer coefficients, 
minimal                 model, generators of torsion group ecimingentor(E) 
			elliptic curve with integer coefficients, 
minimal                 model, local height at the archimedean absolute 
			value eciminlhaav(E,P) elliptic curve with integer 
			coefficients, 
minimal                 model, local heights at all non archimedean 
			absolute values eciminlhnaav(E,P) elliptic curve 
			with integer coefficients, 
minimal                 model, multiplication-map eciminmul(E,P,n) elliptic 
			curve with integer coefficients, 
minimal                 model, multiplicative reduction type modulo prime 
			eciminmrtmp(E,p) elliptic curve with integer 
			coefficients, 
minimal                 model, negative point eciminneg(E,P) elliptic curve 
			with integer coefficients, 
minimal                 model, point comparison modulo torsion 
			eciminpcompmt(E,P1,P2) elliptic curve with integer 
			coefficients, 
minimal                 model, point list union 
			eciminplunion(E,L1,L2,modus) elliptic curve with 
			integer coefficients, 
minimal                 model, point list, insert point 
			eciminplinsp(P,h,PL) elliptic curve with integer 
			coefficients, 
minimal                 model, reduction type eciminredtype(E) elliptic 
			curve with integer coefficients, 
minimal                 model, regulator eciminreg(E,LP,n,modus) elliptic 
			curve with integer coefficients, 
minimal                 model, set NTH_EPS eciminntheps(E,d) elliptic curve 
			with integer coefficients, 
minimal                 model, sum of points eciminsum(E,P,Q) elliptic 
			curve with integer coefficients, 
minimal                 model, torsion group ecimintorgr(E) elliptic curve 
			with integer coefficients, 
minimal                 polynomial afmsp1minpol(p,F,a) algebraic function 
			over modular single primes, transcendence degree 1, 
minimal                 polynomial afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic 
			function over modular single prime, transcendence 
			degree 1, P-primality test and factorization of the 
			defining polynomial or the 
minimal                 polynomial iafmsp1mpol(p,F,a,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, 
minimal                 polynomial infepptfact(F,p,Q,ppot,a0,z) integral 
			number field element p-primality test and 
			factorization of the defining polynomial or the 
minimal                 polynomial modulo p-power infeminpmpp(F,a,p,e,Q) 
			integral number field element 
minimal                 polynomial modulo p-power with respect to integer 
			primes infempmppip(F,a,p,e,Q) integral number field 
			element 
minimal                 polynomial modulo power of an univariate prime 
			polynomial over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, 
minimal                 polynomial with respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and factorization of the 
			defining polynomial or the 
minimal                 polynomial, Collins algorithm, version1 
			nfespecmpc1(F,a) number field element special 
minimal                 polynomial, Collins algorithm, version2 
			nfespecmpc2(F,a) number field element special 
minimal                 representation qnfminrep(D,a) quadratic number 
			field element 
minimum                 imin(A,B) (MACRO) integer 
minimum                 rmin(R,S) (MACRO) rational number 
minimum                 smin(a,b) (MACRO) single-precision 
minimum                 special version lsmins(L1,L2) list of singles 
mipfnsquare(p)          modular integer prime find non square 
mipfsquare(p)           modular integer prime find square 
miprod(M,A,B)           modular integer product 
miprodf(M,A,B)          modular integer product as function 
miproot(Q)              modular integer primitive root 
mipsqrt(p,r)            modular integer prime square root 
miquot(M,A,B)           (MACRO) modular integer quotient 
miscra(M,m,m1,A,a)      modular integer single chinese remainder algorithm 
misqrt(m,a)             modular integer square root 
misqrtas(N,r)           modular integer square root all solutions 
misqrtsrch(m,a)         modular integer square root search 
misum(M,A,B)            (MACRO) modular integer sum 
misumf(M,A,B)           modular integer sum as function 
mitos(M,A)              modular integer to symmetric remainder system 
model                   ( Laska's algorithm ) ecractoecimin(E) elliptic 
			curve over rational numbers, actual curve to global 
			minimal 
model                   eciminbtac(E) elliptic curve with integer 
			coefficients, minimal model, birational 
			transformation to actual ( rational ) 
model                   ecisnfbtac(E) elliptic curve with integer 
			coefficients, short normal form, birational 
			transformation to actual ( rational ) 
model                   ecisnfbtmin(E) elliptic curve with integer 
			coefficients, short normal form, birational 
			transformation to minimal 
model                   ecracbtmin(E) elliptic curve over the rationals, 
			actual curve, birational transformation to minimal 
model                   fputecimin(E,pf) file put elliptic curve with 
			integer coefficients, minimal 
model                   in short normal form isponecisnf(E,P) is point on 
			elliptic curve with integer coefficients, 
model                   isecimintorp(E,P) is torsion point on elliptic 
			curve with integer coefficients, minimal 
model                   isineciminpl(E,P,h,PL) is in list of points on 
			elliptic curve with integer coefficients, minimal 
model                   isponecimin(E,P) is point on elliptic curve with 
			integer coefficients, minimal 
model                   isponecrac(E,P) is point on elliptic curve over 
			rational numbers, actual 
model                   putecimin(E) (MACRO) put elliptic curve with 
			integer coefficients, minimal 
model                   to short normal form ecimintosnf(E) elliptic curve 
			with integer coefficients, minimal 
model,                  Mordell-Weil-group, base eciminmwgbase(E) elliptic 
			curve with integer coefficients, minimal 
model,                  Neron-Tate height eciminnetahe(E,P) elliptic curve 
			with integer coefficients, minimal 
model,                  Neron-Tate pairing eciminnetapa(E,P,Q) elliptic 
			curve with integer coefficients, minimal 
model,                  Tate value b2 ecqnfacb2(E) elliptic curve over 
			quadratic number field, actual 
model,                  Tate value b4 ecqnfacb4(E) elliptic curve over 
			quadratic number field, actual 
model,                  Tate value b6 ecqnfacb6(E) elliptic curve over 
			quadratic number field, actual 
model,                  Tate value b8 ecqnfacb8(E) elliptic curve over 
			quadratic number field, actual 
model,                  Tate value c4 ecqnfacc4(E) elliptic curve over 
			quadratic number field, actual 
model,                  Tate value c6 ecqnfacc6(E) elliptic curve over 
			quadratic number field, actual 
model,                  Tate's algorithm ecimintatealg(E,p,n) elliptic 
			curve with integer coefficients, minimal 
model,                  Tate's values c4, c6 ecitavalc(a1,a2,a3,a4,a6) 
			elliptic curve with integer coefficients, minimal 
model,                  a1 ecimina1(E) elliptic curve with integer 
			coefficients, minimal 
model,                  a2 ecimina2(E) elliptic curve with integer 
			coefficients, minimal 
model,                  a3 ecimina3(E) elliptic curve with integer 
			coefficients, minimal 
model,                  a4 ecimina4(E) elliptic curve with integer 
			coefficients, minimal 
model,                  a6 ecimina6(E) elliptic curve with integer 
			coefficients, minimal 
model,                  b2 eciminb2(E) elliptic curve with integer 
			coefficients, minimal 
model,                  b4 eciminb4(E) elliptic curve with integer 
			coefficients, minimal 
model,                  b6 eciminb6(E) elliptic curve with integer 
			coefficients, minimal 
model,                  b8 eciminb8(E) elliptic curve with integer 
			coefficients, minimal 
model,                  bad reduction type modulo prime eciminbrtmp(E,p,n) 
			elliptic curve with integer coefficients, minimal 
model,                  birational transformation of coefficients 
			eciminbtco(E,BT) elliptic curve with integer 
			coefficients, minimal 
model,                  birational transformation to actual ( rational ) 
			model eciminbtac(E) elliptic curve with integer 
			coefficients, minimal 
model,                  birational transformation to short normal form 
			eciminbtsnf(E) elliptic curve with integer 
			coefficients, minimal 
model,                  c4 eciminc4(E) elliptic curve with integer 
			coefficients, minimal 
model,                  c6 eciminc6(E) elliptic curve with integer 
			coefficients, minimal 
model,                  difference between Weil height and Neron-Tate 
			height ecimindwhnth(E) elliptic curve with integer 
			coefficients, minimal 
model,                  difference of points ecimindif(E,P,Q) elliptic 
			curve with integer coefficients, minimal 
model,                  difference of points ecisnfdif(E,P,Q) elliptic 
			curve with integer coefficients, minimal 
model,                  discriminant ecimindisc(E) elliptic curve with 
			integer coefficients, minimal 
model,                  discriminant ecqnfacdisc(E) elliptic curve over 
			quadratic number field, actual 
model,                  division by 2 of a point ecimindivby2(E,P,h,PL,H) 
			elliptic curve with integer coefficients, minimal 
model,                  division of a point by an integer ecimindiv(E,P,n) 
			elliptic curve with integer coefficients, minimal 
model,                  division of a point by an integer, special version 
			ecimindivs(E,P,h,ug,PL,n) elliptic curve with 
			integer coefficients, minimal 
model,                  double of a point ecimindouble(E,P) elliptic curve 
			with integer coefficients, minimal 
model,                  double of point ecracdouble(E,P) elliptic curve 
			over the rational numbers, minimal 
model,                  factorization of discriminant eciminfdisc(E) 
			elliptic curve with integer coefficients, minimal 
model,                  factorization of the norm of the discriminant 
			ecqnfacfndisc(E) elliptic curve over quadratic 
			number field, actual 
model,                  generators of torsion group ecimingentor(E) 
			elliptic curve with integer coefficients, minimal 
model,                  local height at the archimedean absolute value 
			eciminlhaav(E,P) elliptic curve with integer 
			coefficients, minimal 
model,                  local heights at all non archimedean absolute 
			values eciminlhnaav(E,P) elliptic curve with 
			integer coefficients, minimal 
model,                  multiplication-map eciminmul(E,P,n) elliptic curve 
			with integer coefficients, minimal 
model,                  multiplicative reduction type modulo prime 
			eciminmrtmp(E,p) elliptic curve with integer 
			coefficients, minimal 
model,                  negative point eciminneg(E,P) elliptic curve with 
			integer coefficients, minimal 
model,                  norm of the discriminant ecqnfacndisc(E) elliptic 
			curve over quadratic number field, actual 
model,                  point comparison modulo torsion 
			eciminpcompmt(E,P1,P2) elliptic curve with integer 
			coefficients, minimal 
model,                  point list union eciminplunion(E,L1,L2,modus) 
			elliptic curve with integer coefficients, minimal 
model,                  point list, insert point eciminplinsp(P,h,PL) 
			elliptic curve with integer coefficients, minimal 
model,                  prime ideal factorization of the discriminant 
			ecqnfacpifdi(E) elliptic curve over quadratic 
			number field, actual 
model,                  reduction type eciminredtype(E) elliptic curve with 
			integer coefficients, minimal 
model,                  regulator eciminreg(E,LP,n,modus) elliptic curve 
			with integer coefficients, minimal 
model,                  set NTH_EPS eciminntheps(E,d) elliptic curve with 
			integer coefficients, minimal 
model,                  sum of points eciminsum(E,P,Q) elliptic curve with 
			integer coefficients, minimal 
model,                  torsion group ecimintorgr(E) elliptic curve with 
			integer coefficients, minimal 
modielemtest(B,a)       module over the integers element test 
modified                Shanks' algorithm, first part 
			ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) elliptic 
			curve over Galois-field with characteristic 2, 
modified                Shanks' algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over modular primes, short normal form, 
modilllred(bas)         module over the integers, LLL reduction 
modiorthobas(bas)       module over the integers, orthogonalized basis 
modprmsp1elt(B,p,a)     module over polynomial ring over modular single 
			primes, transcendence degree 1, element test 
mods(A,B)               (MACRO) modulo with reference to SIMATH 
modular                 2 gf2eltoudpm2(G,a) Galois-field with 
			characteristic 2 element to univariate dense 
			polynomial over 
modular                 2 in special bit-representation ? isudpm2sb(A) is 
			univariate dense polynomial over 
modular                 2 sbtoudpm2(a) (MACRO) special bit-representation 
			to univariate dense polynomial over 
modular                 2 to Galois-field with characteristic 2 element 
			udpm2togf2el(G,P) univariate dense polynomial over 
modular                 2 to polynomial over Galois-field with 
			characteristic 2 (rekursiv) pm2topgf2(r,P) 
			polynomial over 
modular                 2 to special bit-representation udpm2tosb(P) 
			univariate dense polynomial over 
modular                 2, irreducible and monic trinomial, generator 
			upm2imtgen(n) univariate polynomial over 
modular                 2, irreducible and monic, generator upm2imgen(n) 
			univariate polynomial over 
modular                 4 homomorphism m4hom(a) (MACRO) 
modular                 exponentiation, special version 
			upgf2modexps(G,F,m,P,pM) univariate polynomial over 
			Galois-field with characteristic 2, 
modular                 ideal homomorphism pimidhom(r,S,P) polynomial over 
			integers 
modular                 ideal product pimidprod(r,S,P1,P2) polynomial over 
			integers 
modular                 ideal product pmimidprod(r,M,S,P1,P2) polynomial 
			over modular integers, 
modular                 ideal quotient and remainder 
			pmimidqrem(r,M,S,P1,P2,pR) polynomial over modular 
			integers monic, 
modular                 ideal solution of equation 
			pmimidse(r,M,S,P1,P2,F1,F2,H,pV) polynomial over 
			modular integers 
modular                 ideal, Hensel lemma quadratic step on a single 
			variable pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) 
			polynomial over modular integers, 
modular                 ideal, Hensel lemma quadratic step 
			pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial over 
			integers, 
modular                 ideal, Hensel lemma quadratic step 
			pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial 
			over modular integers, 
modular                 integer ? (rekursiv) ispmi(r,m,P) is polynomial 
			over 
modular                 integer ? ismi(m,a) is 
modular                 integer Fermat residue ? ismifr(M,A,B) is 
modular                 integer chinese remainder algorithm 
			micra(M1,M2,N1,A1,A2) 
modular                 integer chinese remainder algorithm, n arguments 
			(rekursiv) micran(n,LM,LA) 
modular                 integer difference midif(M,A,B) 
modular                 integer exponentiation ( lists only ) 
			miexp_lo(M,A,E) 
modular                 integer exponentiation miexp(M,A,E) 
modular                 integer fgetmi(M,pf) file get 
modular                 integer fputmi(M,A,pf) file put 
modular                 integer getmi(M) (MACRO) get 
modular                 integer homomorphism mihom(M,A) 
modular                 integer homomorphism, symmetric remainder system 
			mihoms(M,A) 
modular                 integer inverse miinv(M,A) 
modular                 integer inverse, lists only miinv_lo(M,A) 
modular                 integer list chinese remainder algorithm 
			milcra(m1,m2,L1,L2) 
modular                 integer negation as function minegf(M,A) 
modular                 integer negation mineg(M,A) (MACRO) 
modular                 integer prime additive valuation upmiaddval(p,P1,P) 
			univariate polynomial over 
modular                 integer prime find non square mipfnsquare(p) 
modular                 integer prime find square mipfsquare(p) 
modular                 integer prime square root mipsqrt(p,r) 
modular                 integer primes Euklid- Gauss- step for columns 
			maupmipegsc(p,M,A,B) matrix of univariate 
			polynomials over 
modular                 integer primes Euklid- Gauss- step for rows 
			maupmipegsr(p,M,A,B) matrix of univariate 
			polynomials over 
modular                 integer primes Groebner basis augmentation 
			dipmipgba(r,p,PL,P) distributive polynomial over 
modular                 integer primes Groebner basis dipmipgb(r,p,PL) 
			distributive polynomial over 
modular                 integer primes Groebner basis recursion 
			dipmipgbr(r,p,PL) distributive polynomial over 
modular                 integer primes S-polynomial dipmipsp(r,p,P1,P2) 
			distributive polynomial over 
modular                 integer primes difference dipmipdif(r,p,P1,P2) 
			distributive polynomial over 
modular                 integer primes elementary divisor form and 
			cofactors maupmipedfcf(p,M,pA,pB) matrix of 
			univariate polynomials over 
modular                 integer primes in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over 
modular                 integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
modular                 integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			in lexicographical order with inverse exponent 
			vector dipmiplotlio(r,p,P) distributive polynomial 
			over 
modular                 integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			with total degree ordering dipmiplottdo(r,p,P) 
			distributive polynomial over 
modular                 integer primes in lexicographical order with 
			inverse exponent vector dipmiplotlio(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over 
modular                 integer primes list fgetdipmipl(r,p,VL,pf) file get 
			distributive polynomial over 
modular                 integer primes list fputdipmipl(r,p,PL,VL,pf) file 
			put distributive polynomial over 
modular                 integer primes list getdipmipl(r,p,VL) (MACRO) get 
			distributive polynomial over 
modular                 integer primes list putdipmipl(r,p,PL,VL) (MACRO) 
			put distributive polynomial over 
modular                 integer primes monic dipmipmonic(r,p,P) 
			distributive polynomial over 
modular                 integer primes negation dipmipneg(r,p,P) 
			distributive polynomial over 
modular                 integer primes product dipmipmiprod(r,p,P,A) 
			distributive polynomial over modular integer 
			primes, 
modular                 integer primes product dipmipprod(r,p,P1,P2) 
			distributive polynomial over 
modular                 integer primes short normal form number of points 
			special version ecmipsnfnpsv(p,a4,a6) elliptic 
			curve over 
modular                 integer primes sum dipmipsum(r,p,P1,P2) 
			distributive polynomial over 
modular                 integer primes with total degree ordering 
			dipmiplottdo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over 
modular                 integer primes, modular integer primes product 
			dipmipmiprod(r,p,P,A) distributive polynomial over 
modular                 integer primitive root miproot(Q) 
modular                 integer product as function miprodf(M,A,B) 
modular                 integer product miprod(M,A,B) 
modular                 integer product udpmimiprod(m,P,a) univariate dense 
			polynomial over modular integers, 
modular                 integer putmi(M,A) (MACRO) put 
modular                 integer quotient (rekursiv) pmimiquot(r,m,P,a) 
			polynomial over modular integers, 
modular                 integer quotient miquot(M,A,B) (MACRO) 
modular                 integer rtomi(R,M) rational number to 
modular                 integer single chinese remainder algorithm 
			miscra(M,m,m1,A,a) 
modular                 integer square ? ismisquare(M,A) is 
modular                 integer square root all solutions misqrtas(N,r) 
modular                 integer square root misqrt(m,a) 
modular                 integer square root search misqrtsrch(m,a) 
modular                 integer sum as function misumf(M,A,B) 
modular                 integer sum misum(M,A,B) (MACRO) 
modular                 integer to symmetric remainder system mitos(M,A) 
modular                 integer unit ismiunit(M,A) is 
modular                 integers (rekursiv) pitopmi(r,P,M) polynomial over 
			integers to polynomial over 
modular                 integers (rekursiv) prtopmi(r,P,M) polynomial over 
			rationals to polynomial over 
modular                 integers ? (rekursiv) isdpmi(r,m,P) is dense 
			polynomial over 
modular                 integers ? isimupmi(p,A) is irreducible, monic, 
			univariate polynomial over 
modular                 integers ? islistmi(M,A) is list of 
modular                 integers ? ismami(m,M) (MACRO) is matrix of 
modular                 integers ? ismapmi(r,m,M) (MACRO) is matrix of 
			polynomials over 
modular                 integers Ben-Or factorization upmibofact(ip,P) 
			univariate polynomial over 
modular                 integers Ben-Or factorization, special 
			upmibofacts(ip,P) univariate polynomial over 
modular                 integers Berlekamp factorization, last step 
			upmibfls(ip,P,B,d) univariate polynomial over 
modular                 integers Bezout-matrix pmibezout(r,m,P1,P2) 
			polynomial over 
modular                 integers Jacobi-symbol udpmijacsym(m,P1,P2) 
			univariate dense polynomial over 
modular                 integers Jacobi-symbol upmijacsym(m,P1,P2) 
			univariate polynomial over 
modular                 integers characteristic polynomial mamichpol(m,M) 
			(MACRO) matrix of 
modular                 integers characteristic polynomial 
			mapmichpol(r,m,M) (MACRO) matrix of polynomials 
			over 
modular                 integers complete factorization upmicfact(ip,P) 
			univariate polynomial over 
modular                 integers construction 1 mamicons1(m,n) (MACRO) 
			matrix of 
modular                 integers construction 1 mapmicons1(r,m,n) (MACRO) 
			matrix of polynomials over 
modular                 integers derivation udpmideriv(m,P) univariate 
			dense polynomial over 
modular                 integers derivation, main variable pmideriv(r,M,P) 
			polynomial over 
modular                 integers derivation, specified variable (rekursiv) 
			pmiderivsv(r,m,P,n) polynomial over 
modular                 integers determinant mamidet(m,M) matrix of 
modular                 integers determinant mapmidet(r,m,M) matrix of 
			polynomials over 
modular                 integers difference (rekursiv) dpmidif(r,m,P1,P2) 
			dense polynomial over 
modular                 integers difference (rekursiv) pmidif(r,M,P1,P2) 
			polynomial over 
modular                 integers difference mamidif(m,M,N) (MACRO) matrix 
			of 
modular                 integers difference mapmidif(r,m,M,N) (MACRO) 
			matrix of polynomials over 
modular                 integers difference udpmidif(m,P1,P2) univariate 
			dense polynomial over 
modular                 integers difference vecmidif(m,U,V) (MACRO) vector 
			of 
modular                 integers difference vecpmidif(r,m,U,V) (MACRO) 
			vector of polynomials over 
modular                 integers discriminant pmidiscr(r,M,P,n) polynomial 
			over 
modular                 integers discriminant via Hankel matrix 
			pmidiscrhank(r,M,P) polynomial over 
modular                 integers distinct degree factorization 
			upmiddfact(ip,P) univariate polynomial over 
modular                 integers eigenvalues and irreducible factors of the 
			characteristic polynomial mamievifcp(p,M,pL) matrix 
			of 
modular                 integers eigenvalues mamiev(p,M) (MACRO) matrix of 
modular                 integers evaluation, main variable pmieval(r,M,P,A) 
			polynomial over 
modular                 integers evaluation, specified variable (rekursiv) 
			pmievalsv(r,m,P,n,a) polynomial over 
modular                 integers exponentiation mamiexp(m,M,n) matrix of 
modular                 integers exponentiation mapmiexp(r,m,M,n) matrix of 
			polynomials over 
modular                 integers exponentiation pmiexp(r,m,P,n) polynomial 
			over 
modular                 integers extended greatest common divisor 
			udpmiegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over 
modular                 integers extended greatest common divisor 
			upmiegcd(P,P1,P2,pP3,pP4) univariate polynomial 
			over 
modular                 integers factorization, Berlekamp algorithm 
			upmibfact(ip,P,d) univariate polynomial over 
modular                 integers fgetmami(m,pf) (MACRO) file get matrix of 
modular                 integers fgetmapmi(r,m,V,pf) (MACRO) file get 
			matrix of polynomials over 
modular                 integers fgetpmi(r,M,V,pf) file get polynomial over 
modular                 integers fgetvecmi(m,pf) (MACRO) file get vector of 
modular                 integers fgetvecpmi(r,m,VL,pf) (MACRO) file get 
			vector of polynomials over 
modular                 integers fputmami(m,M,pf) (MACRO) file put matrix 
			of 
modular                 integers fputmapmi(r,m,M,V,pf) (MACRO) file put 
			matrix of polynomials over 
modular                 integers fputpmi(r,M,P,V,pf) file put polynomial 
			over 
modular                 integers fputvecmi(m,V,pf) (MACRO) file put vector 
			of 
modular                 integers fputvecpmi(r,m,V,VL,pf) (MACRO) file put 
			vector of polynomials over 
modular                 integers getmami(m) (MACRO) get matrix of 
modular                 integers getmapmi(r,m,V) (MACRO) get matrix of 
			polynomials over 
modular                 integers getpmi(r,M,V) (MACRO) get polynomial over 
modular                 integers getvecmi(m) (MACRO) get vector of 
modular                 integers getvecpmi(r,m,VL) (MACRO) get vector of 
			polynomials over 
modular                 integers greatest common divisor and cofactors 
			(rekursiv) pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial 
			over 
modular                 integers greatest common divisor udpmigcd(m,P1,P2) 
			univariate dense polynomial over 
modular                 integers greatest common divisor upmigcd(ip,P1,P2) 
			univariate polynomial over 
modular                 integers greatest squarefree divisor (rekursiv) 
			upmigsd(ip,P) univariate polynomial over 
modular                 integers half extended greatest common divisor 
			udpmihegcd(m,P1,P2,pP3) univariate dense polynomial 
			over 
modular                 integers half extended greatest common divisor 
			upmihegcd(P,P1,P2,pP3) univariate polynomial over 
modular                 integers interpolation (rekursiv) 
			pmiinter(r,m,P1,P2,P3,a,b) polynomial over 
modular                 integers inverse mamiinv(m,M) matrix of 
modular                 integers inverse mapmiinv(r,m,M) matrix of 
			polynomials over 
modular                 integers linear combination vecmilc(M,S1,S2,L1,L2) 
			vector of 
modular                 integers linear combination 
			vecpmilc(r,m,P1,P2,V1,V2) vector of polynomials 
			over 
modular                 integers maitomami(m,M) matrix of integers to 
			matrix of 
modular                 integers mapitomapmi(r,M,m) matrix of polynomials 
			over integers to matrix of polynomials over 
modular                 integers mapmitomapmp(r,m,P,M) matrix of 
			polynomials over modular integers to matrix of 
			polynomials modulo polynomial over 
modular                 integers maprtomapmi(r,M,m) matrix of polynomials 
			over rationals to matrix of polynomials over 
modular                 integers martomami(m,M) matrix of rationals to 
			matrix of 
modular                 integers modular ideal solution of equation 
			pmimidse(r,M,S,P1,P2,F1,F2,H,pV) polynomial over 
modular                 integers modular polynomial exponentiation 
			upmimpexp(ip,K,E,P) univariate polynomial over 
modular                 integers monic pmimonic(r,M,P) polynomial over 
modular                 integers monic udpmimonic(m,P) univariate dense 
			polynomial over 
modular                 integers monic, modular ideal quotient and 
			remainder pmimidqrem(r,M,S,P1,P2,pR) polynomial 
			over 
modular                 integers mudpitudpmi(M,m) matrix of univariate 
			dense polynomials over integers to matrix of 
			univariate dense polynomials over 
modular                 integers negation (rekursiv) dpmineg(r,m,P) dense 
			polynomial over 
modular                 integers negation (rekursiv) pmineg(r,M,P) 
			polynomial over 
modular                 integers negation mamineg(m,M) (MACRO) matrix of 
modular                 integers negation mapmineg(r,m,M) (MACRO) matrix of 
			polynomials over 
modular                 integers negation udpmineg(m,P) univariate dense 
			polynomial over 
modular                 integers negation vecmineg(m,V) (MACRO) vector of 
modular                 integers negation vecpmineg(r,m,V) (MACRO) vector 
			of polynomials over 
modular                 integers product (rekursiv) dpmiprod(r,M,P1,P2) 
			dense polynomial over 
modular                 integers product (rekursiv) pmimiprod(r,M,P,A) 
			polynomial over modular integers, 
modular                 integers product (rekursiv) pmiprod(r,M,P1,P2) 
			polynomial over 
modular                 integers product (rekursiv) pmiupmiprod(r,m,P1,P2) 
			polynomial over modular integers, univariate 
			polynomial over 
modular                 integers product mamiprod(m,M,N) (MACRO) matrix of 
modular                 integers product mapmiprod(r,m,M,N) (MACRO) matrix 
			of polynomials over 
modular                 integers product udpmiprod(m,P1,P2) univariate 
			dense polynomial over 
modular                 integers pseudo remainder pmipsrem(r,m,P1,P2) 
			polynomial over 
modular                 integers putmami(m,M) (MACRO) put matrix of 
modular                 integers putmapmi(r,m,M,V) (MACRO) put matrix of 
			polynomials over 
modular                 integers putpmi(r,m,P,V) (MACRO) put polynomial 
			over 
modular                 integers putvecmi(m,V) (MACRO) put vector of 
modular                 integers putvecpmi(r,m,V,VL) (MACRO) put vector of 
			polynomials over 
modular                 integers quotient (rekursiv) pmiupmiquot(r,m,P1,P2) 
			polynomial over modular integers, univariate 
			polynomial over 
modular                 integers quotient and remainder (rekursiv) 
			pmiqrem(r,M,P1,P2,pR) polynomial over 
modular                 integers quotient and remainder 
			udpmiqrem(m,P1,P2,pP3) univariate dense polynomial 
			over 
modular                 integers quotient pmiquot(r,M,P1,P2) (MACRO) 
			polynomial over 
modular                 integers quotient udpmiquot(m,P1,P2) (MACRO) 
			univariate dense polynomial over 
modular                 integers randomize upmirand(ip,m) univariate 
			polynomial over 
modular                 integers relative prime factorization 
			upmirelpfact(P,F,Fak,pA2) univariate polynomial 
			over 
modular                 integers remainder pmirem(r,M,P1,P2) (MACRO) 
			polynomial over 
modular                 integers remainder udpmirem(ip,P,P2) univariate 
			dense polynomial over 
modular                 integers remainder upmirem(M,P1,P2) univariate 
			polynomial over 
modular                 integers resultant and cofactor of resultant 
			equation upmiresulc(m,P1,P2,pC) univariate 
			polynomial over 
modular                 integers resultant pmires(r,m,P1,P2,n) polynomial 
			over 
modular                 integers resultant upmires(m,P1,P2) univariate 
			polynomial over 
modular                 integers resultant, Collins algorithm (rekursiv) 
			pmirescoll(r,m,P1,P2) polynomial over 
modular                 integers scalar multiplication mamismul(m,M,el) 
			matrix of 
modular                 integers scalar multiplication mapmismul(r,m,M,P) 
			matrix of polynomials over 
modular                 integers scalar multiplication vecmismul(m,s,V) 
			vector of 
modular                 integers scalar multiplication vecpmismul(r,m,P,V) 
			vector of polynomials over 
modular                 integers scalar product vecmisprod(M,V,W) vector of 
modular                 integers scalar product vecpmisprod(r,m,V,W) vector 
			of polynomials over 
modular                 integers separate factor of equal degree 
			upmisfed(ip,G,d) univariate polynomial over 
modular                 integers squarefree factorization (rekursiv) 
			upmisfact(ip,P) univariate polynomial over 
modular                 integers squarefree part upmisfp(m,P) univariate 
			polynomial over 
modular                 integers substitution with respect to a cubic 
			equation bpmisubcubeq(p,P,R) bivariate polynomial 
			over 
modular                 integers substitution, main variable 
			pmisubst(r,m,P1,P2) polynomial over 
modular                 integers substitution, specified variable 
			(rekursiv) pmisubstsv(r,m,P1,n,P2) polynomial over 
modular                 integers sum (rekursiv) dpmisum(r,M,P1,P2) dense 
			polynomial over 
modular                 integers sum (rekursiv) pmisum(r,M,P1,P2) 
			polynomial over 
modular                 integers sum mamisum(m,M,N) (MACRO) matrix of 
modular                 integers sum mapmisum(r,m,M,N) (MACRO) matrix of 
			polynomials over 
modular                 integers sum udpmisum(m,P1,P2) univariate dense 
			polynomial over 
modular                 integers sum vecmisum(m,U,V) (MACRO) vector of 
modular                 integers sum vecpmisum(r,m,U,V) (MACRO) vector of 
			polynomials over 
modular                 integers to matrix of polynomials modulo polynomial 
			over modular integers mapmitomapmp(r,m,P,M) matrix 
			of polynomials over 
modular                 integers to symmetric remainder system (rekursiv) 
			pmitos(r,M,P) polynomial over 
modular                 integers to vector of polynomials modulo polynomial 
			over modular integers vecpmitovpmp(r,m,P,V) vector 
			of polynomials over 
modular                 integers transformation 
			mapmitransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over 
modular                 integers transformation 
			pmitransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over 
modular                 integers transformation upmitransf(M,P,r,P1) 
			univariate polynomial over 
modular                 integers transformation version2 
			upmitransf2(M,P,r,P1) univariate polynomial over 
modular                 integers transformation 
			vpmitransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over 
modular                 integers translation, all variables (rekursiv) 
			pmitransav(r,m,P,Lmi) polynomial over 
modular                 integers translation, main variable 
			pmitrans(r,m,P,a) polynomial over 
modular                 integers udpitoudpmi(P,M) univariate dense 
			polynomial over integers to univariate dense 
			polynomial over 
modular                 integers unit? ispmiunit(r,m,P) is polynomial over 
modular                 integers univariate content (rekursiv) 
			pmiucont(r,m,P) polynomial over 
modular                 integers vecitovecmi(M,V) vector of integers to 
			vector of 
modular                 integers vecpitovpmi(r,V,m) vector of polynomials 
			over integers to vector of polynomials over 
modular                 integers vecpmitovpmp(r,m,P,V) vector of 
			polynomials over modular integers to vector of 
			polynomials modulo polynomial over 
modular                 integers vecprtovpmi(r,V,m) vector of polynomials 
			over rationals to vector of polynomials over 
modular                 integers vecrtovecmi(m,V) vector of rationals to 
			vector of 
modular                 integers vector multiplication mamivecmul(m,A,x) 
			(MACRO) matrix of 
modular                 integers vector multiplication mapmivecmul(r,m,A,x) 
			(MACRO) matrix of polynomials over 
modular                 integers vudpitudpmi(V,M) vector of univariate 
			dense polynomials over integers to vector of 
			univariate dense polynomials over 
modular                 integers, Berlekamp Q polynomials construction 
			upmibqp(ip,P) univariate polynomial over 
modular                 integers, Berlekamp factorization, Zassenhaus 
			method upmibfzm(ip,s,P,G) univariate polynomial 
			over 
modular                 integers, complete factorization special 
			upmicfacts(P,F) univariate polynomial over 
modular                 integers, modular ideal product 
			pmimidprod(r,M,S,P1,P2) polynomial over 
modular                 integers, modular ideal, Hensel lemma quadratic 
			step on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
modular                 integers, modular ideal, Hensel lemma quadratic 
			step pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) 
			polynomial over 
modular                 integers, modular integer product 
			udpmimiprod(m,P,a) univariate dense polynomial over 
modular                 integers, modular integer quotient (rekursiv) 
			pmimiquot(r,m,P,a) polynomial over 
modular                 integers, modular integers product (rekursiv) 
			pmimiprod(r,M,P,A) polynomial over 
modular                 integers, monomial, polynomial, remainder 
			upmimprem(ip,K,E,P) univariate polynomial over 
modular                 integers, null space basis maminsb(P,M) matrix of 
modular                 integers, number of irreducible factors 
			upminif(m,P) univariate polynomial over 
modular                 integers, root finding (rekursiv) upmirf(ip,P) 
			univariate polynomial over 
modular                 integers, root finding, special (rekursiv) 
			upmirfspec(ip,P) univariate polynomial over 
modular                 integers, trace function, special 
			upmitfsp(ip,G,d,M) univariate polynomial over 
modular                 integers, univariate polynomial over modular 
			integers product (rekursiv) pmiupmiprod(r,m,P1,P2) 
			polynomial over 
modular                 integers, univariate polynomial over modular 
			integers quotient (rekursiv) pmiupmiquot(r,m,P1,P2) 
			polynomial over 
modular                 invariant j cmodinv(q,ln_q) complex 
modular                 polynomial exponentiation upmimpexp(ip,K,E,P) 
			univariate polynomial over modular integers 
modular                 prime power square root mppsqrt(p,n,r,xk,k) 
modular                 primes ? iselecmp(p,a1,a2,a3,a4,a6,P) is element of 
			an elliptic curve over 
modular                 primes Tate's values b2, b4, b6 
			ecmptavb6(p,a1,a2,a3,a4,a6) elliptic curve over 
modular                 primes Tate's values b2, b4, b6, b8 
			ecmptavb8(p,a1,a2,a3,a4,a6) elliptic curve over 
modular                 primes Tate's values c4, c6 
			ecmptavc6(p,a1,a2,a3,a4,a6) elliptic curve over 
modular                 primes equal ? isppecmpeq(p,P1,P2) is projective 
			point of an elliptic curve over 
modular                 primes multiplication-map 
			ecmpmul(p,a1,a2,a3,a4,a6,n,P1) elliptic curve over 
modular                 primes negative point ecmpneg(p,a1,a2,a3,a4,a6,P) 
			elliptic curve over 
modular                 primes point at infinity ? isppecmppai(p,P) is 
			projective point of an elliptic curve over 
modular                 primes square root mpsqrt(p,a) 
modular                 primes to short normal form 
			ecmptosnf(p,a1,a2,a3,a4,a6) elliptic curve over 
modular                 primes, birational transformation of coefficients 
			ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over 
modular                 primes, discriminant ecmpdisc(p,a1,a2,a3,a4,a6) 
			elliptic curve over 
modular                 primes, find point ecmpfp(p,a1,a2,a3,a4,a6) 
			elliptic curve over 
modular                 primes, j-invariant ecmpjinv(p,a1,a2,a3,a4,a6) 
			elliptic curve over 
modular                 primes, line through points 
			ecmplp(p,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
modular                 primes, short normal form ? iselecmpsnf(p,a,b,P) is 
			element of an elliptic curve over 
modular                 primes, short normal form, combined Schoof- Shanks- 
			algorithm ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic 
			curve over 
modular                 primes, short normal form, construction of division 
			polynomials ecmpsnfcdivp(P,a4,a6,n) elliptic curve 
			over 
modular                 primes, short normal form, discriminant 
			ecmpsnfdisc(p,a4,a6) elliptic curve over 
modular                 primes, short normal form, find point 
			ecmpsnffp(p,a4,a6) elliptic curve over 
modular                 primes, short normal form, finding a multiple of 
			the order of a point with the Pollard Lambda method 
			ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
modular                 primes, short normal form, finding a multiple of 
			the order of a point with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
modular                 primes, short normal form, j-invariant 
			ecmpsnfjinv(p,a4,a6) elliptic curve over 
modular                 primes, short normal form, line through points 
			ecmpsnflp(p,a4,a6,P1,P2) elliptic curve over 
modular                 primes, short normal form, modified Shanks' 
			algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over 
modular                 primes, short normal form, multiple of the order of 
			a point to exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
modular                 primes, short normal form, multiplication-map 
			ecmpsnfmul(p,a4,a6,n,P1) elliptic curve over 
modular                 primes, short normal form, multiplication-map, 
			special version ecmpsnfmuls(p,a4,a6,x1,y1,n) 
			elliptic curve over 
modular                 primes, short normal form, negative point 
			ecmpsnfneg(p,a4,a6,P) elliptic curve over 
modular                 primes, short normal form, number of points modulo 
			2 ecmpsnfnpm2(P,a4,a6) elliptic curve over 
modular                 primes, short normal form, number of points modulo 
			a single prime determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
modular                 primes, short normal form, number of points modulo 
			an integer determined with the Schoof algorithm 
			ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve over 
modular                 primes, short normal form, sum of points 
			ecmpsnfsum(p,a4,a6,P1,P2) elliptic curve over 
modular                 primes, short normal form, sum of points, special 
			version ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic 
			curve over 
modular                 primes, standard representation of projective point 
			ecmpsrpp(p,P) elliptic curve over 
modular                 primes, sum of points 
			ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
modular                 single ? isms(m,a) is 
modular                 single Fermat residue list msfrl(m,a) 
modular                 single chinese remainder algorithm 
			mscra(m1,m2,n1,a1,a2) 
modular                 single chinese remainder algorithm, n arguments 
			(rekursiv) mscran(n,Lm,La) 
modular                 single difference msdif(m,a,b) (MACRO) 
modular                 single exponentiation msexp(m,a,n) 
modular                 single fgetms(m,pf) file get 
modular                 single fputms(m,a,pf) file put 
modular                 single getms(m) (MACRO) get 
modular                 single homomorphism mshom(m,A) 
modular                 single inverse msinv(m,a) 
modular                 single list chinese remainder algorithm 
			mslcra(m1,m2,L1,L2) 
modular                 single negation as function msnegf(m,a) 
modular                 single negation msneg(m,a) (MACRO) 
modular                 single prime construction, transcendence degree 1 
			rfmsp1cons(p,P1,P2) rational function over 
modular                 single prime difference, transcendence degree 1 
			rfmsp1dif(p,R1,R2) rational function over 
modular                 single prime negation, transcendence degree 1 
			rfmsp1neg(p,R) rational function over 
modular                 single prime product, transcendence degree 1 
			rfmsp1prod(p,R1,R2) rational function over 
modular                 single prime quotient cdprfmsp1upq(p,F,P) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, 
			univariate polynomial over 
modular                 single prime quotient, transcendence degree 1 
			rfmsp1quot(p,R1,R2) rational function over 
modular                 single prime sum, transcendence degree 1 
			rfmsp1sum(p,R1,R2) rational function over 
modular                 single prime unimodular transformation 
			vecupmsunimt(p,V,W,i,pV1,pW1) vector of univariate 
			polynomials over 
modular                 single prime, complete factorization special 
			upmscfacts(p,A) univariate polynomial over 
modular                 single prime, number of points 
			ecmspnp(p,a1,a2,a3,a4,a6) elliptic curve over 
modular                 single prime, transcendence degree 1 ? 
			isrfmsp1(p,R) is rational function over 
modular                 single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from univariate polynomial 
			over rational functions over 
modular                 single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, list from common 
			denominator matrix of rational functions over 
modular                 single prime, transcendence degree 1 
			clfcdprfmsp1(P,n) coefficient list from common 
			denominator polynomial over rational functions over 
modular                 single prime, transcendence degree 1 
			fputrfmsp1(p,R,V,pf) (MACRO) file put rational 
			function over 
modular                 single prime, transcendence degree 1 
			nepousppmsp1(p,F,a) norm of an element of the 
			polynomial order of an univariate separable 
			polynomial over the polynomial ring over 
modular                 single prime, transcendence degree 1 
			pmstorfmsp1(p,P) (MACRO) polynomial over modular 
			singles to rational function over 
modular                 single prime, transcendence degree 1 
			putrfmsp1(p,R,V) (MACRO) put rational function over 
modular                 single prime, transcendence degree 1 
			sclfuprfmsp1(P,n) special coefficient list from 
			univariate polynomial over rational functions over 
modular                 single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, from common denominator 
			polynomial over rational functions over 
modular                 single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the extensions 
			of the P-adic valuation of an element of the 
			polynomial order of a univariate separable 
			polynomial over the polynomial ring over 
modular                 single prime, transcendence degree 1, Dedekind 
			maximality test ouspprmsp1dm(p,P,F) order of an 
			univariate separable polynomial over polynomial 
			ring over 
modular                 single prime, transcendence degree 1, Hensel 
			factorization approximation upprmsp1hfa(p,F,P,L,k) 
			univariate polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, Hensel lemma 
			initialization upprmsp1hli(p,F,P,L) univariate 
			polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, Hensel 
			quadratic step upprmsp1hqs(p,F,T,L1,L2,A) 
			univariate polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, P-primality 
			test and factorization of the defining polynomial 
			or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
modular                 single prime, transcendence degree 1, P-star 
			valuation iafmsp1psval(p,P,A) integral algebraic 
			function over 
modular                 single prime, transcendence degree 1, algebraic 
			function over modular single prime, transcendence 
			degree 1, evaluation special upprmsp1afes(p,F,P,a) 
			univariate polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, approximation 
			of P-adic factorization uspprmsp1apf(p,P,F,k) 
			univariate separable polynomial over polynomial 
			ring over 
modular                 single prime, transcendence degree 1, basis from 
			generators oprmsp1basfg(p,F,L) order over 
			polynomial ring over 
modular                 single prime, transcendence degree 1, basis of a 
			local maximal over-order ouspprmsp1bl(p,F,P,Q,pk) 
			order of an univariate separable polynomial over 
			polynomial ring over 
modular                 single prime, transcendence degree 1, decomposition 
			law affmsp1decl(p,F,P) algebraic function field 
			over 
modular                 single prime, transcendence degree 1, decomposition 
			law ouspprmsp1dl(p,F,P,k) order of a univariate 
			separable polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, derivation, 
			main variable prfmsp1deriv(r,p,P) polynomial over 
			rational functions over 
modular                 single prime, transcendence degree 1, difference 
			(rekursiv) prfmsp1dif(r,p,P1,P2) polynomial over 
			rational functions over 
modular                 single prime, transcendence degree 1, discriminant 
			upprmsp1disc(p,F) univariate polynomial over 
			polynomial ring over 
modular                 single prime, transcendence degree 1, evaluation 
			special upprmsp1afes(p,F,P,a) univariate polynomial 
			over polynomial ring over modular single prime, 
			transcendence degree 1, algebraic function over 
modular                 single prime, transcendence degree 1, 
			exponentiation special afmsp1expsp(p,F,a,e,M) 
			algebraic function over 
modular                 single prime, transcendence degree 1, extended 
			greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over rational functions over 
modular                 single prime, transcendence degree 1, from 
			coefficient list cdprfmsp1fcl(L,p) common 
			denominator polynomial over rational functions over 
modular                 single prime, transcendence degree 1, from common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over 
modular                 single prime, transcendence degree 1, from special 
			coefficient list uprfmsp1fscl(L) univariate 
			polynomial over rational functions over 
modular                 single prime, transcendence degree 1, from 
			univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common denominator polynomial 
			over rational functions over 
modular                 single prime, transcendence degree 1, hermitian 
			reduction cdmarfmsp1hr(p,M) common denominator 
			matrix of rational functions over 
modular                 single prime, transcendence degree 1, identity 
			construction cdmarfmsp1id(n) common denominator 
			matrix of rational functions over 
modular                 single prime, transcendence degree 1, integral 
			basis ouspprmsp1ib(p,F,pL) order of an univariate 
			separable polynomial over the polynomial ring over 
modular                 single prime, transcendence degree 1, inverse 
			cdprfmsp1inv(p,F,A) common denominator polynomial 
			over rational functions over 
modular                 single prime, transcendence degree 1, list from 
			common denominator matrix of rational functions 
			over modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over 
modular                 single prime, transcendence degree 1, negation 
			(rekursiv) prfmsp1neg(r,p,P) polynomial over 
			rational functions over 
modular                 single prime, transcendence degree 1, product 
			(rekursiv) prfmsp1prod(r,p,P1,P2) polynomial over 
			rational functions over 
modular                 single prime, transcendence degree 1, product 
			(rekursiv) prfmsp1rfprd(r,p,P,a) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, rational function over 
modular                 single prime, transcendence degree 1, product 
			special afmsp1prodsp(p,F,a,b,M) algebraic function 
			over 
modular                 single prime, transcendence degree 1, quotient and 
			remainder (rekursiv) prfmsp1qrem(r,p,P1,P2,pR) 
			polynomial over rational functions over 
modular                 single prime, transcendence degree 1, rational 
			function over modular single prime, transcendence 
			degree 1, product (rekursiv) prfmsp1rfprd(r,p,P,a) 
			polynomial over rational functions over 
modular                 single prime, transcendence degree 1, reduced 
			discriminant upprmsp1redd(p,F) univariate 
			polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, resultant, 
			Sylvester algorithm pprmsp1ress(r,p,P1,P2) 
			polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, resultant, 
			Sylvester algorithm upprmsp1ress(p,P1,P2) 
			univariate polynomial over polynomial ring over 
modular                 single prime, transcendence degree 1, sum 
			(rekursiv) prfmsp1sum(r,p,P1,P2) polynomial over 
			rational functions over 
modular                 single prime, transcendence degree 1, sum 
			cdprfmsp1sum(p,P1,P2) common denominator polynomial 
			over rational functions over 
modular                 single prime, transcendence degree 1, univariate 
			polynomial over modular single prime quotient 
			cdprfmsp1upq(p,F,P) common denominator polynomial 
			over rational functions over 
modular                 single primes Euklid- Gauss- step for columns 
			maupmspegsc(p,M,A,B) matrix of univariate 
			polynomials over 
modular                 single primes Euklid- Gauss- step for rows 
			maupmspegsr(p,M,A,B) matrix of univariate 
			polynomials over 
modular                 single primes Groebner basis augmentation 
			dipmspgba(r,p,PL,P) distributive polynomial over 
modular                 single primes Groebner basis dipmspgb(r,p,PL) 
			distributive polynomial over 
modular                 single primes Groebner basis recursion 
			dipmspgbr(r,p,PL) distributive polynomial over 
modular                 single primes S-polynomial dipmspsp(r,p,P1,P2) 
			distributive polynomial over 
modular                 single primes difference dipmspdif(r,p,P1,P2) 
			distributive polynomial over 
modular                 single primes elementary divisor form and cofactors 
			maupmspedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over 
modular                 single primes hermitian reduction, special 
			maupmshermsp(p,M,r,pD) matrix of univariate 
			polynomials over 
modular                 single primes iafmsp1mpmpp(p,F,a,P,e,Q) integral 
			algebraic function over modular single primes, 
			transcendence degree 1, minimal polynomial modulo 
			power of an univariate prime polynomial over 
modular                 single primes in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over 
modular                 single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
modular                 single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			in lexicographical order with inverse exponent 
			vector dipmsplotlio(r,p,P) distributive polynomial 
			over 
modular                 single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			with total degree ordering dipmsplottdo(r,p,P) 
			distributive polynomial over 
modular                 single primes in lexicographical order with inverse 
			exponent vector dipmsplotlio(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over 
modular                 single primes list fgetdipmspl(r,p,VL,pf) file get 
			distributive polynomial over 
modular                 single primes list fputdipmspl(r,p,PL,VL,pf) file 
			put distributive polynomial over 
modular                 single primes list getdipmspl(r,p,VL) (MACRO) get 
			distributive polynomial over 
modular                 single primes list putdipmspl(r,p,PL,VL) (MACRO) 
			put distributive polynomial over 
modular                 single primes monic dipmspmonic(r,p,P) distributive 
			polynomial over 
modular                 single primes negation dipmspneg(r,p,P) 
			distributive polynomial over 
modular                 single primes product dipmspmsprod(r,p,P,a) 
			distributive polynomial over modular single primes, 
modular                 single primes product dipmspprod(r,p,P1,P2) 
			distributive polynomial over 
modular                 single primes sum dipmspsum(r,p,P1,P2) distributive 
			polynomial over 
modular                 single primes transcendence degree 1, determinant 
			marfmsp1det(p,M) matrix of rational functions over 
modular                 single primes transcendence degree 1, difference 
			marfmsp1dif(p,M,N) (MACRO) matrix of rational 
			functions over 
modular                 single primes with total degree ordering 
			dipmsplottdo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over 
modular                 single primes, modular single primes product 
			dipmspmsprod(r,p,P,a) distributive polynomial over 
modular                 single primes, short normal form, Shanks' algorithm 
			ecmspsnfsha(p,a4,a6) (MACRO) elliptic curve over 
modular                 single primes, short normal form, number of points 
			ecmspsnfnp(p,a4,a6) elliptic curve over 
modular                 single primes, transcendence degree 1 ? 
			ismarfmsp1(p,M) (MACRO) is matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1 ? 
			isvecrfmsp1(p,V) (MACRO) is vector of rational 
			functions over 
modular                 single primes, transcendence degree 1 
			fgetmarfmsp1(p,V,pf) (MACRO) file get matrix of 
			rational functions over 
modular                 single primes, transcendence degree 1 
			fgetrfmsp1(p,V,pf) file get rational function over 
modular                 single primes, transcendence degree 1 
			fgetvrfmsp1(p,VL,pf) (MACRO) file get vector of 
			rational functions over 
modular                 single primes, transcendence degree 1 
			fputmarfmsp1(p,M,V,pf) (MACRO) file put matrix of 
			rational functions over 
modular                 single primes, transcendence degree 1 
			fputvrfmsp1(p,V,VL,pf) (MACRO) file put vector of 
			rational functions over 
modular                 single primes, transcendence degree 1 
			getmarfmsp1(p,V) (MACRO) get matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1 
			getrfmsp1(p,V) (MACRO) get rational function over 
modular                 single primes, transcendence degree 1 
			getvecrfmsp1(p,VL) (MACRO) get vector of rational 
			functions over 
modular                 single primes, transcendence degree 1 
			mpmstmrfmsp1(p,M) matrix of polynomials over 
			modular singles to matrix of rational functions 
			over 
modular                 single primes, transcendence degree 1 
			putmarfmsp1(p,M,V) (MACRO) put matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1 
			putvecrfmsp1(p,V,VL) (MACRO) put vector of rational 
			functions over 
modular                 single primes, transcendence degree 1 
			vpmstvrfmsp1(p,V) vector of polynomials over 
			modular singles to vector of rational functions 
			over 
modular                 single primes, transcendence degree 1, construction 
			1 marfmsp1c1(p,n) (MACRO) matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1, core 
			algorithm afmsp1coreal(p,F,P,Q,mp) algebraic 
			function over 
modular                 single primes, transcendence degree 1, difference 
			vecrfmsp1dif(p,U,V) (MACRO) vector of rational 
			functions over 
modular                 single primes, transcendence degree 1, element test 
			modprmsp1elt(B,p,a) module over polynomial ring 
			over 
modular                 single primes, transcendence degree 1, 
			exponentiation marfmsp1exp(p,M,n) matrix of 
			rational functions over 
modular                 single primes, transcendence degree 1, increasing 
			the denominator of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over 
modular                 single primes, transcendence degree 1, inverse 
			marfmsp1inv(p,M) matrix of rational functions over 
modular                 single primes, transcendence degree 1, inverse 
			rfmsp1inv(p,R) rational function over 
modular                 single primes, transcendence degree 1, linear 
			combination vecrfmsp1lc(p,F1,F2,V1,V2) vector of 
			rational functions over 
modular                 single primes, transcendence degree 1, minimal 
			polynomial afmsp1minpol(p,F,a) algebraic function 
			over 
modular                 single primes, transcendence degree 1, minimal 
			polynomial iafmsp1mpol(p,F,a,Q) integral algebraic 
			function over 
modular                 single primes, transcendence degree 1, minimal 
			polynomial modulo power of an univariate prime 
			polynomial over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over 
modular                 single primes, transcendence degree 1, module 
			homomorphism cdprfmsp1mh(p,P,M) common denominator 
			polynomial over rational functions over 
modular                 single primes, transcendence degree 1, negation 
			marfmsp1neg(p,M) (MACRO) matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1, negation 
			vecrfmsp1neg(p,V) (MACRO) vector of rational 
			functions over 
modular                 single primes, transcendence degree 1, null space 
			basis marfmsp1nsb(p,M) matrix of rational functions 
			over 
modular                 single primes, transcendence degree 1, product 
			marfmsp1prod(p,M,N) (MACRO) matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1, rank 
			marfmsp1rk(p,M) matrix of rational functions over 
modular                 single primes, transcendence degree 1, regulation 
			afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) algebraic 
			function over 
modular                 single primes, transcendence degree 1, scalar 
			multiplication marfmsp1smul(p,M,F) matrix of 
			rational functions over 
modular                 single primes, transcendence degree 1, scalar 
			multiplication vecrfmsp1sm(p,F,V) vector of 
			rational functions over 
modular                 single primes, transcendence degree 1, scalar 
			product vecrfmsp1sp(p,V,W) vector of rational 
			functions over 
modular                 single primes, transcendence degree 1, solution of 
			a system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1, sum 
			marfmsp1sum(p,M,N) (MACRO) matrix of rational 
			functions over 
modular                 single primes, transcendence degree 1, sum 
			vecrfmsp1sum(p,U,V) (MACRO) vector of rational 
			functions over 
modular                 single primes, transcendence degree 1, vector 
			multiplication marfmsp1vmul(p,A,x) (MACRO) matrix 
			of rational functions over 
modular                 single product (rekursiv) pmsmsprod(r,m,P,a) 
			polynomial over modular singles, 
modular                 single product msprod(m,a,b) 
modular                 single product udpmsmsprod(m,P,a) univariate dense 
			polynomial over modular singles, 
modular                 single putms(m,a) (MACRO) put 
modular                 single quotient (rekursiv) pmsmsquot(r,m,P,a) 
			polynomial over modular singles, 
modular                 single quotient msquot(m,a,b) (MACRO) 
modular                 single sum as function mssumf(m,a,b) 
modular                 single sum mssum(m,a,b) (MACRO) 
modular                 single trailing base coefficient udpmstbc(m,P) 
			univariate dense polynomial over 
modular                 single units msunits(m) 
modular                 single-precision homomorphism, symmetric remainder 
			system mshoms(m,A) (MACRO) 
modular                 singles (rekursiv) pitopms(r,P,m) polynomial over 
			integers to polynomial over 
modular                 singles ? (rekursiv) isdpms(r,m,P) is dense 
			polynomial over 
modular                 singles ? (rekursiv) ispms(r,m,P) is polynomial 
			over 
modular                 singles ? isimupms(p,A) is irreducible, monic, 
			univariate polynomial over 
modular                 singles ? islistms(m,A) is list of 
modular                 singles ? ismadpms(r,m,M) (MACRO) is matrix of 
			dense polynomials over 
modular                 singles ? ismams(m,M) (MACRO) is matrix of 
modular                 singles ? ismapms(r,m,M) (MACRO) is matrix of 
			polynomials over 
modular                 singles ? isvecdpms(r,m,V) (MACRO) is vector of 
			dense polynomials over 
modular                 singles ? isvecms(m,A) (MACRO) is vector of 
modular                 singles ? isvecpms(r,m,V) (MACRO) is vector of 
			polynomials over 
modular                 singles Berlekamp factorization, last step 
			upmsbfls(m,P,B,d) univariate polynomial over 
modular                 singles Bezout-matrix pmsbezout(r,m,P1,P2) 
			polynomial over 
modular                 singles Jacobi-symbol udpmsjacsym(m,P1,P2) 
			univariate dense polynomial over 
modular                 singles Jacobi-symbol upmsjacsym(m,P1,P2) 
			univariate polynomial over 
modular                 singles additive valuation upmsaddval(p,P1,P) 
			univariate polynomial over 
modular                 singles characteristic polynomial mamschpol(m,M) 
			(MACRO) matrix of 
modular                 singles characteristic polynomial mapmschpol(r,m,M) 
			(MACRO) matrix of polynomials over 
modular                 singles complete factorization upmscfact(p,A) 
			univariate polynomial over 
modular                 singles construction 1 mamscons1(m,n) (MACRO) 
			matrix of 
modular                 singles construction 1 mapmscons1(r,m,n) (MACRO) 
			matrix of polynomials over 
modular                 singles derivation udpmsderiv(m,P) univariate dense 
			polynomial over 
modular                 singles derivation, main variable pmsderiv(r,m,P) 
			polynomial over 
modular                 singles derivation, specified variable (rekursiv) 
			pmsderivsv(r,m,P,n) polynomial over 
modular                 singles determinant mamsdet(m,M) matrix of 
modular                 singles determinant mapmsdet(r,m,M) matrix of 
			polynomials over 
modular                 singles difference (rekursiv) dpmsdif(r,m,P1,P2) 
			dense polynomial over 
modular                 singles difference (rekursiv) pmsdif(r,m,P1,P2) 
			polynomial over 
modular                 singles difference mamsdif(m,M,N) (MACRO) matrix of 
modular                 singles difference mapmsdif(r,m,M,N) (MACRO) matrix 
			of polynomials over 
modular                 singles difference udpmsdif(m,P1,P2) univariate 
			dense polynomial over 
modular                 singles difference vecmsdif(m,U,V) (MACRO) vector 
			of 
modular                 singles difference vecpmsdif(r,m,U,V) (MACRO) 
			vector of polynomials over 
modular                 singles discriminant pmsdiscr(r,m,P,n) polynomial 
			over 
modular                 singles divisor class number qffmsdcn(m,P) 
			quadratic function field over 
modular                 singles divisor class number subroutine 1 
			qffmsdcns1(m,P) quadratic function field over 
modular                 singles divisor class number subroutine 2 
			qffmsdcns2(m,P) quadratic function field over 
modular                 singles divisor class number subroutine 3 
			qffmsdcns3(m,P) quadratic function field over 
modular                 singles eigenvalues and irreducible factors of the 
			characteristic polynomial mamsevifcp(p,M,pL) matrix 
			of 
modular                 singles eigenvalues mamsev(p,M) (MACRO) matrix of 
modular                 singles evaluation, main variable pmseval(r,m,P,a) 
			polynomial over 
modular                 singles evaluation, specified variable (rekursiv) 
			pmsevalsv(r,m,P,n,a) polynomial over 
modular                 singles exponentiation mamsexp(m,M,n) matrix of 
modular                 singles exponentiation mapmsexp(r,m,M,n) matrix of 
			polynomials over 
modular                 singles exponentiation pmsexp(r,m,P,n) polynomial 
			over 
modular                 singles extended greatest common divisor 
			udpmsegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over 
modular                 singles extended greatest common divisor 
			upmsegcd(m,P1,P2,pP3,pP4) univariate polynomial 
			over 
modular                 singles factorization, Berlekamp algorithm 
			upmsbfact(p,A,d) univariate polynomial over 
modular                 singles fgetmams(m,pf) (MACRO) file get matrix of 
modular                 singles fgetmapms(r,m,V,pf) (MACRO) file get matrix 
			of polynomials over 
modular                 singles fgetpms(r,m,V,pf) file get polynomial over 
modular                 singles fgetvecms(m,pf) (MACRO) file get vector of 
modular                 singles fgetvecpms(r,m,VL,pf) (MACRO) file get 
			vector of polynomials over 
modular                 singles fputmams(m,M,pf) (MACRO) file put matrix of 
modular                 singles fputmapms(r,m,M,V,pf) (MACRO) file put 
			matrix of polynomials over 
modular                 singles fputpms(r,m,P,V,pf) file put polynomial 
			over 
modular                 singles fputvecms(m,V,pf) (MACRO) file put vector 
			of 
modular                 singles fputvecpms(r,m,V,VL,pf) (MACRO) file put 
			vector of polynomials over 
modular                 singles fundamental unit, baby step version 
			qffmsfubs(m,D) quadratic function field over 
modular                 singles fundamental unit, original version 
			qffmsfuobs(m,D) quadratic function field over 
modular                 singles getmams(m) (MACRO) get matrix of 
modular                 singles getmapms(r,m,V) (MACRO) get matrix of 
			polynomials over 
modular                 singles getpms(r,m,V) (MACRO) get polynomial over 
modular                 singles getvecms(m) (MACRO) get vector of 
modular                 singles getvecpms(r,m,VL) (MACRO) get vector of 
			polynomials over 
modular                 singles greatest common divisor and cofactors 
			(rekursiv) pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial 
			over 
modular                 singles greatest common divisor udpmsgcd(m,P1,P2) 
			univariate dense polynomial over 
modular                 singles greatest common divisor upmsgcd(m,P1,P2) 
			univariate polynomial over 
modular                 singles greatest squarefree divisor (rekursiv) 
			upmsgsd(m,P) univariate polynomial over 
modular                 singles half extended greatest common divisor 
			udpmshegcd(m,P1,P2,pP3) univariate dense polynomial 
			over 
modular                 singles half extended greatest common divisor 
			upmshegcd(m,P1,P2,pP3) univariate polynomial over 
modular                 singles ideal class group generators and isomorphy 
			type, imaginary case qffmsicggii(m,D,H,L,pIT) 
			quadratic function field over 
modular                 singles ideal class group generators and isomorphy 
			type, real case qffmsicggir(m,D,d,H,L,pIT) 
			quadratic function field over 
modular                 singles ideal class group structure, imaginary case 
			qffmsicgsti(m,D,L) quadratic function field over 
modular                 singles ideal class group structure, real case 
			qffmsicgstr(m,D,d,LG,pHid) quadratic function field 
			over 
modular                 singles ideal class group system of representatives 
			qffmsicgrep(m,D,pHid) quadratic function field over 
modular                 singles ideal class group system of 
			representatives, imaginary case 
			qffmsicgri(m,D,pHid) quadratic function field over 
modular                 singles ideal class group system of 
			representatives, real case qffmsicgrr(m,D,d) 
			quadratic function field over 
modular                 singles ideal class number qffmsicn(m,P) quadratic 
			function field over 
modular                 singles interpolation (rekursiv) 
			pmsinter(r,m,P1,P2,P3,a,b) polynomial over 
modular                 singles inverse mamsinv(m,M) matrix of 
modular                 singles inverse mapmsinv(r,m,M) matrix of 
			polynomials over 
modular                 singles is element of an ideal class 
			qffmsiselic(m,D,L,Q,P) quadratic function field 
			over 
modular                 singles is equal ideal special 
			qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic function 
			field over 
modular                 singles linear combination vecmslc(m,s1,s2,L1,L2) 
			vector of 
modular                 singles linear combination 
			vecpmslc(r,m,P1,P2,V1,V2) vector of polynomials 
			over 
modular                 singles maitomams(m,M) matrix of integers to matrix 
			of 
modular                 singles mapitomapms(r,M,m) matrix of polynomials 
			over integers to matrix of polynomials over 
modular                 singles mapmstomapmp(r,m,P,M) matrix of polynomials 
			over modular singles to matrix of polynomials 
			modulo polynomial over 
modular                 singles monic pmsmonic(r,m,P) polynomial over 
modular                 singles monic udpmsmonic(m,P) univariate dense 
			polynomial over 
modular                 singles negation (rekursiv) dpmsneg(r,m,P) dense 
			polynomial over 
modular                 singles negation (rekursiv) pmsneg(r,m,P) 
			polynomial over 
modular                 singles negation mamsneg(m,M) (MACRO) matrix of 
modular                 singles negation mapmsneg(r,m,M) (MACRO) matrix of 
			polynomials over 
modular                 singles negation udpmsneg(m,P) univariate dense 
			polynomial over 
modular                 singles negation vecmsneg(m,V) (MACRO) vector of 
modular                 singles negation vecpmsneg(r,m,V) (MACRO) vector of 
			polynomials over 
modular                 singles null space basis mamsnsb(p,A) (MACRO) 
			matrix of 
modular                 singles order of one single ideal class, imaginary 
			case qffmsordsici(m,D,Q,P,OS) quadratic function 
			field over 
modular                 singles order of one single ideal class, real case 
			qffmsordsicr(m,D,d,LE,ID,OS) quadratic function 
			field over 
modular                 singles primitive ideal product 
			qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over 
modular                 singles primitive ideal product, special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over 
modular                 singles primitive ideal square 
			qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
			field over 
modular                 singles primitive ideal square, special version 
			qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over 
modular                 singles product (rekursiv) dpmsprod(r,m,P1,P2) 
			dense polynomial over 
modular                 singles product (rekursiv) pmsprod(r,m,P1,P2) 
			polynomial over 
modular                 singles product (rekursiv) pmsupmsprod(r,m,P1,P2) 
			polynomial over modular singles, univariate 
			polynomial over 
modular                 singles product mamsprod(m,M,N) (MACRO) matrix of 
modular                 singles product mapmsprod(r,m,M,N) (MACRO) matrix 
			of polynomials over 
modular                 singles product udpmsprod(m,P1,P2) univariate dense 
			polynomial over 
modular                 singles pseudo remainder pmspsrem(r,m,P1,P2) 
			polynomial over 
modular                 singles putmams(m,M) (MACRO) put matrix of 
modular                 singles putmapms(r,m,M,V) (MACRO) put matrix of 
			polynomials over 
modular                 singles putpms(r,m,P,V) (MACRO) put polynomial over 
modular                 singles putvecms(m,V) (MACRO) put vector of 
modular                 singles putvecpms(r,m,V,VL) (MACRO) put vector of 
			polynomials over 
modular                 singles quotient (rekursiv) pmsupmsquot(r,m,P1,P2) 
			polynomial over modular singles, univariate 
			polynomial over 
modular                 singles quotient and remainder (rekursiv) 
			pmsqrem(r,m,P1,P2,pR) polynomial over 
modular                 singles quotient and remainder 
			udpmsqrem(m,P1,P2,pP3) univariate dense polynomial 
			over 
modular                 singles quotient pmsquot(r,m,P1,P2) (MACRO) 
			polynomial over 
modular                 singles quotient udpmsquot(m,P1,P2) (MACRO) 
			univariate dense polynomial over 
modular                 singles reduction of a real quadratic irrational 
			qffmsrqired(m,D,d,Q,P,pPr) quadratic function field 
			over 
modular                 singles regulator qffmsreg(m,P) quadratic function 
			field over 
modular                 singles regulator, baby step - giant step version 
			qffmsregbg(m,D) quadratic function field over 
modular                 singles regulator, baby step - giant step version, 
			first case qffmsregbg1(m,D,s) quadratic function 
			field over 
modular                 singles regulator, baby step - giant step version, 
			fourth case qffmsregbg4(m,D,s) quadratic function 
			field over 
modular                 singles regulator, baby step - giant step version, 
			second case qffmsregbg2(m,D,s) quadratic function 
			field over 
modular                 singles regulator, baby step - giant step version, 
			third case qffmsregbg3(m,D,s) quadratic function 
			field over 
modular                 singles regulator, baby step version 
			qffmsregbs(m,D) quadratic function field over 
modular                 singles regulator, original baby step - giant step 
			version qffmsregobg(m,D) quadratic function field 
			over 
modular                 singles regulator, original baby step version 
			qffmsregobs(m,D) quadratic function field over 
modular                 singles relative prime factorization 
			upmsrelpfact(p,P,Fak,pA2) univariate polynomial 
			over 
modular                 singles remainder pmsrem(r,m,P1,P2) (MACRO) 
			polynomial over 
modular                 singles remainder udpmsrem(m,P1,P2) univariate 
			dense polynomial over 
modular                 singles remainder upmsrem(m,P1,P2) univariate 
			polynomial over 
modular                 singles resultant and cofactor of resultant 
			equation upmsresulc(m,P1,P2,pC) univariate 
			polynomial over 
modular                 singles resultant pmsres(r,m,P1,P2,n) polynomial 
			over 
modular                 singles resultant upmsres(m,P1,P2) univariate 
			polynomial over 
modular                 singles resultant, Collins algorithm (rekursiv) 
			pmsrescoll(r,m,P1,P2) polynomial over 
modular                 singles scalar multiplication mamssmul(m,M,el) 
			matrix of 
modular                 singles scalar multiplication mapmssmul(r,m,M,P) 
			matrix of polynomials over 
modular                 singles scalar multiplication vecmssmul(m,s,V) 
			vector of 
modular                 singles scalar multiplication vecpmssmul(r,m,P,V) 
			vector of polynomials over 
modular                 singles scalar product vecmssprod(m,V,W) vector of 
modular                 singles scalar product vecpmssprod(r,m,V,W) vector 
			of polynomials over 
modular                 singles solution of a system of linear equations 
			mamsssle(p,A,b,pX,pN) matrix of 
modular                 singles square root power series upmssrpser(m,P,i) 
			univariate polynomial over 
modular                 singles square root principal part upmssrpp(m,P) 
			univariate polynomial over 
modular                 singles squarefree factorization (rekursiv) 
			upmssfact(m,P) univariate polynomial over 
modular                 singles squarefree part upmssfp(m,P) univariate 
			polynomial over 
modular                 singles substitution, main variable 
			pmssubst(r,m,P1,P2) polynomial over 
modular                 singles substitution, specified variable (rekursiv) 
			pmssubstsv(r,m,P1,n,P2) polynomial over 
modular                 singles sum (rekursiv) dpmssum(r,m,P1,P2) dense 
			polynomial over 
modular                 singles sum (rekursiv) pmssum(r,m,P1,P2) polynomial 
			over 
modular                 singles sum mamssum(m,M,N) (MACRO) matrix of 
modular                 singles sum mapmssum(r,m,M,N) (MACRO) matrix of 
			polynomials over 
modular                 singles sum udpmssum(m,P1,P2) univariate dense 
			polynomial over 
modular                 singles sum vecmssum(m,U,V) (MACRO) vector of 
modular                 singles sum vecpmssum(r,m,U,V) (MACRO) vector of 
			polynomials over 
modular                 singles to matrix of polynomials modulo polynomial 
			over modular singles mapmstomapmp(r,m,P,M) matrix 
			of polynomials over 
modular                 singles to matrix of polynomials over Galois-field 
			with single characteristic mpmstompgfs(r,p,M) 
			matrix of polynomials over 
modular                 singles to matrix of rational functions over 
			modular single primes, transcendence degree 1 
			mpmstmrfmsp1(p,M) matrix of polynomials over 
modular                 singles to polynomial over Galois-field with single 
			characteristic (rekursiv) pmstopgfs(r,p,P) 
			polynomial over 
modular                 singles to rational function over modular single 
			prime, transcendence degree 1 pmstorfmsp1(p,P) 
			(MACRO) polynomial over 
modular                 singles to vector of polynomials modulo polynomial 
			over modular singles vecpmstovpmp(r,m,P,V) vector 
			of polynomials over 
modular                 singles to vector of polynomials over Galois-field 
			with single characteristic vpmstovpgfs(r,p,V) 
			vector of polynomials over 
modular                 singles to vector of rational functions over 
			modular single primes, transcendence degree 1 
			vpmstvrfmsp1(p,V) vector of polynomials over 
modular                 singles transformation 
			mapmstransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over 
modular                 singles transformation 
			pmstransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over 
modular                 singles transformation upmstransf(m,P,r,P1) 
			univariate polynomial over 
modular                 singles transformation 
			vpmstransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over 
modular                 singles translation, all variables (rekursiv) 
			pmstransav(r,m,P,Lms) polynomial over 
modular                 singles translation, main variable 
			pmstrans(r,m,P,a) polynomial over 
modular                 singles unit? ispmsunit(r,m,P) is polynomial over 
modular                 singles univariate content (rekursiv) 
			pmsucont(r,m,P) polynomial over 
modular                 singles vecitovecms(m,V) vector of integers to 
			vector of 
modular                 singles vecpitovpms(r,V,m) vector of polynomials 
			over integers to vector of polynomials over 
modular                 singles vecpmstovpmp(r,m,P,V) vector of polynomials 
			over modular singles to vector of polynomials 
			modulo polynomial over 
modular                 singles vector multiplication mamsvecmul(m,A,x) 
			(MACRO) matrix of 
modular                 singles vector multiplication mapmsvecmul(r,m,A,x) 
			(MACRO) matrix of polynomials over 
modular                 singles zero class group isomorphy type, imaginary 
			case qffmszcgiti(m,D,LG,IT) quadratic function 
			field over 
modular                 singles zero class group isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function 
			field over 
modular                 singles, Berlekamp Q polynomials construction 
			upmsbqp(p,A) univariate polynomial over 
modular                 singles, Berlekamp factorization, Zassenhaus method 
			upmsbfzm(m,s,P,G) univariate polynomial over 
modular                 singles, imaginary case, primitive ideal reduction 
			qffmsipidred(m,D,Q,P,pQr,pPr) quadratic function 
			field over 
modular                 singles, imaginary case, sparse representation, 
			reduction of a primitive ideal 
			qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic function 
			field over 
modular                 singles, irreducible and monic trinomial, generator 
			upmsimtgen(p,n) univariate polynomial over 
modular                 singles, irreducible and monic, generator 
			upmsimgen(p,n) univariate polynomial over 
modular                 singles, modular single product (rekursiv) 
			pmsmsprod(r,m,P,a) polynomial over 
modular                 singles, modular single product udpmsmsprod(m,P,a) 
			univariate dense polynomial over 
modular                 singles, modular single quotient (rekursiv) 
			pmsmsquot(r,m,P,a) polynomial over 
modular                 singles, monomial, polynomial, remainder 
			upmsmprem(m,k,T,P) univariate polynomial over 
modular                 singles, number of irreducible factors upmsnif(m,P) 
			univariate polynomial over 
modular                 singles, principal ideal generating element, real 
			case, qffmspidgenr(m,D,Q,P,G,pB) quadratic function 
			field over 
modular                 singles, real case, reduction of a primitive ideal 
			qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over 
modular                 singles, real case, sparse representation, 
			reduction of a primitive ideal 
			qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over 
modular                 singles, root finding (rekursiv) upmsrf(m,P) 
			univariate polynomial over 
modular                 singles, sparse representation, primitive ideal 
			product qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over 
modular                 singles, sparse representation, primitive ideal 
			product, special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over 
modular                 singles, sparse representation, primitive ideal 
			square qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic 
			function field over 
modular                 singles, sparse representation, primitive ideal 
			square, special version 
			qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over 
modular                 singles, sparse representation, reduction of a real 
			quadratic irrational qffmssrqired(m,D,d,Q,P,pPr) 
			quadratic function field over 
modular                 singles, summation over Jacobi-symbols 
			udpmssumjs(m,P,n) univariate dense polynomial over 
modular                 singles, univariate polynomial over modular singles 
			product (rekursiv) pmsupmsprod(r,m,P1,P2) 
			polynomial over 
modular                 singles, univariate polynomial over modular singles 
			quotient (rekursiv) pmsupmsquot(r,m,P1,P2) 
			polynomial over 
module                  homomorphism cdprfmsp1mh(p,P,M) common denominator 
			polynomial over rational functions over modular 
			single primes, transcendence degree 1, 
module                  over polynomial ring over modular single primes, 
			transcendence degree 1, element test 
			modprmsp1elt(B,p,a) 
module                  over the integers element test modielemtest(B,a) 
module                  over the integers, LLL reduction modilllred(bas) 
module                  over the integers, orthogonalized basis 
			modiorthobas(bas) 
modulo                  2 ecmpsnfnpm2(P,a4,a6) elliptic curve over modular 
			primes, short normal form, number of points 
modulo                  4 ecqnfdmod4(E) (MACRO) elliptic curve over 
			quadratic number field, field discriminant 
modulo                  a power of 2 ecgf2npmp2(G,a6,c,L) elliptic curve 
			over Galois-field with characteristic 2, number of 
			points 
modulo                  a prime ideal qnfsysrmodpi(D,P,pi,z,k) quadratic 
			number field system of representatives 
modulo                  a single prime determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
			modular primes, short normal form, number of points 
modulo                  a single prime determined with the Schoof 
			algorithm, version 1 ecgf2npmspv1(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, number of points 
modulo                  a single prime determined with the Schoof 
			algorithm, version 2 ecgf2npmspv2(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, number of points 
modulo                  an integer determined with the Schoof algorithm 
			ecgf2npmi(G,a6,S,v,pM) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points 
modulo                  an integer determined with the Schoof algorithm 
			ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve over 
			modular primes, short normal form, number of points 
modulo                  integer nfelmodi(F,a,M) number field element 
modulo                  p-power infeminpmpp(F,a,p,e,Q) integral number 
			field element minimal polynomial 
modulo                  p-power with respect to integer primes 
			infempmppip(F,a,p,e,Q) integral number field 
			element minimal polynomial 
modulo                  polynomial over Galois-field with single 
			characteristic mpgfstompmp(r,p,AL,P,M) matrix of 
			polynomials over Galois-field with single 
			characteristic to matrix of polynomials 
modulo                  polynomial over Galois-field with single 
			characteristic vpgfstovpmp(r,p,AL,P,V) vector of 
			polynomials over Galois-field with single 
			characteristic to vector of polynomials 
modulo                  polynomial over integers mapitompmpi(r,M,P) matrix 
			of polynomials over integers to matrix of 
			polynomials 
modulo                  polynomial over integers vecpitvpmpi(r,V,P) vector 
			of polynomials over integers to vector of 
			polynomials 
modulo                  polynomial over modular integers 
			mapmitomapmp(r,m,P,M) matrix of polynomials over 
			modular integers to matrix of polynomials 
modulo                  polynomial over modular integers 
			vecpmitovpmp(r,m,P,V) vector of polynomials over 
			modular integers to vector of polynomials 
modulo                  polynomial over modular singles 
			mapmstomapmp(r,m,P,M) matrix of polynomials over 
			modular singles to matrix of polynomials 
modulo                  polynomial over modular singles 
			vecpmstovpmp(r,m,P,V) vector of polynomials over 
			modular singles to vector of polynomials 
modulo                  polynomial over number field mapnftomapmp(r,F,P,M) 
			matrix of polynomials over number field to matrix 
			of polynomials 
modulo                  polynomial over number field vecpnftovpmp(r,F,P,V) 
			vector of polynomials over number field to vector 
			of polynomials 
modulo                  polynomial over rationals maprtompmpr(r,M,P) matrix 
			of polynomials over rationals to matrix of 
			polynomials 
modulo                  polynomial over rationals vecprtvpmpr(r,V,P) vector 
			of polynomials over rationals to vector of 
			polynomials 
modulo                  power of an univariate prime polynomial over 
			modular single primes iafmsp1mpmpp(p,F,a,P,e,Q) 
			integral algebraic function over modular single 
			primes, transcendence degree 1, minimal polynomial 
modulo                  prime abnfrelclmp(m,q,g) abelian number field 
			relative class number 
modulo                  prime eciminbrtmp(E,p,n) elliptic curve with 
			integer coefficients, minimal model, bad reduction 
			type 
modulo                  prime eciminmrtmp(E,p) elliptic curve with integer 
			coefficients, minimal model, multiplicative 
			reduction type 
modulo                  torsion eciminpcompmt(E,P1,P2) elliptic curve with 
			integer coefficients, minimal model, point 
			comparison 
modulo                  with reference to SIMATH mods(A,B) (MACRO) 
monic                   dipgfsmonic(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic 
monic                   dipmipmonic(r,p,P) distributive polynomial over 
			modular integer primes 
monic                   dipmspmonic(r,p,P) distributive polynomial over 
			modular single primes 
monic                   dipnfmonic(r,F,P) distributive polynomial over 
			number field 
monic                   diprfrmonic(r1,r2,P) distributive polynomial over 
			rational functions over the rationals 
monic                   diprmonic(r,P) distributive polynomial over 
			rationals 
monic                   pgf2monic(r,G,P) polynomial over Galois-field with 
			characteristic 2 
monic                   pgfsmonic(r,p,AL,P) polynomial over Galois-field 
			with single characteristic 
monic                   pmimonic(r,M,P) polynomial over modular integers 
monic                   pmsmonic(r,m,P) polynomial over modular singles 
monic                   pnfmonic(r,F,P) polynomial over number field 
monic                   polynomial in special bit-representation ? 
			isgf2impsb(G) is Galois-field with characteristic 2 
			irreducible and 
monic                   polynomial in special bit-representation generator 
			gf2impsbgen(n,H) Galois-field with characteristic 2 
			irreducible and 
monic                   trinomial, generator upm2imtgen(n) univariate 
			polynomial over modular 2, irreducible and 
monic                   trinomial, generator upmsimtgen(p,n) univariate 
			polynomial over modular singles, irreducible and 
monic                   udpmimonic(m,P) univariate dense polynomial over 
			modular integers 
monic                   udpmsmonic(m,P) univariate dense polynomial over 
			modular singles 
monic,                  generator upm2imgen(n) univariate polynomial over 
			modular 2, irreducible and 
monic,                  generator upmsimgen(p,n) univariate polynomial over 
			modular singles, irreducible and 
monic,                  modular ideal quotient and remainder 
			pmimidqrem(r,M,S,P1,P2,pR) polynomial over modular 
			integers 
monic,                  univariate polynomial over modular integers ? 
			isimupmi(p,A) is irreducible, 
monic,                  univariate polynomial over modular singles ? 
			isimupms(p,A) is irreducible, 
monomial                ? ispmonom(r,P) is polynomial 
monomial                advance dipmoad(r,P,pLBC,pLEV) distributive 
			polynomial 
monomial                dipevl(r,P) distributive polynomial exponent vector 
			of the leading 
monomial                dipfmo(r,BC,EV) (MACRO) distributive polynomial 
			from 
monomial,               integer exponentiation, polynomial, remainder 
			upgfsmieprem(p,AL,a,t,P) univariate polynomial over 
			Galois-field, 
monomial,               polynomial, remainder upgf2mprem(G,a,T,P) 
			univariate polynomial over Galois-field with 
			characteristic 2, 
monomial,               polynomial, remainder upgfsmprem(p,AL,a,T,P) 
			univariate polynomial over Galois-field, 
monomial,               polynomial, remainder upmimprem(ip,K,E,P) 
			univariate polynomial over modular integers, 
monomial,               polynomial, remainder upmsmprem(m,k,T,P) univariate 
			polynomial over modular singles, 
mpgfstompmp(r,p,AL,P,M) matrix of polynomials over Galois-field with single 
			characteristic to matrix of polynomials modulo 
			polynomial over Galois-field with single 
			characteristic 
mpmstmrfmsp1(p,M)       matrix of polynomials over modular singles to 
			matrix of rational functions over modular single 
			primes, transcendence degree 1 
mpmstompgfs(r,p,M)      matrix of polynomials over modular singles to 
			matrix of polynomials over Galois-field with single 
			characteristic 
mppsqrt(p,n,r,xk,k)     modular prime power square root 
mpsqrt(p,a)             modular primes square root 
mscra(m1,m2,n1,a1,a2)   modular single chinese remainder algorithm 
mscran(n,Lm,La)         modular single chinese remainder algorithm, n 
			arguments (rekursiv) 
msdif(m,a,b)            (MACRO) modular single difference 
msexp(m,a,n)            modular single exponentiation 
msfrl(m,a)              modular single Fermat residue list 
mshom(m,A)              modular single homomorphism 
mshoms(m,A)             (MACRO) modular single-precision homomorphism, 
			symmetric remainder system 
msinv(m,a)              modular single inverse 
mslcra(m1,m2,L1,L2)     modular single list chinese remainder algorithm 
msneg(m,a)              (MACRO) modular single negation 
msnegf(m,a)             modular single negation as function 
msprod(m,a,b)           modular single product 
msquot(m,a,b)           (MACRO) modular single quotient 
mssum(m,a,b)            (MACRO) modular single sum 
mssumf(m,a,b)           modular single sum as function 
msunits(m)              modular single units 
mudpitmudpr(M)          matrix of univariate dense polynomials over 
			integers to matrix of univariate dense polynomials 
			over rationals 
mudpitudpmi(M,m)        matrix of univariate dense polynomials over 
			integers to matrix of univariate dense polynomials 
			over modular integers 
multiple                dipevlcm(r,EV1,EV2) distributive polynomial 
			exponent vector least common 
multiple                ilcm(A,B) integer least common 
multiple                of the order of a point to exact order of the point 
			ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve 
			over Galois-field with characteristic 2, 
multiple                of the order of a point to exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular primes, short normal form, 
multiple                of the order of a point with the Pollard Lambda 
			method ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) 
			elliptic curve over Galois-field with 
			characteristic 2, finding a 
multiple                of the order of a point with the Pollard Lambda 
			method ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve 
			over modular primes, short normal form, finding a 
multiple                of the order of a point with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular primes, short normal form, finding a 
multiple                test dipevmt(r,EV1,EV2) distributive polynomial 
			exponent vector 
multiplication          HDimul() Heidelberg arithmetic package: integer 
multiplication          PAFmul() Papanikolaou floating point package: 
multiplication          magfssmul(p,AL,M,el) matrix of Galois-field with 
			single characteristic elements scalar 
multiplication          magfsvecmul(p,AL,A,x) (MACRO) matrix of 
			Galois-field with single characteristic elements 
			vector 
multiplication          maismul(M,el) matrix of integers scalar 
multiplication          maivecmul(A,x) (MACRO) matrix of integers vector 
multiplication          mamismul(m,M,el) matrix of modular integers scalar 
multiplication          mamivecmul(m,A,x) (MACRO) matrix of modular 
			integers vector 
multiplication          mamssmul(m,M,el) matrix of modular singles scalar 
multiplication          mamsvecmul(m,A,x) (MACRO) matrix of modular singles 
			vector 
multiplication          manfsmul(F,M,el) matrix of number field elements 
			scalar 
multiplication          manfssmul(F,M,el) matrix of number field elements, 
			sparse representation, scalar 
multiplication          manfsvecmul(F,A,x) (MACRO) matrix of number field 
			elements, sparse representation, vector 
multiplication          manfvecmul(F,A,x) (MACRO) matrix of number field 
			elements vector 
multiplication          mapgfssmul(r,p,AL,M,el) matrix of polynomials over 
			Galois-field with single characteristic scalar 
multiplication          mapgfsvmul(r,p,AL,A,x) (MACRO) matrix of 
			polynomials over Galois-field with single 
			characteristic vector 
multiplication          mapismul(r,M,P) matrix of polynomials over integers 
			scalar 
multiplication          mapivecmul(r,A,x) (MACRO) matrix of polynomials 
			over integers vector 
multiplication          mapmismul(r,m,M,P) matrix of polynomials over 
			modular integers scalar 
multiplication          mapmivecmul(r,m,A,x) (MACRO) matrix of polynomials 
			over modular integers vector 
multiplication          mapmssmul(r,m,M,P) matrix of polynomials over 
			modular singles scalar 
multiplication          mapmsvecmul(r,m,A,x) (MACRO) matrix of polynomials 
			over modular singles vector 
multiplication          mapnfsmul(r,F,M,el) matrix of polynomials over 
			number field scalar 
multiplication          mapnfvecmul(r,F,A,x) (MACRO) matrix of polynomials 
			over number field vector 
multiplication          maprsmul(r,M,P) matrix of polynomials over 
			rationals scalar 
multiplication          maprvecmul(r,A,x) (MACRO) matrix of polynomials 
			over rationals vector 
multiplication          marfmsp1smul(p,M,F) matrix of rational functions 
			over modular single primes, transcendence degree 1, 
			scalar 
multiplication          marfmsp1vmul(p,A,x) (MACRO) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, vector 
multiplication          marfrsmul(r,M,F) matrix of rational functions over 
			rationals scalar 
multiplication          marfrvecmul(r,A,x) (MACRO) matrix of rational 
			functions over rationals vector 
multiplication          marsmul(M,el) matrix of rationals scalar 
multiplication          marvecmul(A,x) (MACRO) matrix of rationals vector 
multiplication          mavecmul(A,x,prod,sum,anzahlargs,arg1,arg2) matrix 
			vector 
multiplication          special 
			mavmulspec(A,x,prod,sum,anzahlargs,arg1,...,arg5) 
			matrix vector 
multiplication          vecgfssmul(p,AL,V,el) vector of Galois-field with 
			single characteristic elements scalar 
multiplication          vecismul(s,V) vector of integers scalar 
multiplication          vecmismul(m,s,V) vector of modular integers scalar 
multiplication          vecmssmul(m,s,V) vector of modular singles scalar 
multiplication          vecnfsmul(F,V,el) vector of number field elements 
			scalar 
multiplication          vecnfssmul(F,V,el) vector of number field elements, 
			sparse representation, scalar 
multiplication          vecpgfssmul(r,p,AL,V,el) vector of polynomials over 
			Galois-field with single characteristic scalar 
multiplication          vecpismul(r,P,V) vector of polynomials over 
			integers scalar 
multiplication          vecpmismul(r,m,P,V) vector of polynomials over 
			modular integers scalar 
multiplication          vecpmssmul(r,m,P,V) vector of polynomials over 
			modular singles scalar 
multiplication          vecpnfsmul(r,F,U,el) vector of polynomials over 
			number field scalar 
multiplication          vecprsmul(r,P,V) vector of polynomials over 
			rationals scalar 
multiplication          vecrfmsp1sm(p,F,V) vector of rational functions 
			over modular single primes, transcendence degree 1, 
			scalar 
multiplication          vecrfrsmul(r,F,V) vector of rational functions over 
			rationals scalar 
multiplication          vecrsmul(s,V) vector of rationals scalar 
multiplication-map      ecgf2mul(G,a1,a2,a3,a4,a6,k,P1) elliptic curve 
			Galois-field with characteristic 2, 
multiplication-map      eciminmul(E,P,n) elliptic curve with integer 
			coefficients, minimal model, 
multiplication-map      ecisnfmul(E,P,n) elliptic curve with integer 
			coefficients, short normal form, 
multiplication-map      ecmpmul(p,a1,a2,a3,a4,a6,n,P1) elliptic curve over 
			modular primes 
multiplication-map      ecmpsnfmul(p,a4,a6,n,P1) elliptic curve over 
			modular primes, short normal form, 
multiplication-map      ecnfmul(F,a1,a2,a3,a4,a6,n,P1) elliptic curve over 
			number field 
multiplication-map      ecnfsnfmul(F,a,b,n,P1) elliptic curve over number 
			field short normal form 
multiplication-map      ecracmul(E,P,n) elliptic curve over the rational 
			numbers, actual curve, 
multiplication-map,     special version ecgf2sfmuls(p,a6,x1,y1,n) elliptic 
			curve over Galois-field with characteristic 2, 
			special form, 
multiplication-map,     special version ecmpsnfmuls(p,a4,a6,x1,y1,n) 
			elliptic curve over modular primes, short normal 
			form, 
multiplicative          reduction type modulo prime eciminmrtmp(E,p) 
			elliptic curve with integer coefficients, minimal 
			model, 
name                    comparison vncomp(Vn1,Vn2) variable 
natural                 logarithm (rekursiv) fllog(f) floating point 
nearest                 to rational number inearesttor(r) integer 
negation                (rekursiv) dpmineg(r,m,P) dense polynomial over 
			modular integers 
negation                (rekursiv) dpmsneg(r,m,P) dense polynomial over 
			modular singles 
negation                (rekursiv) pgfsneg(r,p,AL,P) polynomial over 
			Galois-field with single characteristic 
negation                (rekursiv) pineg(r,P) polynomial over integers 
negation                (rekursiv) pmineg(r,M,P) polynomial over modular 
			integers 
negation                (rekursiv) pmsneg(r,m,P) polynomial over modular 
			singles 
negation                (rekursiv) pnfneg(r,F,P) polynomial over number 
			field 
negation                (rekursiv) prfmsp1neg(r,p,P) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, 
negation                (rekursiv) prneg(r,P) polynomial over rationals 
negation                Etoineg(e) Essen integer to SIMATH integer 
negation                as function gfsnegf(p,AL,a) Galois-field with 
			single characteristic 
negation                as function minegf(M,A) modular integer 
negation                as function msnegf(m,a) modular single 
negation                as function nfsnegf(F,a) number field, sparse 
			representation, 
negation                dipgfsneg(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic 
negation                dipineg(r,P) distributive polynomial over integers 
negation                dipmipneg(r,p,P) distributive polynomial over 
			modular integer primes 
negation                dipmspneg(r,p,P) distributive polynomial over 
			modular single primes 
negation                dipnfneg(r,F,P) distributive polynomial over number 
			field 
negation                dippineg(r1,r2,P) distributive polynomial over 
			polynomials over integers 
negation                diprfrneg(r1,r2,P) distributive polynomial over 
			rational functions over the rationals 
negation                diprneg(r,P) distributive polynomial over rationals 
negation                flneg(f) floating point 
negation                gf2neg(G,a) (MACRO) Galois-field with 
			characteristic 2 
negation                gfsneg(p,AL,a) (MACRO) Galois-field with single 
			characteristic 
negation                ineg(A) integer 
negation                magfsneg(p,AL,M) (MACRO) matrix of Galois-field 
			with single characteristic elements 
negation                maineg(M) (MACRO) matrix of integers 
negation                mamineg(m,M) (MACRO) matrix of modular integers 
negation                mamsneg(m,M) (MACRO) matrix of modular singles 
negation                maneg(M,neg,anzahlargs,arg1,arg2) matrix 
negation                manfneg(F,M) (MACRO) matrix of number field 
			elements 
negation                manfsneg(F,M) (MACRO) matrix of number field 
			elements, sparse representation, 
negation                mapgfsneg(r,p,AL,M) (MACRO) matrix of polynomials 
			over Galois-field with single characteristic 
negation                mapineg(r,M) (MACRO) matrix of polynomials over 
			integers 
negation                mapmineg(r,m,M) (MACRO) matrix of polynomials over 
			modular integers 
negation                mapmsneg(r,m,M) (MACRO) matrix of polynomials over 
			modular singles 
negation                mapnfneg(r,F,M) (MACRO) matrix of polynomials over 
			number field 
negation                maprneg(r,M) (MACRO) matrix of polynomials over 
			rationals 
negation                marfmsp1neg(p,M) (MACRO) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, 
negation                marfrneg(r,M) (MACRO) matrix of rational functions 
			over rationals 
negation                marneg(M) (MACRO) matrix of rationals 
negation                mineg(M,A) (MACRO) modular integer 
negation                msneg(m,a) (MACRO) modular single 
negation                nfneg(F,a) number field element 
negation                nfsneg(F,a) (MACRO) number field, sparse 
			representation, 
negation                pfneg(p,a) p-adic field element 
negation                pgf2neg(r,G,P) (MACRO) polynomial over Galois-field 
			with characteristic 2 
negation                ppfneg(r,p,P) polynomial over p-adic field 
negation                qnfneg(D,a,b) quadratic number field element 
negation                rfrneg(r,R) rational function over the rationals 
negation                rneg(R) rational number 
negation                special manegspec(M,neg,anzahlargs,arg1,...,arg5) 
			matrix 
negation                special vecnegspec(V,neg,anzahlargs,arg1,...,arg5) 
			vector 
negation                udpineg(P) univariate dense polynomial over 
			integers 
negation                udpmineg(m,P) univariate dense polynomial over 
			modular integers 
negation                udpmsneg(m,P) univariate dense polynomial over 
			modular singles 
negation                udppfneg(p,P) univariate dense polynomial over 
			p-adic field 
negation                udprneg(P) univariate dense polynomial over 
			rationals 
negation                vecgfsneg(p,AL,V) (MACRO) vector of Galois-field 
			with single characteristic elements 
negation                vecineg(V) (MACRO) vector of integers 
negation                vecmineg(m,V) (MACRO) vector of modular integers 
negation                vecmsneg(m,V) (MACRO) vector of modular singles 
negation                vecneg(V,neg,anzahlargs,arg1,arg2) vector 
negation                vecnfneg(F,V) (MACRO) vector of number field 
			elements 
negation                vecnfsneg(F,V) (MACRO) vector of number field 
			elements, sparse representation, 
negation                vecpgfsneg(r,p,AL,V) (MACRO) vector of polynomials 
			over Galois-field with single characteristic 
negation                vecpineg(r,V) (MACRO) vector of polynomials over 
			integers 
negation                vecpmineg(r,m,V) (MACRO) vector of polynomials over 
			modular integers 
negation                vecpmsneg(r,m,V) (MACRO) vector of polynomials over 
			modular singles 
negation                vecpnfneg(r,F,U) (MACRO) vector of polynomials over 
			number field 
negation                vecprneg(r,V) (MACRO) vector of polynomials over 
			rationals 
negation                vecrfmsp1neg(p,V) (MACRO) vector of rational 
			functions over modular single primes, transcendence 
			degree 1, 
negation                vecrfrneg(r,V) (MACRO) vector of rational functions 
			over rationals 
negation                vecrneg(V) (MACRO) vector of rationals 
negation,               transcendence degree 1 rfmsp1neg(p,R) rational 
			function over modular single prime 
negative                entries ) maihermltne(A) (MACRO) matrix of integers 
			Hermite normal form ( lower triangular form with 
negative                of point ecisnfneg(E,P) elliptic curve with integer 
			coefficients, short normal form, 
negative                point ecgf2neg(G,a1,a2,a3,a4,a6,P) elliptic curve 
			over Galois-field with characteristic 2, 
negative                point eciminneg(E,P) elliptic curve with integer 
			coefficients, minimal model, 
negative                point ecmpneg(p,a1,a2,a3,a4,a6,P) elliptic curve 
			over modular primes 
negative                point ecmpsnfneg(p,a4,a6,P) elliptic curve over 
			modular primes, short normal form, 
negative                point ecnfneg(F,a1,a2,a3,a4,a6,P) elliptic curve 
			over number field 
negative                point ecnfsnfneg(F,a,b,P) elliptic curve over 
			number field short normal form 
negative                point ecracneg(E,P) elliptic curve over the 
			rational numbers, actual curve, 
negative                singles ? islistnns(A) is list of non 
nepousppmsp1(p,F,a)     norm of an element of the polynomial order of an 
			univariate separable polynomial over the polynomial 
			ring over modular single prime, transcendence 
			degree 1 
new                     main variable dipnmv(r,P,n) distributive polynomial 
new                     variables (rekursiv) pvinsert(r,P,k) polynomial 
			insertion of 
next                    lrednext(L) list of reductants 
nf3chpol(F,el)          number field of degree 3 characteristic polynomial 
nf3sqrt(F,el)           number field of degree 3 square root 
nfdif(F,a,b)            number field element difference 
nfeexpspec(F,a,e,M)     number field element exponentiation special 
nfeliprod(F,a,i)        number field element integer product 
nfelmodi(F,a,M)         number field element modulo integer 
nfelnormal(L)           number field element normalized representation 
nfelrprod(F,a,R)        number field element rational number product 
nfeltomaln(n,a)         number field element to matrix line 
nfeltoudpr(a)           number field element to univariate dense polynomial 
			over rationals 
nfeprodspec(F,a,b,M)    number field element product special 
nfespecmpc1(F,a)        number field element special minimal polynomial, 
			Collins algorithm, version1 
nfespecmpc2(F,a)        number field element special minimal polynomial, 
			Collins algorithm, version2 
nfexp(F,a,n)            number field element exponentiation 
nffielddiscr(F)         number field, field discriminant 
nfinv(F,a)              number field inverse 
nfipdeclaw(F,P)         number field, integer prime decomposition law 
nfneg(F,a)              number field element negation 
nfnorm(F,a)             number field element norm 
nfprod(F,a,b)           number field element product 
nfquot(F,a,b)           number field quotient 
nfsdif(F,a,b)           (MACRO) number field, sparse representation, 
			difference 
nfsinv(F,a)             number field, sparse representation, inverse 
nfsneg(F,a)             (MACRO) number field, sparse representation, 
			negation 
nfsnegf(F,a)            number field, sparse representation, negation as 
			function 
nfspdeclaw(F,p)         number field, single prime decomposition law 
nfsprod(F,a,b)          number field, sparse representation, product 
nfsquot(F,a,b)          number field, sparse representation, quotient 
nfssum(F,a,b)           (MACRO) number field, sparse representation, sum 
nfssumf(F,a,b)          number field, sparse representation, sum as 
			function 
nfsum(F,a,b)            number field element sum 
nftrace(F,a)            number field element trace 
non                     archimedean absolute values eciminlhnaav(E,P) 
			elliptic curve with integer coefficients, minimal 
			model, local heights at all 
non                     negative singles ? islistnns(A) is list of 
non                     square mipfnsquare(p) modular integer prime find 
norm                    (rekursiv) pieuklnorm(r,P) polynomial over integers 
			Euklid 
norm                    (rekursiv) pimaxnorm(r,P) polynomial over integers 
			maximum 
norm                    (rekursiv) pisumnorm(r,P) polynomial over integers 
			sum 
norm                    in an imaginary quadratic field iprniqf(p,D) 
			integer prime representation as a 
norm                    nfnorm(F,a) number field element 
norm                    of an element of the polynomial order of an 
			univariate separable polynomial over the polynomial 
			ring over modular single prime, transcendence 
			degree 1 nepousppmsp1(p,F,a) 
norm                    of an element of the polynomial ring of an 
			univariate separable polynomial over the integers 
			normelpruspi(P,a) 
norm                    of an element qnfnorm(D,a) quadratic number field 
norm                    of the discriminant ecqnfacfndisc(E) elliptic curve 
			over quadratic number field, actual model, 
			factorization of the 
norm                    of the discriminant ecqnfacndisc(E) elliptic curve 
			over quadratic number field, actual model, 
normal                  form ( lower triangular form with negative entries 
			) maihermltne(A) (MACRO) matrix of integers Hermite 
normal                  form ( lower triangular form with positive entries 
			) maihermltpe(A) (MACRO) matrix of integers Hermite 
normal                  form ? iselecmpsnf(p,a,b,P) is element of an 
			elliptic curve over modular primes, short 
normal                  form ? iselecnfsnf(F,a,b,P) is element of an 
			elliptic curve over number field, short 
normal                  form eciminbtsnf(E) elliptic curve with integer 
			coefficients, minimal model, birational 
			transformation to short 
normal                  form ecimintosnf(E) elliptic curve with integer 
			coefficients, minimal model to short 
normal                  form ecmptosnf(p,a1,a2,a3,a4,a6) elliptic curve 
			over modular primes to short 
normal                  form ecnftosnf(F,a1,a2,a3,a4,a6) elliptic curve 
			over number field to short 
normal                  form ecracbtsnf(E) elliptic curve over rational 
			numbers, actual curve, birational transformation to 
			short 
normal                  form fputecisnf(E,*pf) file put elliptic curve with 
			integer coefficients, short 
normal                  form isponecisnf(E,P) is point on elliptic curve 
			with integer coefficients, model in short 
normal                  form line through points ecnfsnflp(F,a,b,P1,P2) 
			elliptic curve over number field short 
normal                  form maiherm(A,ne) matrix of integers Hermite 
normal                  form multiplication-map ecnfsnfmul(F,a,b,n,P1) 
			elliptic curve over number field short 
normal                  form negative point ecnfsnfneg(F,a,b,P) elliptic 
			curve over number field short 
normal                  form number of points special version 
			ecmipsnfnpsv(p,a4,a6) elliptic curve over modular 
			integer primes short 
normal                  form putecisnf(E) (MACRO) put elliptic curve with 
			integer coefficients, short 
normal                  form sum of points ecnfsnfsum(F,a,b,P1,P2) elliptic 
			curve over number field short 
normal                  form, Mordell-Weil-group, base ecisnfmwgbase(E) 
			elliptic curve with integer coefficients, short 
normal                  form, Shanks' algorithm ecmspsnfsha(p,a4,a6) 
			(MACRO) elliptic curve over modular single primes, 
			short 
normal                  form, a4 ecisnfa4(E) elliptic curve with integer 
			coefficients, short 
normal                  form, a6 ecisnfa6(E) elliptic curve with integer 
			coefficients, short 
normal                  form, b2 ecisnfb2(E) elliptic curve with integer 
			coefficients, short 
normal                  form, b4 ecisnfb4(E) elliptic curve with integer 
			coefficients, short 
normal                  form, b6 ecisnfb6(E) elliptic curve with integer 
			coefficients, short 
normal                  form, b8 ecisnfb8(E) elliptic curve with integer 
			coefficients, short 
normal                  form, birational transformation of coefficients 
			ecisnfbtco(E,BT) elliptic curve with integer 
			coefficients, short 
normal                  form, birational transformation to actual ( 
			rational ) model ecisnfbtac(E) elliptic curve with 
			integer coefficients, short 
normal                  form, birational transformation to minimal model 
			ecisnfbtmin(E) elliptic curve with integer 
			coefficients, short 
normal                  form, c4 ecisnfc4(E) elliptic curve with integer 
			coefficients, short 
normal                  form, c6 ecisnfc6(E) elliptic curve with integer 
			coefficients, short 
normal                  form, combined Schoof- Shanks- algorithm 
			ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic curve over 
			modular primes, short 
normal                  form, construction of division polynomials 
			ecmpsnfcdivp(P,a4,a6,n) elliptic curve over modular 
			primes, short 
normal                  form, difference between Weil height and Neron-Tate 
			height ecisnfdwhnth(E) elliptic curve with integer 
			coefficients, short 
normal                  form, discriminant ecisnfdisc(E) elliptic curve 
			with integer coefficients, short 
normal                  form, discriminant ecmpsnfdisc(p,a4,a6) elliptic 
			curve over modular primes, short 
normal                  form, discriminant ecnfsnfdisc(F,a,b) elliptic 
			curve over number field, short 
normal                  form, double of point ecisnfdouble(E,P) elliptic 
			curve with integer coefficients, short 
normal                  form, elliptic logarithm of point 
			ecisnfelogp(E,P,n) elliptic curve with integer 
			coefficients, short 
normal                  form, factorization of discriminant ecisnffdisc(E) 
			elliptic curve with integer coefficients, short 
normal                  form, find point ecmpsnffp(p,a4,a6) elliptic curve 
			over modular primes, short 
normal                  form, finding a multiple of the order of a point 
			with the Pollard Lambda method 
			ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
			modular primes, short 
normal                  form, finding a multiple of the order of a point 
			with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular primes, short 
normal                  form, generators of the torsion group 
			ecisnfgentor(E) elliptic curve with integer 
			coefficients, short 
normal                  form, j-invariant ecmpsnfjinv(p,a4,a6) elliptic 
			curve over modular primes, short 
normal                  form, j-invariant ecnfsnfjinv(F,a,b) elliptic curve 
			over number field, short 
normal                  form, line through points ecmpsnflp(p,a4,a6,P1,P2) 
			elliptic curve over modular primes, short 
normal                  form, modified Shanks' algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over modular primes, short 
normal                  form, multiple of the order of a point to exact 
			order of the point ecmpsnfmopto(p,a4,a6,P,mul) 
			elliptic curve over modular primes, short 
normal                  form, multiplication-map ecisnfmul(E,P,n) elliptic 
			curve with integer coefficients, short 
normal                  form, multiplication-map ecmpsnfmul(p,a4,a6,n,P1) 
			elliptic curve over modular primes, short 
normal                  form, multiplication-map, special version 
			ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve over 
			modular primes, short 
normal                  form, negative of point ecisnfneg(E,P) elliptic 
			curve with integer coefficients, short 
normal                  form, negative point ecmpsnfneg(p,a4,a6,P) elliptic 
			curve over modular primes, short 
normal                  form, number of points ecmspsnfnp(p,a4,a6) elliptic 
			curve over modular single primes, short 
normal                  form, number of points modulo 2 
			ecmpsnfnpm2(P,a4,a6) elliptic curve over modular 
			primes, short 
normal                  form, number of points modulo a single prime 
			determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
			modular primes, short 
normal                  form, number of points modulo an integer determined 
			with the Schoof algorithm ecmpsnfnpmi(P,a4,a6,S,pM) 
			elliptic curve over modular primes, short 
normal                  form, points of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve 
			with integer coefficients, short 
normal                  form, real roots of the right side 
			ecrsnfrroots(a,b) elliptic curve over rational 
			numbers, short 
normal                  form, sum of points ecisnfsum(E,P,Q) elliptic curve 
			with integer coefficients, short 
normal                  form, sum of points ecmpsnfsum(p,a4,a6,P1,P2) 
			elliptic curve over modular primes, short 
normal                  form, sum of points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve 
			over modular primes, short 
normal                  form, torsion group ecisnftorgr(E) elliptic curve 
			with integer coefficients, short 
normalization           ecipnorm(P) elliptic curve with integer 
			coefficients, point 
normalization           ecrpnorm(P) elliptic curve over rational numbers, 
			point 
normalized              representation nfelnormal(L) number field element 
normelpruspi(P,a)       norm of an element of the polynomial ring of an 
			univariate separable polynomial over the integers 
null                    space basis magfsnsb(p,AL,M) matrix of Galois-field 
			with single characteristic elements, 
null                    space basis maminsb(P,M) matrix of modular 
			integers, 
null                    space basis mamsnsb(p,A) (MACRO) matrix of modular 
			singles 
null                    space basis manfnsb(F,M) matrix of number field 
			elements 
null                    space basis manfsnsb(F,M) matrix of number field 
			elements, sparse representation, 
null                    space basis marfmsp1nsb(p,M) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, 
null                    space basis marfrnsb(r,M) matrix of rational 
			functions over rationals, 
null                    space basis marnsb(M) matrix of rationals 
null-matrix             isnullma(M) (MACRO) is 
null-vector             isnullvec(V) is 
number                  ? israt(R) is rational 
number                  abnfrelcl(q,g) abelian number field relative class 
number                  absolute height rabsheight(r) rational 
number                  absolute value rabs(R) (MACRO) rational 
number                  ceiling rceil(R) rational 
number                  comparison rcomp(R,S) rational 
number                  construction rcons(A,B) rational 
number                  decimal fputrd(R,n,pf) file put rational 
number                  decimal putrd(R,n) (MACRO) put rational 
number                  denominator rden(R) (MACRO) rational 
number                  difference rdif(R,S) (MACRO) rational 
number                  exponentiation rexp(R,n) rational 
number                  fgetr(pf) file get rational 
number                  field (rekursiv) pitopnf(r,P) polynomial over the 
			integers to polynomial over a 
number                  field (rekursiv) prtopnf(r,P) polynomial over 
			rationals to polynomial over 
number                  field ? iselecnf(F,a1,a2,a3,a4,a6,P) is element of 
			an elliptic curve over 
number                  field Dirichlet character qnfdirchar(D,z) quadratic 
number                  field Groebner basis augmentation 
			dipnfgba(r,F,PL,P) distributive polynomial over 
number                  field Groebner basis dipnfgb(r,F,PL) distributive 
			polynomial over 
number                  field Groebner basis recursion dipnfgbr(r,F,PL) 
			distributive polynomial over 
number                  field S-polynomial dipnfsp(r,F,P1,P2) distributive 
			polynomial over 
number                  field Tate's values b2, b4, b6 
			ecnftavb6(F,a1,a2,a3,a4,a6) elliptic curve over 
number                  field Tate's values b2, b4, b6, b8 
			ecnftavb8(F,a1,a2,a3,a4,a6) elliptic curve over 
number                  field Tate's values c4, c6 
			ecnftavc6(F,a1,a2,a3,a4,a6) elliptic curve over 
number                  field additive valuation qnfaval(D,p,a) quadratic 
number                  field birational transformation of coefficients 
			ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over 
number                  field characteristic polynomial mapnfchpol(r,F,M) 
			(MACRO) matrix of polynomials over 
number                  field conjugate element qnfconj(D,a) quadratic 
number                  field construction 1 mapnfcons1(r,F,n) (MACRO) 
			matrix of polynomials over 
number                  field degrees of the residue class fields 
			qnfdegrescf(D,p) quadratic 
number                  field derivation, main variable pnfderiv(r,F,P) 
			polynomial over 
number                  field derivation, specified variable (rekursiv) 
			pnfderivsv(r,F,P,n) polynomial over 
number                  field determinant mapnfdet(r,F,M) matrix of 
			polynomials over 
number                  field difference (rekursiv) pnfdif(r,F,P1,P2) 
			polynomial over 
number                  field difference dipnfdif(r,F,P1,P2) distributive 
			polynomial over 
number                  field difference mapnfdif(r,F,M,N) (MACRO) matrix 
			of polynomials over 
number                  field difference vecpnfdif(r,F,U,V) (MACRO) vector 
			of polynomials over 
number                  field discriminant ecnfdisc(F,a1,a2,a3,a4,a6) 
			elliptic curve over 
number                  field discriminant qnfdisc(D) quadratic 
number                  field element comparison qnfelcomp(D,A,B) quadratic 
number                  field element difference nfdif(F,a,b) 
number                  field element difference qnfdif(D,a,b) (MACRO) 
			quadratic 
number                  field element evaluation first variable special 
			version mapinfevlfvs(r,F,M) matrix of polynomials 
			over integers 
number                  field element evaluation first variable special 
			version maprnfevlfvs(r,F,M) matrix of polynomials 
			over rationals 
number                  field element evaluation first variable special 
			version pinfevalfvs(r,F,P) polynomial over integers 
number                  field element evaluation first variable special 
			version prnfevalfvs(r,F,P) polynomial over 
			rationals 
number                  field element evaluation first variable special 
			version vpinfevalfvs(r,F,V) vector of polynomials 
			over integers 
number                  field element evaluation first variable special 
			version vprnfevalfvs(r,F,V) vector of polynomials 
			over rationals 
number                  field element evaluation special upinfeevals(F,P,a) 
			univariate polynomial over the integers 
number                  field element evaluation upinfeval(P,F,a) 
			univariate polynomial over integers 
number                  field element evaluation uprnfeval(P,F,a) 
			univariate polynomial over rationals 
number                  field element exponentiation nfexp(F,a,n) 
number                  field element exponentiation qnfexp(D,a,e) 
			quadratic 
number                  field element exponentiation special 
			nfeexpspec(F,a,e,M) 
number                  field element factor exponent list 
			fputqnffel(D,L,pf) file put quadratic 
number                  field element factor exponent list putqnffel(D,L) 
			(MACRO) put quadratic 
number                  field element fgetnfel(F,V,pf) file get 
number                  field element fgetqnfel(D,pf) file get quadratic 
number                  field element fputnfel(F,a,V,pf) file put 
number                  field element fputonfel(F,a,V,pf) file put original 
number                  field element fputqnfel(D,a,pf) file put quadratic 
number                  field element getnfel(F,V) (MACRO) get 
number                  field element getqnfel(D) (MACRO) get quadratic 
number                  field element integer product nfeliprod(F,a,i) 
number                  field element integer? isqnfint(D,a) (MACRO) is 
			quadratic 
number                  field element integral element? isqnfiel(D,a) is 
			quadratic 
number                  field element inverse element qnfinv(D,a) quadratic 
number                  field element itonf(A) (MACRO) integer to 
number                  field element itoqnf(D,a) (MACRO) integer to 
			quadratic 
number                  field element minimal polynomial modulo p-power 
			infeminpmpp(F,a,p,e,Q) integral 
number                  field element minimal polynomial modulo p-power 
			with respect to integer primes 
			infempmppip(F,a,p,e,Q) integral 
number                  field element minimal representation qnfminrep(D,a) 
			quadratic 
number                  field element modulo integer nfelmodi(F,a,M) 
number                  field element negation nfneg(F,a) 
number                  field element negation qnfneg(D,a,b) quadratic 
number                  field element norm nfnorm(F,a) 
number                  field element normalized representation 
			nfelnormal(L) 
number                  field element one isnfone(F,A) is 
number                  field element one? isqnfone(D,a) (MACRO) is 
			quadratic 
number                  field element p-primality test and factorization of 
			the defining polynomial or the minimal polynomial 
			infepptfact(F,p,Q,ppot,a0,z) integral 
number                  field element p-primality test and factorization of 
			the defining polynomial or the minimal polynomial 
			with respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) integral 
number                  field element p-star valuation infepstarval(p,A) 
			integral 
number                  field element p-star valuation with respect to 
			integer primes infepstarvip(P,A) integral 
number                  field element power of prime ideal homomorphism 
			zero? isqnfppihom0(D,P,k,pi,z,a) is quadratic 
number                  field element prime ideal factorization 
			qnfpifact(D,a) quadratic 
number                  field element prime ideal order 
			qnfpiord(D,P,pi,z,a) quadratic 
number                  field element product (rekursiv) pnfnfprod(r,F,P,a) 
			polynomial over number field, 
number                  field element product dipnfnfprod(r,F,P,A) 
			distributive polynomial over number field, 
number                  field element product nfprod(F,a,b) 
number                  field element product qnfprod(D,a,b) quadratic 
number                  field element product special nfeprodspec(F,a,b,M) 
number                  field element putnfel(F,a,V) (MACRO) put 
number                  field element putonfel(F,a,V) (MACRO) put original 
number                  field element putqnfel(D,a) (MACRO) put quadratic 
number                  field element quotient (rekursiv) 
			pnfnfquot(r,F,P,a) polynomial over number field, 
number                  field element quotient qnfquot(D,a,b) (MACRO) 
			quadratic 
number                  field element rational isqnfrat(D,a) (MACRO) is 
			quadratic 
number                  field element rational number product 
			nfelrprod(F,a,R) 
number                  field element regulation with respect to integer 
			primes ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary 
number                  field element regulation, version1 
			ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary 
number                  field element regulation, version2 
			ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary 
number                  field element rtonf(R) rational number to 
number                  field element rtoqnf(D,A) (MACRO) rational number 
			to quadratic 
number                  field element special minimal polynomial, Collins 
			algorithm, version1 nfespecmpc1(F,a) 
number                  field element special minimal polynomial, Collins 
			algorithm, version2 nfespecmpc2(F,a) 
number                  field element square qnfsquare(D,a) quadratic 
number                  field element sum nfsum(F,a,b) 
number                  field element sum qnfsum(D,a,b) quadratic 
number                  field element to matrix line nfeltomaln(n,a) 
number                  field element to univariate dense polynomial over 
			rationals nfeltoudpr(a) 
number                  field element trace nftrace(F,a) 
number                  field element udprtonfel(P) univariate dense 
			polynomial over rationals to 
number                  field element uprtonfel(F,P) univariate polynomial 
			over rationals to 
number                  field element, core algorithm 
			ippnfecoreal(F,p,Q,mp) integral p-primary 
number                  field element, core algorithm with respect to 
			integer primes ippnfecalip(F,P,Q,mp) integral 
			P-primary 
number                  field element, difference iqnfdif(D,a,b) (MACRO) 
			integer, quadratic 
number                  field element, difference rqnfdif(D,a,b) (MACRO) 
			rational number, quadratic 
number                  field element, increasing the denominator of the 
			p-star value 
			ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary 
number                  field element, increasing the denominator of the 
			p-star value with respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary 
number                  field element, integer, difference qnfidif(D,a,b) 
			(MACRO) quadratic 
number                  field element, integer, product qnfiprod(D,a,b) 
			quadratic 
number                  field element, integer, quotient qnfiquot(D,a,b) 
			quadratic 
number                  field element, integer, sum qnfisum(D,a,b) 
			quadratic 
number                  field element, quotient iqnfquot(D,a,b) integer, 
			quadratic 
number                  field element, quotient rqnfquot(D,a,b) rational 
			number, quadratic 
number                  field element, rational number, difference 
			qnfrdif(D,a,b) (MACRO) quadratic 
number                  field element, rational number, product 
			qnfrprod(D,a,b) quadratic 
number                  field element, rational number, quotient 
			qnfrquot(D,a,b) (MACRO) quadratic 
number                  field element, rational number, sum qnfrsum(D,a,b) 
			quadratic 
number                  field element, sparse representation ? isnfels(F,a) 
			is 
number                  field element, sparse representation 
			fgetnfels(F,V,pf) file get 
number                  field element, sparse representation 
			fputnfels(F,a,V,pf) file put 
number                  field element, sparse representation getnfels(F,V) 
			(MACRO) get 
number                  field element, sparse representation itonfs(A) 
			integer to 
number                  field element, sparse representation 
			putnfels(F,a,V) (MACRO) put 
number                  field element, sparse representation rtonfs(R) 
			rational number to 
number                  field element, sparse representation, evaluation 
			upinfseval(P,F,a) univariate polynomial over 
			integers 
number                  field element, sparse representation, evaluation 
			uprnfseval(P,F,a) univariate polynomial over 
			rationals 
number                  field element? isnfel(F,a) is 
number                  field elements ? ismanf(F,M) (MACRO) is matrix of 
number                  field elements ? isvecnf(F,V) (MACRO) is vector of 
number                  field elements characteristic polynomial 
			manfchpol(F,M) (MACRO) matrix of 
number                  field elements construction 1 manfcons1(F,n) 
			(MACRO) matrix of 
number                  field elements determinant manfdet(F,M) matrix of 
number                  field elements difference manfdif(F,M,N) (MACRO) 
			matrix of 
number                  field elements difference vecnfdif(F,U,V) (MACRO) 
			vector of 
number                  field elements exponentiation manfexp(F,M,n) matrix 
			of 
number                  field elements fgetmanf(F,VL,pf) (MACRO) file get 
			matrix of 
number                  field elements fgetvecnf(F,VL,pf) (MACRO) file get 
			vector of 
number                  field elements fputmanf(F,M,VL,pf) (MACRO) file put 
			matrix of 
number                  field elements fputvecnf(F,V,VL,pf) (MACRO) file 
			put vector of 
number                  field elements getmanf(F,VL) (MACRO) get matrix of 
number                  field elements getvecnf(F,VL) (MACRO) get vector of 
number                  field elements inverse manfinv(F,M) matrix of 
number                  field elements linear combination 
			vecnflc(F,s1,s2,L1,L2) vector of 
number                  field elements maitomanf(M) matrix of integers to 
			matrix of 
number                  field elements martomanf(M) matrix of rationals to 
			matrix of 
number                  field elements maudprtomnf(M) matrix of univariate 
			dense polynomials over rationals to matrix of 
number                  field elements negation manfneg(F,M) (MACRO) matrix 
			of 
number                  field elements negation vecnfneg(F,V) (MACRO) 
			vector of 
number                  field elements null space basis manfnsb(F,M) matrix 
			of 
number                  field elements product manfprod(F,M,N) (MACRO) 
			matrix of 
number                  field elements putmanf(F,M,VL) (MACRO) put matrix 
			of 
number                  field elements putvecnf(F,V,VL) (MACRO) put vector 
			of 
number                  field elements rank manfrk(F,M) matrix of 
number                  field elements scalar multiplication 
			manfsmul(F,M,el) matrix of 
number                  field elements scalar multiplication 
			vecnfsmul(F,V,el) vector of 
number                  field elements scalar product vecnfsprod(F,V,W) 
			vector of 
number                  field elements solution of a system of linear 
			equations manfssle(F,A,b,pX,pN) matrix of 
number                  field elements sum manfsum(F,M,N) (MACRO) matrix of 
number                  field elements sum vecnfsum(F,U,V) (MACRO) vector 
			of 
number                  field elements to matrix of univariate dense 
			polynomials over rationals manftomudpr(F,M) matrix 
			of 
number                  field elements to vector of univariate dense 
			polynomials over rationals vnftovudpr(F,V) vector 
			of 
number                  field elements vecitovecnf(V) vector of integers to 
			vector of 
number                  field elements vecrtovecnf(V) vector of rationals 
			to vector of 
number                  field elements vector multiplication 
			manfvecmul(F,A,x) (MACRO) matrix of 
number                  field elements vudprtovnf(V) vector of univariate 
			dense polynomials over rationals to vector of 
number                  field elements, sparse representation ? 
			ismanfs(F,M) (MACRO) is matrix of 
number                  field elements, sparse representation ? 
			isvecnfs(F,V) (MACRO) is vector of 
number                  field elements, sparse representation 
			fgetmanfs(F,VL,pf) (MACRO) file get matrix of 
number                  field elements, sparse representation 
			fgetvecnfs(F,VL,pf) (MACRO) file get vector of 
number                  field elements, sparse representation 
			fputmanfs(F,M,VL,pf) (MACRO) file put matrix of 
number                  field elements, sparse representation 
			fputvecnfs(F,V,VL,pf) (MACRO) file put vector of 
number                  field elements, sparse representation 
			getmanfs(F,VL) (MACRO) get matrix of 
number                  field elements, sparse representation 
			getvecnfs(F,VL) (MACRO) get vector of 
number                  field elements, sparse representation maitomanfs(M) 
			matrix of integers to matrix of 
number                  field elements, sparse representation martomanfs(M) 
			matrix of rationals to matrix of 
number                  field elements, sparse representation 
			putmanfs(F,M,VL) (MACRO) put matrix of 
number                  field elements, sparse representation 
			putvecnfs(F,V,VL) (MACRO) put vector of 
number                  field elements, sparse representation vecitovnfs(V) 
			vector of integers to vector of 
number                  field elements, sparse representation vecrtovnfs(V) 
			vector of rationals to vector of 
number                  field elements, sparse representation, construction 
			1 manfscons1(F,n) (MACRO) matrix of 
number                  field elements, sparse representation, determinant 
			manfsdet(F,M) matrix of 
number                  field elements, sparse representation, difference 
			manfsdif(F,M,N) (MACRO) matrix of 
number                  field elements, sparse representation, difference 
			vecnfsdif(F,U,V) (MACRO) vector of 
number                  field elements, sparse representation, 
			exponentiation manfsexp(F,M,n) matrix of 
number                  field elements, sparse representation, inverse 
			manfsinv(F,M) matrix of 
number                  field elements, sparse representation, linear 
			combination vecnfslc(F,s1,s2,L1,L2) vector of 
number                  field elements, sparse representation, negation 
			manfsneg(F,M) (MACRO) matrix of 
number                  field elements, sparse representation, negation 
			vecnfsneg(F,V) (MACRO) vector of 
number                  field elements, sparse representation, null space 
			basis manfsnsb(F,M) matrix of 
number                  field elements, sparse representation, product 
			manfsprod(F,M,N) (MACRO) matrix of 
number                  field elements, sparse representation, rank 
			manfsrk(F,M) matrix of 
number                  field elements, sparse representation, scalar 
			multiplication manfssmul(F,M,el) matrix of 
number                  field elements, sparse representation, scalar 
			multiplication vecnfssmul(F,V,el) vector of 
number                  field elements, sparse representation, scalar 
			product vecnfssprod(F,V,W) vector of 
number                  field elements, sparse representation, solution of 
			a system of linear equations manfsssle(F,A,b,pX,pN) 
			matrix of 
number                  field elements, sparse representation, sum 
			manfssum(F,M,N) (MACRO) matrix of 
number                  field elements, sparse representation, sum 
			vecnfssum(F,U,V) (MACRO) vector of 
number                  field elements, sparse representation, vector 
			multiplication manfsvecmul(F,A,x) (MACRO) matrix of 
number                  field equal? isppecnfeq(F,P1,P2) is projective 
			point of an elliptic curve over 
number                  field evaluation upnfeval(F,P,A) univariate 
			polynomial over a 
number                  field evaluation, main variable pnfeval(r,F,P,a) 
			polynomial over 
number                  field evaluation, specified variable (rekursiv) 
			pnfevalsv(r,F,P,n,a) polynomial over 
number                  field exponentiation mapnfexp(r,F,M,n) matrix of 
			polynomials over 
number                  field exponentiation pnfexp(r,F,P,n) polynomial 
			over 
number                  field fgetmapnf(r,F,V,Vnf,pf) (MACRO) file get 
			matrix of polynomials over 
number                  field fgetpnf(r,F,V,Vnf,pf) file get polynomial 
			over 
number                  field fgetvecpnf(r,F,VL,VLnf,pf) (MACRO) file get 
			vector of polynomials over 
number                  field fputmapnf(r,F,M,V,Vnf,pf) (MACRO) file put 
			matrix of polynomials over 
number                  field fputpnf(r,F,P,V,Vnf,pf) file put polynomial 
			over 
number                  field fputvecpnf(r,F,W,VL,VLnf,pf) (MACRO) file put 
			vector of polynomials over 
number                  field fundamental unit rqnffu(D,pl) real quadratic 
number                  field getmapnf(r,F,V,Vnf) (MACRO) get matrix of 
			polynomials over 
number                  field getpnf(r,F,V,Vnf) (MACRO) get polynomial over 
number                  field getvecpnf(r,F,VL,VLnf) (MACRO) get vector of 
			polynomials over 
number                  field greatest common divisor and cofactors 
			upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate polynomial 
			over 
number                  field greatest common divisor upnfgcd(F,P1,P2) 
			univariate polynomial over 
number                  field ideal comparison qnfidcomp(D,A,B) quadratic 
number                  field ideal exponentiation qnfidexp(D,A,e) 
			quadratic 
number                  field ideal fputqnfid(D,A,pf) file put quadratic 
number                  field ideal one qnfidone(D) (MACRO) quadratic 
number                  field ideal one? isqnfidone(D,A) is quadratic 
number                  field ideal product qnfidprod(D,A,B) quadratic 
number                  field ideal putqnfid(D,A) (MACRO) put quadratic 
number                  field ideal square qnfidsquare(D,A) quadratic 
number                  field in graduated lexicographical order 
			dipnflotoglo(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over 
number                  field in lexicographical order to distributive 
			polynomial over number field in graduated 
			lexicographical order dipnflotoglo(r,F,P) 
			distributive polynomial over 
number                  field in lexicographical order to distributive 
			polynomial over number field in lexicographical 
			order with inverse exponent vector 
			dipnflotolio(r,F,P) distributive polynomial over 
number                  field in lexicographical order to distributive 
			polynomial over number field with total degree 
			ordering dipnflototdo(r,F,P) distributive 
			polynomial over 
number                  field in lexicographical order with inverse 
			exponent vector dipnflotolio(r,F,P) distributive 
			polynomial over number field in lexicographical 
			order to distributive polynomial over 
number                  field integral basis qnfintbas(D) quadratic 
number                  field integral element prime ideal factorization, 
			special version qnfielpifacts(D,a,L) quadratic 
number                  field inverse mapnfinv(r,F,M) matrix of polynomials 
			over 
number                  field inverse nfinv(F,a) 
number                  field j-invariant ecnfjinv(F,a1,a2,a3,a4,a6) 
			elliptic curve over 
number                  field line through points 
			ecnflp(F,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
number                  field linear combination vecpnflc(r,F,s1,s2,L1,L2) 
			vector of polynomials over 
number                  field list fgetdipnfl(r,F,VL,Vnf,pf) file get 
			distributive polynomial over 
number                  field list fputdipnfl(r,F,PL,VL,Vnf,pf) file put 
			distributive polynomial over 
number                  field list getdipnfl(r,F,VL,Vnf) (MACRO) get 
			distributive polynomial over 
number                  field list putdipnfl(r,F,PL,VL,Vnf) (MACRO) put 
			distributive polynomial over 
number                  field mapitomapnf(r,M) matrix of polynomials over 
			integers to matrix of polynomials over 
number                  field mapnftomapmp(r,F,P,M) matrix of polynomials 
			over number field to matrix of polynomials modulo 
			polynomial over 
number                  field maprtomapnf(r,M) matrix of polynomials over 
			rationals to matrix of polynomials over 
number                  field monic dipnfmonic(r,F,P) distributive 
			polynomial over 
number                  field monic pnfmonic(r,F,P) polynomial over 
number                  field multiplication-map 
			ecnfmul(F,a1,a2,a3,a4,a6,n,P1) elliptic curve over 
number                  field negation (rekursiv) pnfneg(r,F,P) polynomial 
			over 
number                  field negation dipnfneg(r,F,P) distributive 
			polynomial over 
number                  field negation mapnfneg(r,F,M) (MACRO) matrix of 
			polynomials over 
number                  field negation vecpnfneg(r,F,U) (MACRO) vector of 
			polynomials over 
number                  field negative point ecnfneg(F,a1,a2,a3,a4,a6,P) 
			elliptic curve over 
number                  field norm of an element qnfnorm(D,a) quadratic 
number                  field of degree 3 characteristic polynomial 
			nf3chpol(F,el) 
number                  field of degree 3 equal to number field of degree 3 
			isnf3eqnf3(F,P,pFD,pPD,pQ) is 
number                  field of degree 3 isnf3eqnf3(F,P,pFD,pPD,pQ) is 
			number field of degree 3 equal to 
number                  field of degree 3 square root nf3sqrt(F,el) 
number                  field point at infinity ? isppecnfpai(P) is 
			projective point of an elliptic curve over 
number                  field prime ideal homomorphism qnfpihom(D,P,pi,z,a) 
			quadratic 
number                  field product (rekursiv) pnfprod(r,F,P1,P2) 
			polynomial over 
number                  field product dipnfprod(r,F,P1,P2) distributive 
			polynomial over 
number                  field product mapnfprod(r,F,M,N) (MACRO) matrix of 
			polynomials over 
number                  field putmapnf(r,F,M,V,Vnf) (MACRO) put matrix of 
			polynomials over 
number                  field putpnf(r,F,P,V,Vnf) (MACRO) put polynomial 
			over 
number                  field putvecpnf(r,F,W,VL,VLnf) (MACRO) put vector 
			of polynomials over 
number                  field quotient and remainder (rekursiv) 
			pnfqrem(r,F,P1,P2,pR) polynomial over 
number                  field quotient nfquot(F,a,b) 
number                  field quotient pnfquot(r,F,P1,P2) (MACRO) 
			polynomial over 
number                  field ramification indices qnframind(D,p) quadratic 
number                  field relative class number abnfrelcl(q,g) abelian 
number                  field relative class number modulo prime 
			abnfrelclmp(m,q,g) abelian 
number                  field remainder pnfrem(r,F,P1,P2) (MACRO) 
			polynomial over 
number                  field scalar multiplication mapnfsmul(r,F,M,el) 
			matrix of polynomials over 
number                  field scalar multiplication vecpnfsmul(r,F,U,el) 
			vector of polynomials over 
number                  field scalar product vpnfsprod(r,F,V,W) vector of 
			polynomials over 
number                  field short normal form line through points 
			ecnfsnflp(F,a,b,P1,P2) elliptic curve over 
number                  field short normal form multiplication-map 
			ecnfsnfmul(F,a,b,n,P1) elliptic curve over 
number                  field short normal form negative point 
			ecnfsnfneg(F,a,b,P) elliptic curve over 
number                  field short normal form sum of points 
			ecnfsnfsum(F,a,b,P1,P2) elliptic curve over 
number                  field squarefree factorization upnfsfact(F,P) 
			univariate polynomial over 
number                  field standard representation of projective point 
			ecnfsrpp(F,P) elliptic curve over 
number                  field sum (rekursiv) pnfsum(r,F,P1,P2) polynomial 
			over 
number                  field sum dipnfsum(r,F,P1,P2) distributive 
			polynomial over 
number                  field sum mapnfsum(r,F,M,N) (MACRO) matrix of 
			polynomials over 
number                  field sum of points ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over 
number                  field sum vecpnfsum(r,F,U,V) (MACRO) vector of 
			polynomials over 
number                  field system of representatives modulo a prime 
			ideal qnfsysrmodpi(D,P,pi,z,k) quadratic 
number                  field to elliptic curve with integral coefficients 
			ecqnftoeci(D,L) elliptic curve over quadratic 
number                  field to matrix of polynomials modulo polynomial 
			over number field mapnftomapmp(r,F,P,M) matrix of 
			polynomials over 
number                  field to matrix of polynomials over rationals 
			mapnftomapr(r,M) matrix of polynomials over 
number                  field to polynomial over rationals pnftopr(r,P) 
			polynomial over 
number                  field to short normal form 
			ecnftosnf(F,a1,a2,a3,a4,a6) elliptic curve over 
number                  field to vector of polynomials modulo polynomial 
			over number field vecpnftovpmp(r,F,P,V) vector of 
			polynomials over 
number                  field to vector of polynomials over rationals 
			vecpnftovpr(r,V) vector of polynomials over 
number                  field trace of an element qnftrace(D,a) quadratic 
number                  field transformation 
			mapnftransf(r1,F,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over 
number                  field transformation 
			pnftransf(r1,F,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over 
number                  field transformation 
			vpnftransf(r1,F,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over 
number                  field unit group qnfunit(D) quadratic 
number                  field vecpitovpnf(r,V) vector of polynomials over 
			integers to vector of polynomials over 
number                  field vecpnftovpmp(r,F,P,V) vector of polynomials 
			over number field to vector of polynomials modulo 
			polynomial over 
number                  field vecprtovpnf(r,V) vector of polynomials over 
			rationals to vector of polynomials over 
number                  field vector multiplication mapnfvecmul(r,F,A,x) 
			(MACRO) matrix of polynomials over 
number                  field with total degree ordering 
			dipnflototdo(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over 
number                  field, Tate's algorithm 
			ecqnftatealg(D,LC,LTV,P,pi,z,n) elliptic curve over 
			quadratic 
number                  field, actual model, Tate value b2 ecqnfacb2(E) 
			elliptic curve over quadratic 
number                  field, actual model, Tate value b4 ecqnfacb4(E) 
			elliptic curve over quadratic 
number                  field, actual model, Tate value b6 ecqnfacb6(E) 
			elliptic curve over quadratic 
number                  field, actual model, Tate value b8 ecqnfacb8(E) 
			elliptic curve over quadratic 
number                  field, actual model, Tate value c4 ecqnfacc4(E) 
			elliptic curve over quadratic 
number                  field, actual model, Tate value c6 ecqnfacc6(E) 
			elliptic curve over quadratic 
number                  field, actual model, discriminant ecqnfacdisc(E) 
			elliptic curve over quadratic 
number                  field, actual model, factorization of the norm of 
			the discriminant ecqnfacfndisc(E) elliptic curve 
			over quadratic 
number                  field, actual model, norm of the discriminant 
			ecqnfacndisc(E) elliptic curve over quadratic 
number                  field, actual model, prime ideal factorization of 
			the discriminant ecqnfacpifdi(E) elliptic curve 
			over quadratic 
number                  field, conductor ecqnfcond(E) elliptic curve over 
			quadratic 
number                  field, field discriminant ecqnfflddisc(E) (MACRO) 
			elliptic curve over quadratic 
number                  field, field discriminant modulo 4 ecqnfdmod4(E) 
			(MACRO) elliptic curve over quadratic 
number                  field, field discriminant nffielddiscr(F) 
number                  field, initialization ecqnfinit(D,a1,a2,a3,a4,a6) 
			elliptic curve over quadratic 
number                  field, integer prime decomposition law 
			nfipdeclaw(F,P) 
number                  field, integral element, prime ideal order 
			qnfielpiord(D,P,pi,z,a) quadratic 
number                  field, j-invariant ecqnfjinv(E) elliptic curve over 
			quadratic 
number                  field, number field element product (rekursiv) 
			pnfnfprod(r,F,P,a) polynomial over 
number                  field, number field element product 
			dipnfnfprod(r,F,P,A) distributive polynomial over 
number                  field, number field element quotient (rekursiv) 
			pnfnfquot(r,F,P,a) polynomial over 
number                  field, short normal form ? iselecnfsnf(F,a,b,P) is 
			element of an elliptic curve over 
number                  field, short normal form, discriminant 
			ecnfsnfdisc(F,a,b) elliptic curve over 
number                  field, short normal form, j-invariant 
			ecnfsnfjinv(F,a,b) elliptic curve over 
number                  field, single prime decomposition law 
			nfspdeclaw(F,p) 
number                  field, sparse representation, difference 
			nfsdif(F,a,b) (MACRO) 
number                  field, sparse representation, inverse nfsinv(F,a) 
number                  field, sparse representation, negation as function 
			nfsnegf(F,a) 
number                  field, sparse representation, negation nfsneg(F,a) 
			(MACRO) 
number                  field, sparse representation, product 
			nfsprod(F,a,b) 
number                  field, sparse representation, quotient 
			nfsquot(F,a,b) 
number                  field, sparse representation, sum as function 
			nfssumf(F,a,b) 
number                  field, sparse representation, sum nfssum(F,a,b) 
			(MACRO) 
number                  floor rfloor(R) rational 
number                  fltor(f) floating point to rational 
number                  fputcn(a,v,n,pf) file put complex 
number                  fputr(R,pf) file put rational 
number                  getr() (MACRO) get rational 
number                  in ball ? iscinball(z,r,eps) is complex 
number                  inearesttor(r) integer nearest to rational 
number                  inverse rinv(R) rational 
number                  itor(A) integer to rational 
number                  logarithm, base 2 rlog2(R) rational 
number                  maximum rmax(R,S) (MACRO) rational 
number                  minimum rmin(R,S) (MACRO) rational 
number                  modulo prime abnfrelclmp(m,q,g) abelian number 
			field relative class 
number                  negation rneg(R) rational 
number                  numerator rnum(R) (MACRO) rational 
number                  of columns manrcol(M) (MACRO) matrix 
number                  of irreducible factors upgfsnif(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic 
number                  of irreducible factors upminif(m,P) univariate 
			polynomial over modular integers, 
number                  of irreducible factors upmsnif(m,P) univariate 
			polynomial over modular singles, 
number                  of points after field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
			curve over Galois field with characteristic 2, 
number                  of points ecmspnp(p,a1,a2,a3,a4,a6) elliptic curve 
			over modular single prime, 
number                  of points ecmspsnfnp(p,a4,a6) elliptic curve over 
			modular single primes, short normal form, 
number                  of points modulo 2 ecmpsnfnpm2(P,a4,a6) elliptic 
			curve over modular primes, short normal form, 
number                  of points modulo a power of 2 ecgf2npmp2(G,a6,c,L) 
			elliptic curve over Galois-field with 
			characteristic 2, 
number                  of points modulo a single prime determined with the 
			Schoof algorithm ecmpsnfnpmsp(P,a4,a6,p,L) elliptic 
			curve over modular primes, short normal form, 
number                  of points modulo a single prime determined with the 
			Schoof algorithm, version 1 ecgf2npmspv1(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, 
number                  of points modulo a single prime determined with the 
			Schoof algorithm, version 2 ecgf2npmspv2(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, 
number                  of points modulo an integer determined with the 
			Schoof algorithm ecgf2npmi(G,a6,S,v,pM) elliptic 
			curve over Galois-field with characteristic 2, 
number                  of points modulo an integer determined with the 
			Schoof algorithm ecmpsnfnpmi(P,a4,a6,S,pM) elliptic 
			curve over modular primes, short normal form, 
number                  of points special version ecmipsnfnpsv(p,a4,a6) 
			elliptic curve over modular integer primes short 
			normal form 
number                  of points, j-invariant iecgnpj(p,m,h1,h2,D) integer 
			elliptic curve of given 
number                  of rows manrrow(M) (MACRO) matrix 
number                  one ? isrone(A) is rational 
number                  power of 2 rp2(n) rational 
number                  product (rekursiv) ppfrprod(r,p,P,R) polynomial 
			over p-adic field rational 
number                  product (rekursiv) prrprod(r,P,A) polynomial over 
			rationals, rational 
number                  product diprrprod(r,P,A) distributive polynomial 
			over rationals, rational 
number                  product nfelrprod(F,a,R) number field element 
			rational 
number                  product pfelrprod(p,a,R) p-adic field element 
			rational 
number                  product rprod(R,S) rational 
number                  product udprrprod(P,A) univariate dense polynomial 
			over rationals, rational 
number                  putcn(a,v,n) (MACRO) put complex 
number                  putr(R) (MACRO) put rational 
number                  qffmsdcn(m,P) quadratic function field over modular 
			singles divisor class 
number                  qffmsicn(m,P) quadratic function field over modular 
			singles ideal class 
number                  quotient rquot(R,S) (MACRO) rational 
number                  sgetr(ps) string get rational 
number                  signum rsign(R) (MACRO) rational 
number                  sputr(R,str) string put rational 
number                  square ? isrsqr(R) is rational 
number                  subroutine 1 qffmsdcns1(m,P) quadratic function 
			field over modular singles divisor class 
number                  subroutine 2 qffmsdcns2(m,P) quadratic function 
			field over modular singles divisor class 
number                  subroutine 3 qffmsdcns3(m,P) quadratic function 
			field over modular singles divisor class 
number                  sum rsum(R,S) rational 
number                  to floating point rtofl(r) rational 
number                  to modular integer rtomi(R,M) rational 
number                  to number field element rtonf(R) rational 
number                  to number field element, sparse representation 
			rtonfs(R) rational 
number                  to quadratic number field element rtoqnf(D,A) 
			(MACRO) rational 
number                  to rational function over rationals rtorfr(r,R) 
			rational 
number,                 difference qnfrdif(D,a,b) (MACRO) quadratic number 
			field element, rational 
number,                 product qnfrprod(D,a,b) quadratic number field 
			element, rational 
number,                 quadratic number field element, difference 
			rqnfdif(D,a,b) (MACRO) rational 
number,                 quadratic number field element, quotient 
			rqnfquot(D,a,b) rational 
number,                 quotient qnfrquot(D,a,b) (MACRO) quadratic number 
			field element, rational 
number,                 sum qnfrsum(D,a,b) quadratic number field element, 
			rational 
numbers                 fgetecr(pf) file get elliptic curve over rational 
numbers                 fgetecrp(pf) file get point on elliptic curve over 
			rational 
numbers                 fgetlr(pf) file get list of rational 
numbers                 getecr() get elliptic curve over rational 
numbers                 getlr() (MACRO) get list of rational 
numbers                 initialization ecrinit(a1r,a2r,a3r,a4r,a6r) 
			elliptic curve over the rational 
numbers                 point getecrp() (MACRO) get elliptic curve over 
			rational 
numbers                 putecr(E) (MACRO) put elliptic curve over rational 
numbers                 reduction list ecrrl(E) elliptic curve over 
			rational 
numbers                 reduction type ecrrt(E,p) elliptic curve over 
			rational 
numbers,                Fourier expansion of the L-series 
			ecrfelser(E,A,z,result) elliptic curve over 
			rational 
numbers,                L-series ecrlser(E) elliptic curve over rational 
numbers,                L-series, first derivative ecrlserfd(E) elliptic 
			curve over rational 
numbers,                L-series, higher derivative ecrlserhd(E,r) elliptic 
			curve over rational 
numbers,                L-series, higher derivative, small conductor 
			ecrlserhdsc(E,A,r,result) elliptic curve over 
			rational 
numbers,                Manin algorithm ecrmaninalg(E) elliptic curve over 
			rational 
numbers,                Tate's values b2, b4, b6, b8 
			ecrtavalb(a1,a2,a3,a4,a6) elliptic curve over 
			rational 
numbers,                Weil height ecracweilhe(E,P) elliptic curve over 
			the rational 
numbers,                actual curve fputecrac(E,pf) file put elliptic 
			curve over rational 
numbers,                actual curve putecrac(E) (MACRO) put elliptic curve 
			over rational 
numbers,                actual curve to global minimal model ( Laska's 
			algorithm ) ecractoecimin(E) elliptic curve over 
			rational 
numbers,                actual curve, Mordell-Weil-group, base 
			ecracmwgbase(E) elliptic curve over the rational 
numbers,                actual curve, a1 ecraca1(E) (MACRO) elliptic curve 
			over rational 
numbers,                actual curve, a2 ecraca2(E) (MACRO) elliptic curve 
			over rational 
numbers,                actual curve, a3 ecraca3(E) (MACRO) elliptic curve 
			over rational 
numbers,                actual curve, a4 ecraca4(E) (MACRO) elliptic curve 
			over rational 
numbers,                actual curve, a6 ecraca6(E) (MACRO) elliptic curve 
			over rational 
numbers,                actual curve, b2 ecracb2(E) elliptic curve over 
			rational 
numbers,                actual curve, b4 ecracb4(E) elliptic curve over 
			rational 
numbers,                actual curve, b6 ecracb6(E) elliptic curve over 
			rational 
numbers,                actual curve, b8 ecracb8(E) elliptic curve over 
			rational 
numbers,                actual curve, birational transformation to short 
			normal form ecracbtsnf(E) elliptic curve over 
			rational 
numbers,                actual curve, c4 ecracc4(E) elliptic curve over 
			rational 
numbers,                actual curve, c6 ecracc6(E) elliptic curve over 
			rational 
numbers,                actual curve, discriminant ecracdisc(E) elliptic 
			curve over rational 
numbers,                actual curve, factorization of discriminant 
			ecracfdisc(E) elliptic curve over rational 
numbers,                actual curve, generators of torsion group 
			ecracgentor(E) elliptic curve over rational 
numbers,                actual curve, multiplication-map ecracmul(E,P,n) 
			elliptic curve over the rational 
numbers,                actual curve, negative point ecracneg(E,P) elliptic 
			curve over the rational 
numbers,                actual curve, sum of points ecracsum(E,P,Q) 
			elliptic curve over the rational 
numbers,                actual curve, torsion group ecractorgr(E) elliptic 
			curve over rational 
numbers,                actual model isponecrac(E,P) is point on elliptic 
			curve over rational 
numbers,                birational transformation of coefficients 
			ecracbtco(E,BT) elliptic curve over rational 
numbers,                birational transformation of coefficients 
			ecrbtco(LC,BT) elliptic curve over rational 
numbers,                birational transformation of list of points 
			ecrbtlistp(LP,BT,modus) elliptic curve over 
			rational 
numbers,                birational transformation of point ecrbtp(P,BT) 
			elliptic curve over rational 
numbers,                birational transformation, concatenation of 
			transformations ecrbtconc(BT1,BT2) elliptic curve 
			over rational 
numbers,                birational transformation, inverse transformation 
			ecrbtinv(BT) elliptic curve over rational 
numbers,                complex period ecrcperiod(E) elliptic curve over 
			the rational 
numbers,                conductor ecrcond(E) elliptic curve over rational 
numbers,                exponent of torsion group ecrexptor(E) elliptic 
			curve over rational 
numbers,                factorization of conductor ecrfcond(E) elliptic 
			curve over rational 
numbers,                invariants fputecrinv(E,pf) file put elliptic curve 
			over the rational 
numbers,                invariants putecrinv(E) (MACRO) put elliptic curve 
			over the rational 
numbers,                j-invariant ecrjinv(E) elliptic curve over rational 
numbers,                list of points fputecrlistp(P,modus,pf) file put 
			elliptic curve over the rational 
numbers,                list of points putecrlistp(P,modus) (MACRO) put 
			elliptic curve over rational 
numbers,                minimal model, double of point ecracdouble(E,P) 
			elliptic curve over the rational 
numbers,                order of Tate- Shafarevic group ecrordtsg(E) 
			elliptic curve over the rational 
numbers,                order of torsion group ecrordtor(E) elliptic curve 
			over rational 
numbers,                point comparison ecrpcomp(P1,P2) elliptic curve 
			over rational 
numbers,                point fputecrp(P,pf) file put elliptic curve over 
			rational 
numbers,                point normalization ecrpnorm(P) elliptic curve over 
			rational 
numbers,                point putecrp(P) (MACRO) put elliptic curve over 
			rational 
numbers,                point to projective representation ecrptoproj(P) 
			elliptic curve over rational 
numbers,                real period ecrrperiod(E) elliptic curve over the 
			rational 
numbers,                regulator ecrregulator(E) elliptic curve over the 
			rational 
numbers,                short normal form, real roots of the right side 
			ecrsnfrroots(a,b) elliptic curve over rational 
numbers,                sign of the functional equation ecrsign(E) elliptic 
			curve over rational 
numbers,                structure of torsion group ecrstrtor(E) elliptic 
			curve over rational 
numerator               and denominator prnumden(r,P,pA) polynomial over 
			the rationals 
numerator               rnum(R) (MACRO) rational number 
object                  ? isobj(a) (MACRO) is 
object                  equal (rekursiv) oequal(a,b) 
object                  extent (rekursiv) oextent(a) 
object                  fgeto(pf) file get 
object                  fputo(a,pf) (MACRO) file put 
object                  geto() (MACRO) get 
object                  list1(a) (MACRO) list of one 
object                  llast(L) list last 
object                  puto(a) (MACRO) put 
objects                 lcomp2(a,b,L) (MACRO) list composition, 2 
objects                 lcomp3(a,b,c,L) (MACRO) list composition, 3 
objects                 lcomp4(a,b,c,d,L) (MACRO) list composition, 4 
objects                 lcomp5(a,b,c,d,e,L) (MACRO) list composition, 5 
objects                 lcomp6(a,b,c,d,e,f,L) (MACRO) list composition, 6 
objects                 list2(a,b) (MACRO) list of 2 
objects                 list3(a,b,c) (MACRO) list of 3 
objects                 list4(a,b,c,d) (MACRO) list of 4 
objects                 list5(a,b,c,d,e) (MACRO) list of 5 
objects                 list6(a,b,c,d,e,f) (MACRO) list of 6 
objects                 lred2(L) (MACRO) list reductum, 2 
objects                 lred3(L) (MACRO) list reductum, 3 
objects                 lred4(L) (MACRO) list reductum, 4 
objects                 lred5(L) (MACRO) list reductum, 5 
objects                 lred6(L) list reductum, 6 
odd                     iodd(A) (MACRO) integer 
odd                     sodd(a) (MACRO) single-precision 
oequal(a,b)             object equal (rekursiv) 
oextent(a)              object extent (rekursiv) 
oibasisfgen(F,L)        order over the integers basis from generators 
old                     version (rekursiv) ifact_o(N) integer 
			factorization, 
old                     version iqrem_2(A,B,pQ,pR) integer quotient and 
			remainder, 
one                     ? isdipione(r,P) is distributive polynomial over 
			integers 
one                     ? isdippione(r1,r2,P) is distributive polynomial 
			over polynomials over integers 
one                     ? isdiprfrone(r1,r2,P) is distributive polynomial 
			over rational functions over the rationals 
one                     ? isdiprone(r,P) is distributive polynomial over 
			rationals 
one                     ? isgfsone(p,AL,a) is Galois-field with single 
			characteristic element 
one                     ? ispione(r,P) is polynomial over integers equal 
one                     ? isrone(A) is rational number 
one                     isnfone(F,A) is number field element 
one                     isrfrone(r,A) is rational function over rationals 
one                     object list1(a) (MACRO) list of 
one                     qnfidone(D) (MACRO) quadratic number field ideal 
one                     single ideal class, imaginary case 
			qffmsordsici(m,D,Q,P,OS) quadratic function field 
			over modular singles order of 
one                     single ideal class, real case 
			qffmsordsicr(m,D,d,LE,ID,OS) quadratic function 
			field over modular singles order of 
one?                    isqnfidone(D,A) is quadratic number field ideal 
one?                    isqnfone(D,a) (MACRO) is quadratic number field 
			element 
only                    ) ijacsym_lo(A,B) integer Jacobi-symbol ( lists 
only                    ) ispd_lo(N,pM) integer small prime divisors ( 
			lists 
only                    ) isqrt_lo(A) integer square root ( lists 
only                    ) miexp_lo(M,A,E) modular integer exponentiation ( 
			lists 
only                    ) rhopds_lo(N,b,z) rho- method by Pollard divisor 
			search ( lists 
only                    igcd_lo(A,B) integer greatest common divisor, lists 
only                    iprod_lo(A,B) integer product, lists 
only                    iqrem_lo(A,B,pQ,pR) integer quotient and remainder, 
			lists 
only                    miinv_lo(M,A) modular integer inverse, lists 
oprmsp1basfg(p,F,L)     order over polynomial ring over modular single 
			prime, transcendence degree 1, basis from 
			generators 
order                   dipgfslotglo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
			graduated lexicographical 
order                   dipilotoglo(r,P) distributive polynomial over 
			integers in lexicographical order to distributive 
			polynomial over integers in graduated 
			lexicographical 
order                   dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			in graduated lexicographical 
order                   dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			in graduated lexicographical 
order                   dipnflotoglo(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over number field in 
			graduated lexicographical 
order                   dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over polynomials over 
			integers in graduated lexicographical 
order                   diprfrlotglo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			graduated lexicographical 
order                   diprlotoglo(r,P) distributive polynomial over 
			rationals in lexicographical order to distributive 
			polynomial over rationals in graduated 
			lexicographical 
order                   lscomp(L1,L2) list of singles comparison, 
			lexicographical 
order                   of Tate- Shafarevic group ecrordtsg(E) elliptic 
			curve over the rational numbers, 
order                   of a point to exact order of the point 
			ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve 
			over Galois-field with characteristic 2, multiple 
			of the 
order                   of a point to exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular primes, short normal form, multiple of the 
order                   of a point with the Pollard Lambda method 
			ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) elliptic curve 
			over Galois-field with characteristic 2, finding a 
			multiple of the 
order                   of a point with the Pollard Lambda method 
			ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
			modular primes, short normal form, finding a 
			multiple of the 
order                   of a point with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular primes, short normal form, finding a 
			multiple of the 
order                   of a univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, decomposition law 
			ouspprmsp1dl(p,F,P,k) 
order                   of a univariate separable polynomial over the 
			polynomial ring over modular single prime, 
			transcendence degree 1 vepepuspmsp1(p,F,a,P,k,v) 
			values of the extensions of the P-adic valuation of 
			an element of the polynomial 
order                   of an univariate polynomial over the integers, 
			Dedekind maximality test oupidedekmt(M,P) 
order                   of an univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, Dedekind maximality test 
			ouspprmsp1dm(p,P,F) 
order                   of an univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, basis of a local maximal 
			over-order ouspprmsp1bl(p,F,P,Q,pk) 
order                   of an univariate separable polynomial over the 
			integers approximation of p-adic factorization of 
			the defining polynomial, generators of p-maximal 
			orders of the p-adic divisors of the defining 
			polynomial and p-minimal polynomials of the 
			generators ouspiapfgmic(p,P,k) 
order                   of an univariate separable polynomial over the 
			integers basis of a local maximal over-order 
			ouspibaslmo(F,p,Q,pk) 
order                   of an univariate separable polynomial over the 
			integers basis of a local maximal over-order with 
			respect to integer primes ouspibaslmoi(F,P,Q,pk) 
order                   of an univariate separable polynomial over the 
			integers basis of the integral closure ( ORDMAX, 
			Ordmax, ordmax, integral basis ) ouspibasisic(F,pL) 
order                   of an univariate separable polynomial over the 
			polynomial ring over modular single prime, 
			transcendence degree 1 nepousppmsp1(p,F,a) norm of 
			an element of the polynomial 
order                   of an univariate separable polynomial over the 
			polynomial ring over modular single prime, 
			transcendence degree 1, integral basis 
			ouspprmsp1ib(p,F,pL) 
order                   of one single ideal class, imaginary case 
			qffmsordsici(m,D,Q,P,OS) quadratic function field 
			over modular singles 
order                   of one single ideal class, real case 
			qffmsordsicr(m,D,d,LE,ID,OS) quadratic function 
			field over modular singles 
order                   of the point ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) 
			elliptic curve over Galois-field with 
			characteristic 2, multiple of the order of a point 
			to exact 
order                   of the point ecmpsnfmopto(p,a4,a6,P,mul) elliptic 
			curve over modular primes, short normal form, 
			multiple of the order of a point to exact 
order                   of torsion group ecrordtor(E) elliptic curve over 
			rational numbers, 
order                   over polynomial ring over modular single prime, 
			transcendence degree 1, basis from generators 
			oprmsp1basfg(p,F,L) 
order                   over the integers basis from generators 
			oibasisfgen(F,L) 
order                   ppford(r,p,P) polynomial over p-adic field 
order                   qnfielpiord(D,P,pi,z,a) quadratic number field, 
			integral element, prime ideal 
order                   qnfpiord(D,P,pi,z,a) quadratic number field element 
			prime ideal 
order                   to distributive polynomial over Galois-field with 
			single characteristic in graduated lexicographical 
			order dipgfslotglo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical 
order                   to distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical 
order                   to distributive polynomial over Galois-field with 
			single characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical 
order                   to distributive polynomial over integers in 
			graduated lexicographical order dipilotoglo(r,P) 
			distributive polynomial over integers in 
			lexicographical 
order                   to distributive polynomial over integers in 
			lexicographical order with inverse exponent vector 
			dipilotolio(r,P) distributive polynomial over 
			integers in lexicographical 
order                   to distributive polynomial over integers with total 
			degree ordering dipilototdo(r,P) distributive 
			polynomial over integers in lexicographical 
order                   to distributive polynomial over modular integer 
			primes in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical 
order                   to distributive polynomial over modular integer 
			primes in lexicographical order with inverse 
			exponent vector dipmiplotlio(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical 
order                   to distributive polynomial over modular integer 
			primes with total degree ordering 
			dipmiplottdo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical 
order                   to distributive polynomial over modular single 
			primes in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical 
order                   to distributive polynomial over modular single 
			primes in lexicographical order with inverse 
			exponent vector dipmsplotlio(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical 
order                   to distributive polynomial over modular single 
			primes with total degree ordering 
			dipmsplottdo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical 
order                   to distributive polynomial over number field in 
			graduated lexicographical order dipnflotoglo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical 
order                   to distributive polynomial over number field in 
			lexicographical order with inverse exponent vector 
			dipnflotolio(r,F,P) distributive polynomial over 
			number field in lexicographical 
order                   to distributive polynomial over number field with 
			total degree ordering dipnflototdo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical 
order                   to distributive polynomial over polynomials over 
			integers in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical 
order                   to distributive polynomial over polynomials over 
			integers in lexicographical order with inverse 
			exponent vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical 
order                   to distributive polynomial over polynomials over 
			integers with total degree ordering 
			dippilototdo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical 
order                   to distributive polynomial over rational functions 
			over the rationals in graduated lexicographical 
			order diprfrlotglo(r1,r2,P) distributive polynomial 
			over rational functions over the rationals in 
			lexicographical 
order                   to distributive polynomial over rational functions 
			over the rationals in lexicographical order with 
			inverse exponent vector diprfrlotlio(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical 
order                   to distributive polynomial over rational functions 
			over the rationals with total degree ordering 
			diprfrlottdo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical 
order                   to distributive polynomial over rationals in 
			graduated lexicographical order diprlotoglo(r,P) 
			distributive polynomial over rationals in 
			lexicographical 
order                   to distributive polynomial over rationals in 
			lexicographical order with inverse exponent vector 
			diprlotolio(r,P) distributive polynomial over 
			rationals in lexicographical 
order                   to distributive polynomial over rationals with 
			total degree ordering diprlototdo(r,P) distributive 
			polynomial over rationals in lexicographical 
order                   with inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical 
order                   with inverse exponent vector dipilotolio(r,P) 
			distributive polynomial over integers in 
			lexicographical order to distributive polynomial 
			over integers in lexicographical 
order                   with inverse exponent vector dipmiplotlio(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over modular integer primes in lexicographical 
order                   with inverse exponent vector dipmsplotlio(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order to distributive polynomial 
			over modular single primes in lexicographical 
order                   with inverse exponent vector dipnflotolio(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order to distributive polynomial 
			over number field in lexicographical 
order                   with inverse exponent vector dippilotolio(r1,r2,P) 
			distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
			polynomial over polynomials over integers in 
			lexicographical 
order                   with inverse exponent vector diprfrlotlio(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the rationals in lexicographical 
order                   with inverse exponent vector diprlotolio(r,P) 
			distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over rationals in lexicographical 
ordering                dipgfslottdo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic with 
			total degree 
ordering                dipilototdo(r,P) distributive polynomial over 
			integers in lexicographical order to distributive 
			polynomial over integers with total degree 
ordering                dipmiplottdo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			with total degree 
ordering                dipmsplottdo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			with total degree 
ordering                dipnflototdo(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over number field with 
			total degree 
ordering                dippilototdo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over polynomials over 
			integers with total degree 
ordering                diprfrlottdo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals with 
			total degree 
ordering                diprlototdo(r,P) distributive polynomial over 
			rationals in lexicographical order to distributive 
			polynomial over rationals with total degree 
orders                  of the p-adic divisors of the defining polynomial 
			and p-minimal polynomials of the generators 
			ouspiapfgmic(p,P,k) order of an univariate 
			separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal 
ordmax,                 integral basis ) ouspibasisic(F,pL) order of an 
			univariate separable polynomial over the integers 
			basis of the integral closure ( ORDMAX, Ordmax, 
original                baby step - giant step version qffmsregobg(m,D) 
			quadratic function field over modular singles 
			regulator, 
original                baby step version qffmsregobs(m,D) quadratic 
			function field over modular singles regulator, 
original                number field element fputonfel(F,a,V,pf) file put 
original                number field element putonfel(F,a,V) (MACRO) put 
original                version qffmsfuobs(m,D) quadratic function field 
			over modular singles fundamental unit, 
orthogonalized          basis modiorthobas(bas) module over the integers, 
oupidedekmt(M,P)        order of an univariate polynomial over the 
			integers, Dedekind maximality test 
ouspiapfgmic(p,P,k)     order of an univariate separable polynomial over 
			the integers approximation of p-adic factorization 
			of the defining polynomial, generators of p-maximal 
			orders of the p-adic divisors of the defining 
			polynomial and p-minimal polynomials of the 
			generators 
ouspibasisic(F,pL)      order of an univariate separable polynomial over 
			the integers basis of the integral closure ( 
			ORDMAX, Ordmax, ordmax, integral basis ) 
ouspibaslmo(F,p,Q,pk)   order of an univariate separable polynomial over 
			the integers basis of a local maximal over-order 
ouspibaslmoi(F,P,Q,pk)  order of an univariate separable polynomial over 
			the integers basis of a local maximal over-order 
			with respect to integer primes 
ouspprmsp1bl(p,F,P,Q,pk) order of an univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, basis of a local maximal 
			over-order 
ouspprmsp1dl(p,F,P,k)   order of a univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, decomposition law 
ouspprmsp1dm(p,P,F)     order of an univariate separable polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, Dedekind maximality test 
ouspprmsp1ib(p,F,pL)    order of an univariate separable polynomial over 
			the polynomial ring over modular single prime, 
			transcendence degree 1, integral basis 
output-counter          getocnt(pf) get 
output-counter          setocnt(pf,n) set 
over-order              ouspibaslmo(F,p,Q,pk) order of an univariate 
			separable polynomial over the integers basis of a 
			local maximal 
over-order              ouspprmsp1bl(p,F,P,Q,pk) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, basis 
			of a local maximal 
over-order              with respect to integer primes 
			ouspibaslmoi(F,P,Q,pk) order of an univariate 
			separable polynomial over the integers basis of a 
			local maximal 
overflow                error floverflow(a) floating point 
overflow                error handling flerr() (MACRO) floating point 
p-adic                  divisors of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable polynomial over 
			the integers approximation of p-adic factorization 
			of the defining polynomial, generators of p-maximal 
			orders of the 
p-adic                  factorization of the defining polynomial, 
			generators of p-maximal orders of the p-adic 
			divisors of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable polynomial over 
			the integers approximation of 
p-adic                  factorization uspiapf(p,P,k) univariate separable 
			polynomial over the integers, approximation of 
p-adic                  field ? isdppf(r,p,P) is dense polynomial over 
p-adic                  field additive valuation pfaval(p,a) 
p-adic                  field derivation, main variable (rekursiv) 
			ppfderiv(r,p,P) polynomial over 
p-adic                  field derivation, selected variable 
			ppfderivsv(r,p,P,n) polynomial over 
p-adic                  field difference ppfdif(r,p,P1,P2) polynomial over 
p-adic                  field difference udppfdif(p,P1,P2) univariate dense 
			polynomial over 
p-adic                  field element difference pfdif(p,a,b) 
p-adic                  field element exponentiation pfexp(p,a,n) 
p-adic                  field element fgetpfel(p,pf) file get 
p-adic                  field element fgetspfel(p,pf) file get special 
p-adic                  field element fputpfel(p,a,pf) file put 
p-adic                  field element fputspfel(p,a,pf) file put special 
p-adic                  field element getpfel(p) (MACRO) get 
p-adic                  field element getspfel(p) (MACRO) get special 
p-adic                  field element integer product pfeliprod(p,a,i) 
p-adic                  field element inverse pfinv(p,a) 
p-adic                  field element itopfel(p,d,A) integer to 
p-adic                  field element negation pfneg(p,a) 
p-adic                  field element prime power product pfpprod(p,a,i) 
p-adic                  field element product pfprod(p,a,b) 
p-adic                  field element product ppfpfprod(r,p,P,b) polynomial 
			over p-adic field 
p-adic                  field element product udppfpfprod(p,P,a) univariate 
			dense polynomial over p-adic field 
p-adic                  field element putpfel(p,a) (MACRO) put 
p-adic                  field element putspfel(p,a) (MACRO) put special 
p-adic                  field element rational number product 
			pfelrprod(p,a,R) 
p-adic                  field element rtopfel(p,d,R) rational to 
p-adic                  field element sum pfsum(p,a,b) 
p-adic                  field element? ispfel(p,a) is 
p-adic                  field evaluation, main variable ppfeval(r,p,P,A) 
			polynomial over 
p-adic                  field evaluation, selected variable 
			ppfevalsv(r,p,P,n,A) polynomial over 
p-adic                  field exponentiation ppfexp(r,p,P,n) polynomial 
			over 
p-adic                  field exponentiation udppfexp(p,P,n) univariate 
			dense polynomial over 
p-adic                  field fgetppf(r,p,V,pf) file get polynomial over 
p-adic                  field fitting ppffit(r,p,P,d) polynomial over 
p-adic                  field fitting udppffit(p,P,Pd) univariate dense 
			polynomial over 
p-adic                  field fputppf(r,p,P,V,pf) file put polynomial over 
p-adic                  field getppf(r,p,V) get polynomial over 
p-adic                  field integer product ppfiprod(r,p,P,i) polynomial 
			over 
p-adic                  field negation ppfneg(r,p,P) polynomial over 
p-adic                  field negation udppfneg(p,P) univariate dense 
			polynomial over 
p-adic                  field order ppford(r,p,P) polynomial over 
p-adic                  field p-adic field element product 
			ppfpfprod(r,p,P,b) polynomial over 
p-adic                  field p-adic field element product 
			udppfpfprod(p,P,a) univariate dense polynomial over 
p-adic                  field pitoppf(r,P,p,d) polynomial over integers to 
			polynomial over 
p-adic                  field prime power product ppfpprod(r,p,P,i) 
			polynomial over 
p-adic                  field prime power product udppfpprod(p,P,i) 
			univariate dense polynomial over 
p-adic                  field product ppfprod(r,p,P1,P2) polynomial over 
p-adic                  field product udppfprod(p,P1,P2) univariate dense 
			polynomial over 
p-adic                  field prtoppf(r,P,p,d) polynomial over rationals to 
			polynomial over 
p-adic                  field putppf(r,p,P,V) put polynomial over 
p-adic                  field quotient pfquot(p,a,b) 
p-adic                  field rational number product (rekursiv) 
			ppfrprod(r,p,P,R) polynomial over 
p-adic                  field substitution, main variable 
			ppfsubst(r,p,P1,P2) polynomial over 
p-adic                  field substitution, selected variable 
			ppfsubstsv(r,p,P1,n,P2) polynomial over 
p-adic                  field sum ppfsum(r,p,P1,P2) polynomial over 
p-adic                  field sum udppfsum(p,P1,P2) univariate dense 
			polynomial over 
p-adic                  field transformation 
			ppftransf(r1,p,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over 
p-adic                  field translation, all variables 
			ppftransav(r,p,P,Lpf) polynomial over 
p-adic                  field translation, main variable ppftrans(r,p,P,A) 
			polynomial over 
p-adic                  field udpitoudppf(P,p,d) univariate dense 
			polynomial over integers to univariate dense 
			polynomial over 
p-adic                  field udprtoudppf(P,p,d) univariate dense 
			polynomial over rationals to univariate dense 
			polynomial over 
p-adic                  valuation of an element of the polynomial ring of 
			an univariate separable polynomial over the 
			integers vepvelpruspi(F,a,p,k,v) values of the 
			extensions of the 
p-maximal               orders of the p-adic divisors of the defining 
			polynomial and p-minimal polynomials of the 
			generators ouspiapfgmic(p,P,k) order of an 
			univariate separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of 
p-minimal               polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable polynomial over 
			the integers approximation of p-adic factorization 
			of the defining polynomial, generators of p-maximal 
			orders of the p-adic divisors of the defining 
			polynomial and 
p-part                  intpp(p,m) integer 
p-power                 infeminpmpp(F,a,p,e,Q) integral number field 
			element minimal polynomial modulo 
p-power                 with respect to integer primes 
			infempmppip(F,a,p,e,Q) integral number field 
			element minimal polynomial modulo 
p-primality             test and factorization of the defining polynomial 
			or the minimal polynomial 
			infepptfact(F,p,Q,ppot,a0,z) integral number field 
			element 
p-primality             test and factorization of the defining polynomial 
			or the minimal polynomial with respect to integer 
			primes infepptfip(F,p,Q,ppot,a0,z) integral number 
			field element 
p-primary               number field element regulation with respect to 
			integer primes ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) 
			integral 
p-primary               number field element regulation, version1 
			ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) integral 
p-primary               number field element regulation, version2 
			ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) integral 
p-primary               number field element, core algorithm 
			ippnfecoreal(F,p,Q,mp) integral 
p-primary               number field element, increasing the denominator of 
			the p-star value 
			ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
p-primary               number field element, increasing the denominator of 
			the p-star value with respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
p-star                  valuation infepstarval(p,A) integral number field 
			element 
p-star                  valuation with respect to integer primes 
			infepstarvip(P,A) integral number field element 
p-star                  value ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) 
			integral p-primary number field element, increasing 
			the denominator of the 
p-star                  value with respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
			denominator of the 
package                 Earith() Essen arithmetic 
package:                I/O functions HDiio() Heidelberg arithmetic 
package:                I/O-functions PAFio() Papanikolaou floating point 
package:                addition PAFadd() Papanikolaou floating point 
package:                assignments PAFassign() Papanikolaou floating point 
package:                comparisons PAFcomp() Papanikolaou floating point 
package:                construction PAFcon() Papanikolaou floating point 
package:                digit functions HDidigit() Heidelberg arithmetic 
package:                division PAFdiv() Papanikolaou floating point 
package:                globals PAFglob() Papanikolaou floating point 
package:                greatest common divisor HDigcd() Heidelberg 
			arithmetic 
package:                integer addition HDiadd() Heidelberg arithmetic 
package:                integer division HDidiv() Heidelberg arithmetic 
package:                integer multiplication HDimul() Heidelberg 
			arithmetic 
package:                memory management HDimem() Heidelberg arithmetic 
package:                multiplication PAFmul() Papanikolaou floating point 
package:                shiftings PAFshift() Papanikolaou floating point 
package:                subtraction PAFsub() Papanikolaou floating point 
package:                transcendental functions 1 PAFtrans1() Papanikolaou 
			floating point 
package:                transcendental functions 2 PAFtrans2() Papanikolaou 
			floating point 
package:                transcendental functions 3 PAFtrans3() Papanikolaou 
			floating point 
package:                typer PAFtype() Papanikolaou floating point 
package:                utilities HDiutil() Heidelberg arithmetic 
package:                utilities PAFutil() Papanikolaou floating point 
package:                vector functions HDidigitvec() Heidelberg 
			arithmetic 
pair                    lpair(L1,L2) list 
pairing                 eciminnetapa(E,P,Q) elliptic curve with integer 
			coefficients, minimal model, Neron-Tate 
pairs                   power maximum lipairspmax(L) list of integer 
parametric              ideal membership test 
			dippipim(r1,r2,s,PL,PTL,CONDS,OPL) distributive 
			polynomial over polynomials over integers 
parametric              ideal membership test 
			fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers 
parametric              ideal membership test 
			putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers 
part                    (rekursiv) lsizerec(l,n) list size recursive 
part                    ccri(re,im) (MACRO) complex construction from real 
			and imaginary 
part                    cimag(z) (MACRO) complex imaginary 
part                    creal(z) (MACRO) complex real 
part                    dipicp(r,P,pPP) distributive polynomial over 
			integers content and primitive 
part                    dippicp(r1,r2,P,pPP) distributive polynomial over 
			polynomials over integers content and primitive 
part                    ecgf2msha1(G,a1,a2,a3,a4,a6,P,a,m,pl,ts) elliptic 
			curve over Galois-field with characteristic 2, 
			modified Shanks' algorithm, first 
part                    ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over modular primes, short normal form, modified 
			Shanks' algorithm, first 
part                    isfp(A) integer squarefree 
part                    picontpp(r,P,pPP) polynomial over integers content 
			and primitive 
part                    piprimpart(r,P) (MACRO) polynomial over integers 
			primitive 
part                    udpicontpp(P,pPP) univariate dense polynomial over 
			integers content and primitive 
part                    upgfssfp(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic squarefree 
part                    upmisfp(m,P) univariate polynomial over modular 
			integers squarefree 
part                    upmssfp(m,P) univariate polynomial over modular 
			singles squarefree 
part                    upmssrpp(m,P) univariate polynomial over modular 
			singles square root principal 
partition               csetpart(L) characteristic set from 
pdegree(r,P)            (MACRO) polynomial degree, main variable 
pdegreesv(r,P,n)        polynomial degree, specified variable (rekursiv) 
pdegvec(r,P)            polynomial degree vector (rekursiv) 
period                  ecrcperiod(E) elliptic curve over the rational 
			numbers, complex 
period                  ecrrperiod(E) elliptic curve over the rational 
			numbers, real 
permutation             lpermut(L,PI) list 
permutation             lsrandperm(n) list of singles random 
permutation             mavpermut(r,M,PI) matrix of polynomials variable 
permutation             pvpermut(r,P,PI) polynomial variable 
permutation             vecvpermut(r,V,PI) vector of polynomials variable 
permutations            generator lepermg(L) list element 
pfaval(p,a)             p-adic field additive valuation 
pfdif(p,a,b)            p-adic field element difference 
pfeliprod(p,a,i)        p-adic field element integer product 
pfelrprod(p,a,R)        p-adic field element rational number product 
pfexp(p,a,n)            p-adic field element exponentiation 
pfinv(p,a)              p-adic field element inverse 
pflsum(r,P1,P2)         polynomial over floating points sum (rekursiv) 
pfneg(p,a)              p-adic field element negation 
pfpprod(p,a,i)          p-adic field element prime power product 
pfprod(p,a,b)           p-adic field element product 
pfquot(p,a,b)           p-adic field quotient 
pfsum(p,a,b)            p-adic field element sum 
pgf2deriv(r,G,P)        polynomial over Galois-field with characteristic 2 
			derivation, main variable 
pgf2derivsv(r,G,P,i)    polynomial over Galois-field with characteristic 2 
			derivation, specified variable (rekursiv) 
pgf2dif(r,G,P1,P2)      (MACRO) polynomial over Galois-field with 
			characteristic 2 difference 
pgf2efe(r,GmtoGn,P)     polynomial over Galois-field with characteristic 2 
			embedding in field extension (rekursiv) 
pgf2eval(r,G,P,a)       polynomial over Galois-field with characteristic 2 
			evaluation, main variable 
pgf2exp(r,G,P,n)        polynomial over Galois-field with characteristic 2 
			exponentiation 
pgf2expprem(r,G,F,E,M)  polynomial over Galois-field with characteristic 2, 
			exponentiation, polynomial remainder 
pgf2gf2prod(r,G,P,a)    polynomial over Galois-field with characteristic 2, 
			Galois-field with characteristic 2 element product 
			(rekursiv) 
pgf2monic(r,G,P)        polynomial over Galois-field with characteristic 2 
			monic 
pgf2neg(r,G,P)          (MACRO) polynomial over Galois-field with 
			characteristic 2 negation 
pgf2prod(r,G,P1,P2)     polynomial over Galois-field with characteristic 2 
			product (rekursiv) 
pgf2qrem(r,G,P1,P2,pR)  polynomial over Galois-field with characteristic 2 
			quotient and remainder (rekursiv) 
pgf2quot(r,G,P1,P2)     (MACRO) polynomial over Galois-field with 
			characteristic 2 quotient 
pgf2rem(r,G,P1,P2)      (MACRO) polynomial over Galois-field with 
			characteristic 2 remainder 
pgf2square(r,G,P)       polynomial over Galois-field with characteristic 2 
			square (rekursiv) 
pgf2sum(r,G,P1,P2)      polynomial over Galois-field with characteristic 2 
			sum (rekursiv) 
pgf2topgfs(r,G,P)       polynomial over Galois-field with characteristic 2 
			to polynomial over Galois-field with single 
			characteristic (rekursiv) 
pgf2transf(r1,G,P1,V1,r2,P2,V2,Vn,pV3) polynomial over Galois-field with 
			characteristic 2 transformation 
pgfsderiv(r,p,AL,P)     polynomial over Galois-field with single 
			characteristic derivation, main variable 
pgfsderivsv(r,p,AL,P,i) polynomial over Galois-field with single 
			characteristic derivation, specified variable 
			(rekursiv) 
pgfsdif(r,p,AL,P1,P2)   polynomial over Galois-field with single 
			characteristic difference (rekursiv) 
pgfsefe(r,p,ALm,P,g)    polynomial over Galois-field with single 
			characteristic embedding in field extension 
			(rekursiv) 
pgfseval(r,p,AL,P,a)    polynomial over Galois-field with single 
			characteristic evaluation, main variable 
pgfsevalsv(r,p,AL,P,d,a) polynomial over Galois-field with single 
			characteristic evaluation, specified variable 
			(rekursiv) 
pgfsexp(r,p,AL,P,m)     polynomial over Galois-field with single 
			characteristic exponentiation 
pgfsexpprem(r,p,AL,F,E,M) polynomial over Galois-field with single 
			characteristic, exponentiation, polynomial 
			remainder 
pgfsgfsprod(r,p,AL,P,a) polynomial over Galois-field with single 
			characteristic, Galois-field with single 
			characteristic element product (rekursiv) 
pgfsgfsquot(r,p,AL,P,a) polynomial over Galois-field with single 
			characteristic, Galois-field with single 
			characteristic element quotient (rekursiv) 
pgfsmonic(r,p,AL,P)     polynomial over Galois-field with single 
			characteristic monic 
pgfsneg(r,p,AL,P)       polynomial over Galois-field with single 
			characteristic negation (rekursiv) 
pgfsprod(r,p,AL,P1,P2)  polynomial over Galois-field with single 
			characteristic product (rekursiv) 
pgfsqrem(r,p,AL,P1,P2,pR) polynomial over Galois-field with single 
			characteristic quotient and remainder (rekursiv) 
pgfsquot(r,p,AL,P1,P2)  (MACRO) polynomial over Galois-field with single 
			characteristic quotient 
pgfsrem(r,p,AL,P1,P2)   (MACRO) polynomial over Galois-field with single 
			characteristic remainder 
pgfsres(r,p,AL,P1,P2)   polynomial over Galois-field with single 
			characteristic resultant 
pgfssum(r,p,AL,P1,P2)   polynomial over Galois-field with single 
			characteristic sum (rekursiv) 
pgfstopgf2(r,G,P)       polynomial over Galois-field with single 
			characteristic to polynomial over Galois-field with 
			characteristic 2 (rekursiv) 
pgfstransf(r1,p,AL,P1,V1,r2,P2,V2,Vn,pV3) polynomial over Galois-field with 
			single characteristic transformation 
phi-value               iphi(N) integer eulerian 
piabs(r,P)              polynomial over integers absolute value 
pibezout(r,P1,P2)       polynomial over integers Bezout-matrix 
picevalp(r,P,sA)        polynomial over integers choice of evaluation 
			points 
picont(r,P)             polynomial over integers content 
picontpp(r,P,pPP)       polynomial over integers content and primitive part 
picra(r,P1,P2,M,m,a)    polynomial over integers chinese remainder 
			algorithm (rekursiv) 
pideriv(r,P)            polynomial over integers derivation, main variable 
piderivsv(r,P,n)        polynomial over integers derivation, specified 
			variable (rekursiv) 
pidif(r,P1,P2)          polynomial over integers difference (rekursiv) 
pidiscr(r,P,n)          polynomial over integers discriminant 
pidiscrhank(r,P)        polynomial over integers discriminant via Hankel- 
			matrix 
pieuklnorm(r,P)         polynomial over integers Euklid norm (rekursiv) 
pieval(r,P,A)           polynomial over integers evaluation, main variable 
pievalsv(r,P,n,A)       polynomial over integers evaluation, specified 
			variable (rekursiv) 
piexp(r,P,n)            polynomial over integers exponentiation 
pifact(r,P)             polynomial over integers factorization (rekursiv) 
pifcb(L)                polynomial over integers factor coefficient bound 
pigcdcf(r,P1,P2,pQ1,pQ2) polynomial over integers greatest common divisor 
			and cofactors 
pigf2evalfvs(r,G,P)     polynomial over integers Galois-field with 
			characteristic 2 element evaluation first variable 
			special version (rekursiv) 
pigfcb(r,P)             polynomial over integers Gelfond-factor coefficient 
			bound 
pigfsevalfvs(r,p,AL,P)  polynomial over integers Galois-field with single 
			characteristic element evaluation first variable 
			special version (rekursiv) 
pihlfa(r,p,L,M,S,P)     polynomial over integers, Hensel lemma 
			factorization approximation 
piicont(r,P)            polynomial over integers integer content (rekursiv) 
piiprod(r,P,A)          polynomial over integers, integer product 
			(rekursiv) 
piiquot(r,P,A)          polynomial over integers, integer quotient 
			(rekursiv) 
pilmfcb(r,P)            polynomial over integers Landau- Mignotte- factor 
			coefficient bound 
pimaxnorm(r,P)          polynomial over integers maximum norm (rekursiv) 
pimidhom(r,S,P)         polynomial over integers modular ideal homomorphism 
pimidprod(r,S,P1,P2)    polynomial over integers modular ideal product 
pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial over integers, modular ideal, 
			Hensel lemma quadratic step 
pineg(r,P)              polynomial over integers negation (rekursiv) 
pinfevalfvs(r,F,P)      polynomial over integers number field element 
			evaluation first variable special version 
piprimpart(r,P)         (MACRO) polynomial over integers primitive part 
piprod(r,P1,P2)         polynomial over integers product (rekursiv) 
pipsrem(r,P1,P2)        polynomial over integers pseudo remainder 
piqrem(r,P1,P2,pR)      polynomial over integers quotient and remainder 
			(rekursiv) 
piquot(r,P1,P2)         (MACRO) polynomial over integers quotient 
pirem(r,P1,P2)          (MACRO) polynomial over integers remainder 
piresbez(r,P1,P2)       polynomial over integers resultant, Bezout 
			algorithm 
pirescoll(r,P1,P2,n)    polynomial over integers resultant, Collins 
			algorithm 
pirescspec(r,P1,P2,n)   polynomial over the integers resultant, Collins 
			algorithm special 
piressylv(r,P1,P2)      polynomial over integers resultant, Sylvester 
			algorithm 
pirtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) polynomial over the integers rational 
			transformation 
pisfact(r,P)            polynomial over integers squarefree factorization 
pisign(r,P)             polynomial over integers sign, base variable 
pisubst(r,P1,P2)        polynomial over integers substitution, main 
			variable 
pisubstsv(r,P1,n,P2)    polynomial over integers substitution, specified 
			variable (rekursiv) 
pisum(r,P1,P2)          polynomial over integers sum (rekursiv) 
pisumnorm(r,P)          polynomial over integers sum norm (rekursiv) 
pitopmi(r,P,M)          polynomial over integers to polynomial over modular 
			integers (rekursiv) 
pitopms(r,P,m)          polynomial over integers to polynomial over modular 
			singles (rekursiv) 
pitopnf(r,P)            polynomial over the integers to polynomial over a 
			number field (rekursiv) 
pitoppf(r,P,p,d)        polynomial over integers to polynomial over p-adic 
			field 
pitopr(r,P)             polynomial over integers to polynomial over 
			rationals (rekursiv) 
pitorfr(r,P)            polynomial over integers to rational function over 
			the rationals 
pitrans(r,P,A)          polynomial over integers translation, main variable 
pitransav(r,P,LI)       polynomial over integers translation, all variables 
			(rekursiv) 
pitransf(r1,P1,V1,r2,P2,V2,Vn,pV3) polynomial over the integers 
			transformation 
pitrprod(r,S,P1,P2)     polynomial over integers truncation product 
			(rekursiv) 
pitrunc(r,S,P)          polynomial over integers truncation (rekursiv) 
plbc(r,P)               polynomial leading base coefficient, main variable 
plc(r,P)                (MACRO) polynomial leading coefficient, main 
			variable 
pm2topgf2(r,P)          polynomial over modular 2 to polynomial over 
			Galois-field with characteristic 2 (rekursiv) 
pmakevl(s)              polynomial make list of variables 
pmibezout(r,m,P1,P2)    polynomial over modular integers Bezout-matrix 
pmideriv(r,M,P)         polynomial over modular integers derivation, main 
			variable 
pmiderivsv(r,m,P,n)     polynomial over modular integers derivation, 
			specified variable (rekursiv) 
pmidif(r,M,P1,P2)       polynomial over modular integers difference 
			(rekursiv) 
pmidiscr(r,M,P,n)       polynomial over modular integers discriminant 
pmidiscrhank(r,M,P)     polynomial over modular integers discriminant via 
			Hankel matrix 
pmieval(r,M,P,A)        polynomial over modular integers evaluation, main 
			variable 
pmievalsv(r,m,P,n,a)    polynomial over modular integers evaluation, 
			specified variable (rekursiv) 
pmiexp(r,m,P,n)         polynomial over modular integers exponentiation 
pmigcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular integers greatest common 
			divisor and cofactors (rekursiv) 
pmiinter(r,m,P1,P2,P3,a,b) polynomial over modular integers interpolation 
			(rekursiv) 
pmimidprod(r,M,S,P1,P2) polynomial over modular integers, modular ideal 
			product 
pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial over modular integers, 
			modular ideal, Hensel lemma quadratic step 
pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over modular integers, 
			modular ideal, Hensel lemma quadratic step on a 
			single variable 
pmimidqrem(r,M,S,P1,P2,pR) polynomial over modular integers monic, modular 
			ideal quotient and remainder 
pmimidse(r,M,S,P1,P2,F1,F2,H,pV) polynomial over modular integers modular 
			ideal solution of equation 
pmimiprod(r,M,P,A)      polynomial over modular integers, modular integers 
			product (rekursiv) 
pmimiquot(r,m,P,a)      polynomial over modular integers, modular integer 
			quotient (rekursiv) 
pmimonic(r,M,P)         polynomial over modular integers monic 
pmineg(r,M,P)           polynomial over modular integers negation 
			(rekursiv) 
pmiprod(r,M,P1,P2)      polynomial over modular integers product (rekursiv) 
pmipsrem(r,m,P1,P2)     polynomial over modular integers pseudo remainder 
pmiqrem(r,M,P1,P2,pR)   polynomial over modular integers quotient and 
			remainder (rekursiv) 
pmiquot(r,M,P1,P2)      (MACRO) polynomial over modular integers quotient 
pmirem(r,M,P1,P2)       (MACRO) polynomial over modular integers remainder 
pmires(r,m,P1,P2,n)     polynomial over modular integers resultant 
pmirescoll(r,m,P1,P2)   polynomial over modular integers resultant, Collins 
			algorithm (rekursiv) 
pmisubst(r,m,P1,P2)     polynomial over modular integers substitution, main 
			variable 
pmisubstsv(r,m,P1,n,P2) polynomial over modular integers substitution, 
			specified variable (rekursiv) 
pmisum(r,M,P1,P2)       polynomial over modular integers sum (rekursiv) 
pmitos(r,M,P)           polynomial over modular integers to symmetric 
			remainder system (rekursiv) 
pmitrans(r,m,P,a)       polynomial over modular integers translation, main 
			variable 
pmitransav(r,m,P,Lmi)   polynomial over modular integers translation, all 
			variables (rekursiv) 
pmitransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial over modular integers 
			transformation 
pmiucont(r,m,P)         polynomial over modular integers univariate content 
			(rekursiv) 
pmiupmiprod(r,m,P1,P2)  polynomial over modular integers, univariate 
			polynomial over modular integers product (rekursiv) 
pmiupmiquot(r,m,P1,P2)  polynomial over modular integers, univariate 
			polynomial over modular integers quotient 
			(rekursiv) 
pmsbezout(r,m,P1,P2)    polynomial over modular singles Bezout-matrix 
pmsderiv(r,m,P)         polynomial over modular singles derivation, main 
			variable 
pmsderivsv(r,m,P,n)     polynomial over modular singles derivation, 
			specified variable (rekursiv) 
pmsdif(r,m,P1,P2)       polynomial over modular singles difference 
			(rekursiv) 
pmsdiscr(r,m,P,n)       polynomial over modular singles discriminant 
pmseval(r,m,P,a)        polynomial over modular singles evaluation, main 
			variable 
pmsevalsv(r,m,P,n,a)    polynomial over modular singles evaluation, 
			specified variable (rekursiv) 
pmsexp(r,m,P,n)         polynomial over modular singles exponentiation 
pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular singles greatest common 
			divisor and cofactors (rekursiv) 
pmsinter(r,m,P1,P2,P3,a,b) polynomial over modular singles interpolation 
			(rekursiv) 
pmsmonic(r,m,P)         polynomial over modular singles monic 
pmsmsprod(r,m,P,a)      polynomial over modular singles, modular single 
			product (rekursiv) 
pmsmsquot(r,m,P,a)      polynomial over modular singles, modular single 
			quotient (rekursiv) 
pmsneg(r,m,P)           polynomial over modular singles negation (rekursiv) 
pmsprod(r,m,P1,P2)      polynomial over modular singles product (rekursiv) 
pmspsrem(r,m,P1,P2)     polynomial over modular singles pseudo remainder 
pmsqrem(r,m,P1,P2,pR)   polynomial over modular singles quotient and 
			remainder (rekursiv) 
pmsquot(r,m,P1,P2)      (MACRO) polynomial over modular singles quotient 
pmsrem(r,m,P1,P2)       (MACRO) polynomial over modular singles remainder 
pmsres(r,m,P1,P2,n)     polynomial over modular singles resultant 
pmsrescoll(r,m,P1,P2)   polynomial over modular singles resultant, Collins 
			algorithm (rekursiv) 
pmssubst(r,m,P1,P2)     polynomial over modular singles substitution, main 
			variable 
pmssubstsv(r,m,P1,n,P2) polynomial over modular singles substitution, 
			specified variable (rekursiv) 
pmssum(r,m,P1,P2)       polynomial over modular singles sum (rekursiv) 
pmstopgfs(r,p,P)        polynomial over modular singles to polynomial over 
			Galois-field with single characteristic (rekursiv) 
pmstorfmsp1(p,P)        (MACRO) polynomial over modular singles to rational 
			function over modular single prime, transcendence 
			degree 1 
pmstrans(r,m,P,a)       polynomial over modular singles translation, main 
			variable 
pmstransav(r,m,P,Lms)   polynomial over modular singles translation, all 
			variables (rekursiv) 
pmstransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial over modular singles 
			transformation 
pmsucont(r,m,P)         polynomial over modular singles univariate content 
			(rekursiv) 
pmsupmsprod(r,m,P1,P2)  polynomial over modular singles, univariate 
			polynomial over modular singles product (rekursiv) 
pmsupmsquot(r,m,P1,P2)  polynomial over modular singles, univariate 
			polynomial over modular singles quotient (rekursiv) 
pnfderiv(r,F,P)         polynomial over number field derivation, main 
			variable 
pnfderivsv(r,F,P,n)     polynomial over number field derivation, specified 
			variable (rekursiv) 
pnfdif(r,F,P1,P2)       polynomial over number field difference (rekursiv) 
pnfeval(r,F,P,a)        polynomial over number field evaluation, main 
			variable 
pnfevalsv(r,F,P,n,a)    polynomial over number field evaluation, specified 
			variable (rekursiv) 
pnfexp(r,F,P,n)         polynomial over number field exponentiation 
pnfmonic(r,F,P)         polynomial over number field monic 
pnfneg(r,F,P)           polynomial over number field negation (rekursiv) 
pnfnfprod(r,F,P,a)      polynomial over number field, number field element 
			product (rekursiv) 
pnfnfquot(r,F,P,a)      polynomial over number field, number field element 
			quotient (rekursiv) 
pnfprod(r,F,P1,P2)      polynomial over number field product (rekursiv) 
pnfqrem(r,F,P1,P2,pR)   polynomial over number field quotient and remainder 
			(rekursiv) 
pnfquot(r,F,P1,P2)      (MACRO) polynomial over number field quotient 
pnfrem(r,F,P1,P2)       (MACRO) polynomial over number field remainder 
pnfsum(r,F,P1,P2)       polynomial over number field sum (rekursiv) 
pnftopr(r,P)            polynomial over number field to polynomial over 
			rationals 
pnftransf(r1,F,P1,V1,r2,P2,V2,Vn,pV3) polynomial over number field 
			transformation 
point                   ? isfloat(A) is floating 
point                   Cfltofl(x) C-floating point to floating 
point                   PAFtofl(x) Papanikolaou floating point to ( SIMATH 
			) floating 
point                   Pi flPi() floating 
point                   absolute value flabs(f) (MACRO) floating 
point                   arcus tangens special version flatn_sp(f) floating 
point                   area tangens hyperbolicus special version 
			flath_sp(f) floating 
point                   aritho-geometric mean flagm(a,b) floating 
point                   at infinity ? ispecrpai(P) (MACRO) is point of an 
			elliptic curve over the rationals 
point                   at infinity ? isppecgf2pai(G,P) is projective point 
			of an elliptic curve over Galois-field with 
			characteristic 2 
point                   at infinity ? isppecmppai(p,P) is projective point 
			of an elliptic curve over modular primes 
point                   at infinity ? isppecnfpai(P) is projective point of 
			an elliptic curve over number field 
point                   by an integer ecimindiv(E,P,n) elliptic curve with 
			integer coefficients, minimal model, division of a 
point                   by an integer, special version 
			ecimindivs(E,P,h,ug,PL,n) elliptic curve with 
			integer coefficients, minimal model, division of a 
point                   by fix point fputflfx(f,vk,nk,pf) file put floating 
point                   by fix point putflfx(f,vk,nk) (MACRO) put floating 
point                   chartofl(A) character to floating 
point                   comparison ecrpcomp(P1,P2) elliptic curve over 
			rational numbers, 
point                   comparison flcomp(f,g) floating 
point                   comparison modulo torsion eciminpcompmt(E,P1,P2) 
			elliptic curve with integer coefficients, minimal 
			model, 
point                   construction by cutting flcut(A,e,lA) floating 
point                   construction flcons(A,e,lA) floating 
point                   cosinus flcos(a) floating 
point                   cosinus special version flcos_sp(f) floating 
point                   difference fldif(f,g) (MACRO) floating 
point                   ecgf2fp(G,a1,a2,a3,a4,a6) elliptic curve over 
			Galois-field with characteristic 2, find 
point                   ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve 
			over Galois-field with characteristic 2, multiple 
			of the order of a point to exact order of the 
point                   ecgf2neg(G,a1,a2,a3,a4,a6,P) elliptic curve over 
			Galois-field with characteristic 2, negative 
point                   ecgf2srpp(G,P) elliptic curve over Galois-field 
			with characteristic 2, standard representation of 
			projective 
point                   ecimindivby2(E,P,h,PL,H) elliptic curve with 
			integer coefficients, minimal model, division by 2 
			of a 
point                   ecimindouble(E,P) elliptic curve with integer 
			coefficients, minimal model, double of a 
point                   eciminneg(E,P) elliptic curve with integer 
			coefficients, minimal model, negative 
point                   eciminplinsp(P,h,PL) elliptic curve with integer 
			coefficients, minimal model, point list, insert 
point                   ecisnfdouble(E,P) elliptic curve with integer 
			coefficients, short normal form, double of 
point                   ecisnfelogp(E,P,n) elliptic curve with integer 
			coefficients, short normal form, elliptic logarithm 
			of 
point                   ecisnfneg(E,P) elliptic curve with integer 
			coefficients, short normal form, negative of 
point                   ecmpfp(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular primes, find 
point                   ecmpneg(p,a1,a2,a3,a4,a6,P) elliptic curve over 
			modular primes negative 
point                   ecmpsnffp(p,a4,a6) elliptic curve over modular 
			primes, short normal form, find 
point                   ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular primes, short normal form, multiple of the 
			order of a point to exact order of the 
point                   ecmpsnfneg(p,a4,a6,P) elliptic curve over modular 
			primes, short normal form, negative 
point                   ecmpsrpp(p,P) elliptic curve over modular primes, 
			standard representation of projective 
point                   ecnfneg(F,a1,a2,a3,a4,a6,P) elliptic curve over 
			number field negative 
point                   ecnfsnfneg(F,a,b,P) elliptic curve over number 
			field short normal form negative 
point                   ecnfsrpp(F,P) elliptic curve over number field 
			standard representation of projective 
point                   ecracdouble(E,P) elliptic curve over the rational 
			numbers, minimal model, double of 
point                   ecracneg(E,P) elliptic curve over the rational 
			numbers, actual curve, negative 
point                   ecrbtp(P,BT) elliptic curve over rational numbers, 
			birational transformation of 
point                   exponent flexpo(f) (MACRO) floating 
point                   exponential function flexp(f) floating 
point                   fgetfl(pf) file get floating 
point                   floor flfloor(f) floating 
point                   fltoCfl(f) floating point to C-floating 
point                   fltoPAF(f,x) ( SIMATH ) floating point to 
			Papanikolaou floating 
point                   fltofl(f) (MACRO) floating point to floating 
point                   fputecrp(P,pf) file put elliptic curve over 
			rational numbers, 
point                   fputfl(f,n,pf) file put floating 
point                   fputflfx(f,vk,nk,pf) file put floating point by fix 
point                   fputmaflfx(M,v,n,pf) file put matrix of floatings 
			by fix 
point                   functions flPAFfu(func,anzahlargs,arg1,arg2) 
			floating point using Papanikolaou floating 
point                   getecrp() (MACRO) get elliptic curve over rational 
			numbers 
point                   getfl() (MACRO) get floating 
point                   iecfindp(p,a,b) integer elliptic curve find 
point                   initialization flinit(k) floating 
point                   itofl(A) (MACRO) integer to floating 
point                   list union eciminplunion(E,L1,L2,modus) elliptic 
			curve with integer coefficients, minimal model, 
point                   list, insert point eciminplinsp(P,h,PL) elliptic 
			curve with integer coefficients, minimal model, 
point                   mantissa flmant(f) (MACRO) floating 
point                   natural logarithm (rekursiv) fllog(f) floating 
point                   negation flneg(f) floating 
point                   normalization ecipnorm(P) elliptic curve with 
			integer coefficients, 
point                   normalization ecrpnorm(P) elliptic curve over 
			rational numbers, 
point                   of an elliptic curve over Galois-field with 
			characteristic 2 equal ? isppecgf2eq(p,P1,P2) is 
			projective 
point                   of an elliptic curve over Galois-field with 
			characteristic 2 point at infinity ? 
			isppecgf2pai(G,P) is projective 
point                   of an elliptic curve over modular primes equal ? 
			isppecmpeq(p,P1,P2) is projective 
point                   of an elliptic curve over modular primes point at 
			infinity ? isppecmppai(p,P) is projective 
point                   of an elliptic curve over number field equal? 
			isppecnfeq(F,P1,P2) is projective 
point                   of an elliptic curve over number field point at 
			infinity ? isppecnfpai(P) is projective 
point                   of an elliptic curve over the rationals point at 
			infinity ? ispecrpai(P) (MACRO) is 
point                   on elliptic curve over rational numbers 
			fgetecrp(pf) file get 
point                   on elliptic curve over rational numbers, actual 
			model isponecrac(E,P) is 
point                   on elliptic curve with integer coefficients, 
			minimal model isecimintorp(E,P) is torsion 
point                   on elliptic curve with integer coefficients, 
			minimal model isponecimin(E,P) is 
point                   on elliptic curve with integer coefficients, model 
			in short normal form isponecisnf(E,P) is 
point                   overflow error floverflow(a) floating 
point                   overflow error handling flerr() (MACRO) floating 
point                   package: I/O-functions PAFio() Papanikolaou 
			floating 
point                   package: addition PAFadd() Papanikolaou floating 
point                   package: assignments PAFassign() Papanikolaou 
			floating 
point                   package: comparisons PAFcomp() Papanikolaou 
			floating 
point                   package: construction PAFcon() Papanikolaou 
			floating 
point                   package: division PAFdiv() Papanikolaou floating 
point                   package: globals PAFglob() Papanikolaou floating 
point                   package: multiplication PAFmul() Papanikolaou 
			floating 
point                   package: shiftings PAFshift() Papanikolaou floating 
point                   package: subtraction PAFsub() Papanikolaou floating 
point                   package: transcendental functions 1 PAFtrans1() 
			Papanikolaou floating 
point                   package: transcendental functions 2 PAFtrans2() 
			Papanikolaou floating 
point                   package: transcendental functions 3 PAFtrans3() 
			Papanikolaou floating 
point                   package: typer PAFtype() Papanikolaou floating 
point                   package: utilities PAFutil() Papanikolaou floating 
point                   power flpow(f,g) floating 
point                   product flprod(f,g) floating 
point                   product iecpprod(p,E,P,a) integer elliptic curve 
point                   putecrp(P) (MACRO) put elliptic curve over rational 
			numbers, 
point                   putfl(f,n) (MACRO) put floating 
point                   putflfx(f,vk,nk) (MACRO) put floating point by fix 
point                   putmaflfx(M,v,n) (MACRO) put matrix of floatings by 
			fix 
point                   quotient flquot(f,g) floating 
point                   round flround(f) floating 
point                   rtofl(r) rational number to floating 
point                   set precision flsetprec(k,N) floating 
point                   sgetfl(ps) string get floating 
point                   sign flsign(f) (MACRO) floating 
point                   single exponentiation flsexp(f,n) floating 
point                   single quotient flsquot(f,n) floating 
point                   sinus flsin(a) floating 
point                   sinus special version flsin_sp(f) floating 
point                   special version sgetflsp(ps) string get floating 
point                   special version sputflsp(prec,f,str) string put 
			floating 
point                   square root flsqrt(f) floating 
point                   sum flsum(f,g) floating 
point                   sum iecpsum(p,P,Q,a) integer elliptic curve 
point                   to ( SIMATH ) floating point PAFtofl(x) 
			Papanikolaou floating 
point                   to C-floating point fltoCfl(f) floating 
point                   to Papanikolaou floating point fltoPAF(f,x) ( 
			SIMATH ) floating 
point                   to exact order of the point 
			ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve 
			over Galois-field with characteristic 2, multiple 
			of the order of a 
point                   to exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular primes, short normal form, multiple of the 
			order of a 
point                   to floating point Cfltofl(x) C-floating 
point                   to floating point fltofl(f) (MACRO) floating 
point                   to projective representation ecrptoproj(P) elliptic 
			curve over rational numbers, 
point                   to rational number fltor(f) floating 
point                   trigonometric functions fltrig(Ffunc,f) (MACRO) 
			floating 
point                   using Papanikolaou floating point functions 
			flPAFfu(func,anzahlargs,arg1,arg2) floating 
point                   with the Pollard Lambda method 
			ecgf2fmoplam(G,a1,a2,a3,a4,a6,P,L,N) elliptic curve 
			over Galois-field with characteristic 2, finding a 
			multiple of the order of a 
point                   with the Pollard Lambda method 
			ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
			modular primes, short normal form, finding a 
			multiple of the order of a 
point                   with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular primes, short normal form, finding a 
			multiple of the order of a 
pointer                 ltop(L) (MACRO) list to 
pointer                 to list ptol(pc) (MACRO) 
points                  after field extension 
			ecgf2npfe(Gm,a1,a2,a3,a4,a6,Nm,GmtoGn) elliptic 
			curve over Galois field with characteristic 2, 
			number of 
points                  ecgf2lp(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
			Galois-field with characteristic 2, line through 
points                  ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) elliptic curve 
			over Galois-field with characteristic 2, sum of 
points                  ecimindif(E,P,Q) elliptic curve with integer 
			coefficients, minimal model, difference of 
points                  eciminsum(E,P,Q) elliptic curve with integer 
			coefficients, minimal model, sum of 
points                  ecisnfdif(E,P,Q) elliptic curve with integer 
			coefficients, minimal model, difference of 
points                  ecisnfsum(E,P,Q) elliptic curve with integer 
			coefficients, short normal form, sum of 
points                  ecmplp(p,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
			modular primes, line through 
points                  ecmpsnflp(p,a4,a6,P1,P2) elliptic curve over 
			modular primes, short normal form, line through 
points                  ecmpsnfsum(p,a4,a6,P1,P2) elliptic curve over 
			modular primes, short normal form, sum of 
points                  ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
			modular primes, sum of 
points                  ecmspnp(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular single prime, number of 
points                  ecmspsnfnp(p,a4,a6) elliptic curve over modular 
			single primes, short normal form, number of 
points                  ecnflp(F,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
			number field line through 
points                  ecnfsnflp(F,a,b,P1,P2) elliptic curve over number 
			field short normal form line through 
points                  ecnfsnfsum(F,a,b,P1,P2) elliptic curve over number 
			field short normal form sum of 
points                  ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) elliptic curve over 
			number field sum of 
points                  ecracdif(E,P,Q) elliptic curve with integer 
			coefficients, actual curve, difference of 
points                  ecracsum(E,P,Q) elliptic curve over the rational 
			numbers, actual curve, sum of 
points                  ecrbtlistp(LP,BT,modus) elliptic curve over 
			rational numbers, birational transformation of list 
			of 
points                  fputecrlistp(P,modus,pf) file put elliptic curve 
			over the rational numbers, list of 
points                  modulo 2 ecmpsnfnpm2(P,a4,a6) elliptic curve over 
			modular primes, short normal form, number of 
points                  modulo a power of 2 ecgf2npmp2(G,a6,c,L) elliptic 
			curve over Galois-field with characteristic 2, 
			number of 
points                  modulo a single prime determined with the Schoof 
			algorithm ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve 
			over modular primes, short normal form, number of 
points                  modulo a single prime determined with the Schoof 
			algorithm, version 1 ecgf2npmspv1(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, number of 
points                  modulo a single prime determined with the Schoof 
			algorithm, version 2 ecgf2npmspv2(G,a6,p,L) 
			elliptic curve over Galois-field with 
			characteristic 2, number of 
points                  modulo an integer determined with the Schoof 
			algorithm ecgf2npmi(G,a6,S,v,pM) elliptic curve 
			over Galois-field with characteristic 2, number of 
points                  modulo an integer determined with the Schoof 
			algorithm ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve 
			over modular primes, short normal form, number of 
points                  of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve 
			with integer coefficients, short normal form, 
points                  on elliptic curve with integer coefficients, 
			minimal model isineciminpl(E,P,h,PL) is in list of 
points                  picevalp(r,P,sA) polynomial over integers choice of 
			evaluation 
points                  putecrlistp(P,modus) (MACRO) put elliptic curve 
			over rational numbers, list of 
points                  special version ecmipsnfnpsv(p,a4,a6) elliptic 
			curve over modular integer primes short normal form 
			number of 
points                  sum (rekursiv) pflsum(r,P1,P2) polynomial over 
			floating 
points,                 j-invariant iecgnpj(p,m,h1,h2,D) integer elliptic 
			curve of given number of 
points,                 special version ecgf2sfsums(G,a6,x1,y1,x2,y2) 
			elliptic curve over Galois-field with 
			characteristic 2, special form, sum of 
points,                 special version ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) 
			elliptic curve over modular primes, short normal 
			form, sum of 
polynomial              (rekursiv) diptop(r,P) distributive polynomial to 
polynomial              (rekursiv) dptop(r,P) dense polynomial to 
polynomial              (rekursiv) ptodip(r,P) polynomial to distributive 
polynomial              (rekursiv) ptodp(r,P) polynomial to dense 
polynomial              ? (rekursiv) isdpol(r,P) is dense 
polynomial              ? (rekursiv) ispol(r,P) is 
polynomial              ? isdipol(r,P) is distributive 
polynomial              Sylvester matrix psylvester(r,P1,P2) 
polynomial              afmsp1minpol(p,F,a) algebraic function over modular 
			single primes, transcendence degree 1, minimal 
polynomial              afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
			modular single prime, transcendence degree 1, 
			P-primality test and factorization of the defining 
			polynomial or the minimal 
polynomial              and p-minimal polynomials of the generators 
			ouspiapfgmic(p,P,k) order of an univariate 
			separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal orders 
			of the p-adic divisors of the defining 
polynomial              bubble sort dipbsort(r,P) distributive 
polynomial              constant ? ispconst(r,P,pC) is 
polynomial              degree vector (rekursiv) dpdegvec(r,P) dense 
polynomial              degree vector (rekursiv) pdegvec(r,P) 
polynomial              degree, main variable pdegree(r,P) (MACRO) 
polynomial              degree, specified variable (rekursiv) 
			pdegreesv(r,P,n) 
polynomial              dimension fputdipdim(r,dim,S,M,VL,pf) file put 
			distributive 
polynomial              dimension of a polynomial ideal 
			dipdimpolid(r,G,pS,pM) distributive 
polynomial              dimension putdipdim(r,dim,S,M,VL) (MACRO) put 
			distributive 
polynomial              distinct degree factorization upmsddfact(p,F) 
			univariate 
polynomial              exponent vector compare dipevcomp(r,EV1,EV2) 
			distributive 
polynomial              exponent vector difference dipevdif(r,EV1,EV2) 
			distributive 
polynomial              exponent vector least common multiple 
			dipevlcm(r,EV1,EV2) distributive 
polynomial              exponent vector multiple test dipevmt(r,EV1,EV2) 
			distributive 
polynomial              exponent vector of the leading monomial dipevl(r,P) 
			distributive 
polynomial              exponent vector signum dipevsign(r,EV) distributive 
polynomial              exponent vector sum dipevsum(r,EV1,EV2) 
			distributive 
polynomial              exponentiation upmimpexp(ip,K,E,P) univariate 
			polynomial over modular integers modular 
polynomial              from monomial dipfmo(r,BC,EV) (MACRO) distributive 
polynomial              homogenize diphomog(r,P) distributive 
polynomial              homogenize specified variable diphomogsv(r,P,n) 
			distributive 
polynomial              iafmsp1mpol(p,F,a,Q) integral algebraic function 
			over modular single primes, transcendence degree 1, 
			minimal 
polynomial              ideal dipdimpolid(r,G,pS,pM) distributive 
			polynomial dimension of a 
polynomial              in special bit-representation ? isgf2impsb(G) is 
			Galois-field with characteristic 2 irreducible and 
			monic 
polynomial              in special bit-representation generator 
			gf2impsbgen(n,H) Galois-field with characteristic 2 
			irreducible and monic 
polynomial              infepptfact(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and factorization of the 
			defining polynomial or the minimal 
polynomial              insertion of new variables (rekursiv) 
			pvinsert(r,P,k) 
polynomial              leading base coefficient diplbc(r,P) (MACRO) 
			distributive 
polynomial              leading base coefficient, main variable plbc(r,P) 
polynomial              leading coefficient, main variable plc(r,P) (MACRO) 
polynomial              machpol(M,det,minusEins,anzahlargs,arg1,arg2) 
			matrix characteristic 
polynomial              magfschpol(p,AL,M) (MACRO) matrix of Galois-field 
			with single characteristic elements characteristic 
polynomial              magfsevifcp(p,AL,M,pL) matrix over Galois-field 
			with single characteristic eigenvalues and 
			irreducible factors of the characteristic 
polynomial              maichpol(M) (MACRO) matrix of integers 
			characteristic 
polynomial              maievifcp(M,pL) matrix of integers eigenvalues and 
			irreducible factors of the characteristic 
polynomial              make list of variables pmakevl(s) 
polynomial              mamichpol(m,M) (MACRO) matrix of modular integers 
			characteristic 
polynomial              mamievifcp(p,M,pL) matrix of modular integers 
			eigenvalues and irreducible factors of the 
			characteristic 
polynomial              mamschpol(m,M) (MACRO) matrix of modular singles 
			characteristic 
polynomial              mamsevifcp(p,M,pL) matrix of modular singles 
			eigenvalues and irreducible factors of the 
			characteristic 
polynomial              manfchpol(F,M) (MACRO) matrix of number field 
			elements characteristic 
polynomial              mapgfschpol(r,p,AL,M) (MACRO) matrix of polynomials 
			over Galois-field with single characteristic 
			characteristic 
polynomial              mapichpol(r,M) (MACRO) matrix of polynomials over 
			integers characteristic 
polynomial              mapmichpol(r,m,M) (MACRO) matrix of polynomials 
			over modular integers characteristic 
polynomial              mapmschpol(r,m,M) (MACRO) matrix of polynomials 
			over modular singles characteristic 
polynomial              mapnfchpol(r,F,M) (MACRO) matrix of polynomials 
			over number field characteristic 
polynomial              maprchpol(r,M) (MACRO) matrix of polynomials over 
			rationals characteristic 
polynomial              marchpol(M) (MACRO) matrix of rationals 
			characteristic 
polynomial              marevifcp(M,*pL) matrix of rationals eigenvalues 
			and irreducible factors of the characteristic 
polynomial              marfrchpol(r,M) matrix of rational functions over 
			rationals characteristic 
polynomial              modulo p-power infeminpmpp(F,a,p,e,Q) integral 
			number field element minimal 
polynomial              modulo p-power with respect to integer primes 
			infempmppip(F,a,p,e,Q) integral number field 
			element minimal 
polynomial              modulo power of an univariate prime polynomial over 
			modular single primes iafmsp1mpmpp(p,F,a,P,e,Q) 
			integral algebraic function over modular single 
			primes, transcendence degree 1, minimal 
polynomial              monomial ? ispmonom(r,P) is 
polynomial              monomial advance dipmoad(r,P,pLBC,pLEV) 
			distributive 
polynomial              new main variable dipnmv(r,P,n) distributive 
polynomial              nf3chpol(F,el) number field of degree 3 
			characteristic 
polynomial              or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
			modular single prime, transcendence degree 1, 
			P-primality test and factorization of the defining 
polynomial              or the minimal polynomial 
			infepptfact(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and factorization of the 
			defining 
polynomial              or the minimal polynomial with respect to integer 
			primes infepptfip(F,p,Q,ppot,a0,z) integral number 
			field element p-primality test and factorization of 
			the defining 
polynomial              order of a univariate separable polynomial over the 
			polynomial ring over modular single prime, 
			transcendence degree 1 vepepuspmsp1(p,F,a,P,k,v) 
			values of the extensions of the P-adic valuation of 
			an element of the 
polynomial              order of an univariate separable polynomial over 
			the polynomial ring over modular single prime, 
			transcendence degree 1 nepousppmsp1(p,F,a) norm of 
			an element of the 
polynomial              over Galois-field fputpgfs(r,p,AL,P,V,Vgfs,pf) file 
			put 
polynomial              over Galois-field putpgfs(r,p,AL,P,V,Vgfs) (MACRO) 
			put 
polynomial              over Galois-field with characteristic 2 (rekursiv) 
			pgfstopgf2(r,G,P) polynomial over Galois-field with 
			single characteristic to 
polynomial              over Galois-field with characteristic 2 (rekursiv) 
			pm2topgf2(r,P) polynomial over modular 2 to 
polynomial              over Galois-field with characteristic 2 Ben-Or 
			factorization, special upgf2bofacts(G,P) univariate 
polynomial              over Galois-field with characteristic 2 Berlekamp Q 
			polynomials construction upgf2bqp(G,P) univariate 
polynomial              over Galois-field with characteristic 2 derivation, 
			main variable pgf2deriv(r,G,P) 
polynomial              over Galois-field with characteristic 2 derivation, 
			specified variable (rekursiv) pgf2derivsv(r,G,P,i) 
polynomial              over Galois-field with characteristic 2 difference 
			pgf2dif(r,G,P1,P2) (MACRO) 
polynomial              over Galois-field with characteristic 2 distinct 
			degree factorization upgf2ddfact(G,P) univariate 
polynomial              over Galois-field with characteristic 2 embedding 
			in field extension (rekursiv) pgf2efe(r,GmtoGn,P) 
polynomial              over Galois-field with characteristic 2 evaluation 
			upgf2eval(G,P,a) 
polynomial              over Galois-field with characteristic 2 evaluation, 
			main variable pgf2eval(r,G,P,a) 
polynomial              over Galois-field with characteristic 2 
			exponentiation pgf2exp(r,G,P,n) 
polynomial              over Galois-field with characteristic 2 
			fgetpgf2(r,G,V,Vgf2,pf) file get 
polynomial              over Galois-field with characteristic 2 
			fputpgf2(r,G,P,V,Vgf2,pf) file put 
polynomial              over Galois-field with characteristic 2 
			getpgf2(r,G,V,Vgf2) (MACRO) get 
polynomial              over Galois-field with characteristic 2 greatest 
			common divisor upgf2gcd(G,P1,P2) univariate 
polynomial              over Galois-field with characteristic 2 monic 
			pgf2monic(r,G,P) 
polynomial              over Galois-field with characteristic 2 negation 
			pgf2neg(r,G,P) (MACRO) 
polynomial              over Galois-field with characteristic 2 product 
			(rekursiv) pgf2prod(r,G,P1,P2) 
polynomial              over Galois-field with characteristic 2 
			putpgf2(r,G,P,V,Vgf2) (MACRO) put 
polynomial              over Galois-field with characteristic 2 quotient 
			and remainder (rekursiv) pgf2qrem(r,G,P1,P2,pR) 
polynomial              over Galois-field with characteristic 2 quotient 
			pgf2quot(r,G,P1,P2) (MACRO) 
polynomial              over Galois-field with characteristic 2 remainder 
			pgf2rem(r,G,P1,P2) (MACRO) 
polynomial              over Galois-field with characteristic 2 remainder, 
			special version udpgf2remsp(G,P1,P2,ilc) univariate 
			dense 
polynomial              over Galois-field with characteristic 2 square 
			(rekursiv) pgf2square(r,G,P) 
polynomial              over Galois-field with characteristic 2 squarefree 
			factorization (rekursiv) upgf2sfact(G,P) univariate 
polynomial              over Galois-field with characteristic 2 sum 
			(rekursiv) pgf2sum(r,G,P1,P2) 
polynomial              over Galois-field with characteristic 2 to 
			polynomial over Galois-field with single 
			characteristic (rekursiv) pgf2topgfs(r,G,P) 
polynomial              over Galois-field with characteristic 2 
			transformation 
			pgf2transf(r1,G,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over Galois-field with characteristic 2, 2^m-th 
			power of variable, polynomial, remainder 
			upgf22pvprem(G,m,P) univariate 
polynomial              over Galois-field with characteristic 2, Ben-Or 
			factorization upgf2bofact(G,P) univariate 
polynomial              over Galois-field with characteristic 2, 
			Galois-field with characteristic 2 element product 
			(rekursiv) pgf2gf2prod(r,G,P,a) 
polynomial              over Galois-field with characteristic 2, 
			exponentiation, polynomial remainder 
			pgf2expprem(r,G,F,E,M) 
polynomial              over Galois-field with characteristic 2, modular 
			exponentiation, special version 
			upgf2modexps(G,F,m,P,pM) univariate 
polynomial              over Galois-field with characteristic 2, monomial, 
			polynomial, remainder upgf2mprem(G,a,T,P) 
			univariate 
polynomial              over Galois-field with characteristic 2, random 
			generator upgf2gen(G,m) univariate 
polynomial              over Galois-field with characteristic 2, separate 
			factor of equal degree upgf2sfed(G,H,d) univariate 
polynomial              over Galois-field with characteristic 2, trace 
			function, special upgf2tf(G,F,d,M) 
polynomial              over Galois-field with single characteristic 
			(rekursiv) pgf2topgfs(r,G,P) polynomial over 
			Galois-field with characteristic 2 to 
polynomial              over Galois-field with single characteristic 
			(rekursiv) pmstopgfs(r,p,P) polynomial over modular 
			singles to 
polynomial              over Galois-field with single characteristic ? 
			(rekursiv) ispgfs(r,p,AL,P) is 
polynomial              over Galois-field with single characteristic 
			Berlekamp Q polynomials construction 
			upgfsbqp(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic 
			Berlekamp factorization upgfsbfact(p,AL,P,d) 
			univariate 
polynomial              over Galois-field with single characteristic 
			Berlekamp factorization, Zassenhaus method 
			upgfsbfzm(p,AL,s,P,G) univariate 
polynomial              over Galois-field with single characteristic 
			Berlekamp factorization, last step 
			upgfsbfls(p,AL,P,B,d) univariate 
polynomial              over Galois-field with single characteristic 
			Groebner basis augmentation dipgfsgba(r,p,AL,PL,P) 
			distributive 
polynomial              over Galois-field with single characteristic 
			Groebner basis dipgfsgb(r,p,AL,PL) distributive 
polynomial              over Galois-field with single characteristic 
			Groebner basis recursion dipgfsgbr(r,p,AL,PL) 
			distributive 
polynomial              over Galois-field with single characteristic 
			S-polynomial dipgfssp(r,p,AL,P1,P2) distributive 
polynomial              over Galois-field with single characteristic 
			complete factorization special upgfscfacts(p,AL,P) 
			univariate 
polynomial              over Galois-field with single characteristic 
			complete factorization upgfscfact(p,AL,P) 
			univariate 
polynomial              over Galois-field with single characteristic 
			derivation, main variable pgfsderiv(r,p,AL,P) 
polynomial              over Galois-field with single characteristic 
			derivation, specified variable (rekursiv) 
			pgfsderivsv(r,p,AL,P,i) 
polynomial              over Galois-field with single characteristic 
			difference (rekursiv) pgfsdif(r,p,AL,P1,P2) 
polynomial              over Galois-field with single characteristic 
			difference dipgfsdif(r,p,AL,P1,P2) distributive 
polynomial              over Galois-field with single characteristic 
			distinct degree factorization upgfsddfact(p,AL,P) 
			univariate 
polynomial              over Galois-field with single characteristic 
			embedding in field extension (rekursiv) 
			pgfsefe(r,p,ALm,P,g) 
polynomial              over Galois-field with single characteristic 
			evaluation, main variable pgfseval(r,p,AL,P,a) 
polynomial              over Galois-field with single characteristic 
			evaluation, specified variable (rekursiv) 
			pgfsevalsv(r,p,AL,P,d,a) 
polynomial              over Galois-field with single characteristic 
			exponentiation pgfsexp(r,p,AL,P,m) 
polynomial              over Galois-field with single characteristic 
			extended greatest common divisor 
			upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate 
polynomial              over Galois-field with single characteristic 
			fgetpgfs(r,p,AL,V,Vgfs,pf) file get 
polynomial              over Galois-field with single characteristic 
			getpgfs(r,p,AL,V,Vgfs) (MACRO) get 
polynomial              over Galois-field with single characteristic 
			greatest common divisor upgfsgcd(p,AL,P1,P2) 
			univariate 
polynomial              over Galois-field with single characteristic 
			greatest squarefree divisor (rekursiv) 
			upgfsgsd(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic half 
			extended greatest common divisor 
			upgfshegcd(p,AL,P1,P2,pP3) univariate 
polynomial              over Galois-field with single characteristic in 
			graduated lexicographical order 
			dipgfslotglo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive 
polynomial              over Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
			graduated lexicographical order 
			dipgfslotglo(r,p,AL,P) distributive 
polynomial              over Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
			lexicographical order with inverse exponent vector 
			dipgfslotlio(r,p,AL,P) distributive 
polynomial              over Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic with 
			total degree ordering dipgfslottdo(r,p,AL,P) 
			distributive 
polynomial              over Galois-field with single characteristic in 
			lexicographical order with inverse exponent vector 
			dipgfslotlio(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive 
polynomial              over Galois-field with single characteristic list 
			fgetdipgfsl(r,p,AL,VL,Vgfs,pf) file get 
			distributive 
polynomial              over Galois-field with single characteristic list 
			fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put 
			distributive 
polynomial              over Galois-field with single characteristic list 
			getdipgfsl(r,p,AL,VL,Vgfs) (MACRO) get distributive 
polynomial              over Galois-field with single characteristic list 
			putdipgfsl(r,p,AL,PL,VL,Vgfs) (MACRO) put 
			distributive 
polynomial              over Galois-field with single characteristic monic 
			dipgfsmonic(r,p,AL,P) distributive 
polynomial              over Galois-field with single characteristic monic 
			pgfsmonic(r,p,AL,P) 
polynomial              over Galois-field with single characteristic 
			mpgfstompmp(r,p,AL,P,M) matrix of polynomials over 
			Galois-field with single characteristic to matrix 
			of polynomials modulo 
polynomial              over Galois-field with single characteristic 
			negation (rekursiv) pgfsneg(r,p,AL,P) 
polynomial              over Galois-field with single characteristic 
			negation dipgfsneg(r,p,AL,P) distributive 
polynomial              over Galois-field with single characteristic number 
			of irreducible factors upgfsnif(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic 
			product (rekursiv) pgfsprod(r,p,AL,P1,P2) 
polynomial              over Galois-field with single characteristic 
			product dipgfsprod(r,p,AL,P1,P2) distributive 
polynomial              over Galois-field with single characteristic 
			quotient and remainder (rekursiv) 
			pgfsqrem(r,p,AL,P1,P2,pR) 
polynomial              over Galois-field with single characteristic 
			quotient pgfsquot(r,p,AL,P1,P2) (MACRO) 
polynomial              over Galois-field with single characteristic 
			randomize upgfsrand(p,AL,m) univariate 
polynomial              over Galois-field with single characteristic 
			randomize, positive degree upgfsrandpd(p,AL,m) 
			univariate 
polynomial              over Galois-field with single characteristic 
			relative prime factorization 
			upgfsrelpfac(p,AL,P,Fak,pA2) univariate 
polynomial              over Galois-field with single characteristic 
			remainder pgfsrem(r,p,AL,P1,P2) (MACRO) 
polynomial              over Galois-field with single characteristic 
			resultant pgfsres(r,p,AL,P1,P2) 
polynomial              over Galois-field with single characteristic root 
			finding (rekursiv) upgfsrf(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic 
			squarefree factorization (rekursiv) 
			upgfssfact(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic 
			squarefree part upgfssfp(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic sum 
			(rekursiv) pgfssum(r,p,AL,P1,P2) 
polynomial              over Galois-field with single characteristic sum 
			dipgfssum(r,p,AL,P1,P2) distributive 
polynomial              over Galois-field with single characteristic to 
			polynomial over Galois-field with characteristic 2 
			(rekursiv) pgfstopgf2(r,G,P) 
polynomial              over Galois-field with single characteristic 
			transformation 
			pgfstransf(r1,p,AL,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over Galois-field with single characteristic 
			vpgfstovpmp(r,p,AL,P,V) vector of polynomials over 
			Galois-field with single characteristic to vector 
			of polynomials modulo 
polynomial              over Galois-field with single characteristic with 
			total degree ordering dipgfslottdo(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive 
polynomial              over Galois-field with single characteristic, 
			Ben-Or factorization upgfsbofact(p,AL,P) univariate 
polynomial              over Galois-field with single characteristic, 
			Ben-Or factorization, special upgfsbofacts(p,AL,P) 
			univariate 
polynomial              over Galois-field with single characteristic, 
			Galois-field with single characteristic element 
			product (rekursiv) pgfsgfsprod(r,p,AL,P,a) 
polynomial              over Galois-field with single characteristic, 
			Galois-field with single characteristic element 
			product dipgfsgfprod(r,p,AL,P,a) distributive 
polynomial              over Galois-field with single characteristic, 
			Galois-field with single characteristic element 
			quotient (rekursiv) pgfsgfsquot(r,p,AL,P,a) 
polynomial              over Galois-field with single characteristic, 
			exponentiation, polynomial remainder 
			pgfsexpprem(r,p,AL,F,E,M) 
polynomial              over Galois-field with single characteristic, 
			separate factors of equal degree 
			upgfssfed(p,AL,G,d) univariate 
polynomial              over Galois-field with single characteristic, trace 
			function upgfstf(p,AL,G,d,M) univariate 
polynomial              over Galois-field, monomial, integer 
			exponentiation, polynomial, remainder 
			upgfsmieprem(p,AL,a,t,P) univariate 
polynomial              over Galois-field, monomial, polynomial, remainder 
			upgfsmprem(p,AL,a,T,P) univariate 
polynomial              over a number field (rekursiv) pitopnf(r,P) 
			polynomial over the integers to 
polynomial              over a number field evaluation upnfeval(F,P,A) 
			univariate 
polynomial              over floating points sum (rekursiv) pflsum(r,P1,P2) 
polynomial              over integer itopi(r,A) (MACRO) integer to 
polynomial              over integers ? (rekursiv) ispi(r,P) is 
polynomial              over integers ? isiupi(P) is irreducible univariate 
polynomial              over integers ? isiuspi(P) is irreducible 
			univariate squarefree 
polynomial              over integers Bezout-matrix pibezout(r,P1,P2) 
polynomial              over integers Euklid norm (rekursiv) 
			pieuklnorm(r,P) 
polynomial              over integers Galois-field with characteristic 2 
			element evaluation first variable special version 
			(rekursiv) pigf2evalfvs(r,G,P) 
polynomial              over integers Galois-field with single 
			characteristic element evaluation first variable 
			special version (rekursiv) pigfsevalfvs(r,p,AL,P) 
polynomial              over integers Gelfond-factor coefficient bound 
			pigfcb(r,P) 
polynomial              over integers Groebner basis augmentation 
			dipigba(r,PL,P) distributive 
polynomial              over integers Groebner basis dipigb(r,PL) 
			distributive 
polynomial              over integers Groebner basis recursion 
			dipigbr(r,PL) distributive 
polynomial              over integers Landau- Mignotte- factor coefficient 
			bound pilmfcb(r,P) 
polynomial              over integers S-polynomial dipisp(r,P1,P2) 
			distributive 
polynomial              over integers absolute value piabs(r,P) 
polynomial              over integers chinese remainder algorithm 
			(rekursiv) picra(r,P1,P2,M,m,a) 
polynomial              over integers choice of evaluation points 
			picevalp(r,P,sA) 
polynomial              over integers content and primitive part 
			dipicp(r,P,pPP) distributive 
polynomial              over integers content and primitive part 
			picontpp(r,P,pPP) 
polynomial              over integers content and primitive part 
			udpicontpp(P,pPP) univariate dense 
polynomial              over integers content picont(r,P) 
polynomial              over integers derivation, main variable 
			pideriv(r,P) 
polynomial              over integers derivation, specified variable 
			(rekursiv) piderivsv(r,P,n) 
polynomial              over integers difference (rekursiv) pidif(r,P1,P2) 
polynomial              over integers difference dipidif(r,P1,P2) 
			distributive 
polynomial              over integers difference udpidif(P1,P2) univariate 
			dense 
polynomial              over integers discriminant pidiscr(r,P,n) 
polynomial              over integers discriminant via Hankel- matrix 
			pidiscrhank(r,P) 
polynomial              over integers equal one ? ispione(r,P) is 
polynomial              over integers evaluation, main variable 
			pieval(r,P,A) 
polynomial              over integers evaluation, specified variable 
			(rekursiv) pievalsv(r,P,n,A) 
polynomial              over integers exponentiation piexp(r,P,n) 
polynomial              over integers factor coefficient bound pifcb(L) 
polynomial              over integers factorization (rekursiv) pifact(r,P) 
polynomial              over integers factorization spifact(r,P) squarefree 
polynomial              over integers factorization upifact(P) univariate 
polynomial              over integers factorization uspifact(P) univariate 
			squarefree 
polynomial              over integers fgetpi(r,V,pf) file get 
polynomial              over integers fputpi(r,P,V,pf) file put 
polynomial              over integers getpi(r,V) (MACRO) get 
polynomial              over integers greatest common divisor and cofactors 
			pigcdcf(r,P1,P2,pQ1,pQ2) 
polynomial              over integers in graduated lexicographical order 
			dipilotoglo(r,P) distributive polynomial over 
			integers in lexicographical order to distributive 
polynomial              over integers in lexicographical order to 
			distributive polynomial over integers in graduated 
			lexicographical order dipilotoglo(r,P) distributive 
polynomial              over integers in lexicographical order to 
			distributive polynomial over integers in 
			lexicographical order with inverse exponent vector 
			dipilotolio(r,P) distributive 
polynomial              over integers in lexicographical order to 
			distributive polynomial over integers with total 
			degree ordering dipilototdo(r,P) distributive 
polynomial              over integers in lexicographical order with inverse 
			exponent vector dipilotolio(r,P) distributive 
			polynomial over integers in lexicographical order 
			to distributive 
polynomial              over integers integer content (rekursiv) 
			piicont(r,P) 
polynomial              over integers integer product udpiiprod(P,A) 
			univariate dense 
polynomial              over integers isuspi(P) is univariate squarefree 
polynomial              over integers list fgetdipil(r,VL,pf) file get 
			distributive 
polynomial              over integers list fputdipil(r,PL,VL,pf) file put 
			distributive 
polynomial              over integers list getdipil(r,VL) (MACRO) get 
			distributive 
polynomial              over integers list putdipil(r,PL,VL) (MACRO) put 
			distributive 
polynomial              over integers mapitompmpi(r,M,P) matrix of 
			polynomials over integers to matrix of polynomials 
			modulo 
polynomial              over integers maximum norm (rekursiv) 
			pimaxnorm(r,P) 
polynomial              over integers modular ideal homomorphism 
			pimidhom(r,S,P) 
polynomial              over integers modular ideal product 
			pimidprod(r,S,P1,P2) 
polynomial              over integers negation (rekursiv) pineg(r,P) 
polynomial              over integers negation dipineg(r,P) distributive 
polynomial              over integers negation udpineg(P) univariate dense 
polynomial              over integers number field element evaluation first 
			variable special version pinfevalfvs(r,F,P) 
polynomial              over integers number field element evaluation 
			upinfeval(P,F,a) univariate 
polynomial              over integers number field element, sparse 
			representation, evaluation upinfseval(P,F,a) 
			univariate 
polynomial              over integers of degree 4 cubic resolvent 
			upid4cubres(P) univariate 
polynomial              over integers of degree 4 real ? isupid4real(P) is 
			univariate 
polynomial              over integers one ? isdipione(r,P) is distributive 
polynomial              over integers primitive part piprimpart(r,P) 
			(MACRO) 
polynomial              over integers product (rekursiv) piprod(r,P1,P2) 
polynomial              over integers product dipiprod(r,P1,P2) 
			distributive 
polynomial              over integers product dippipiprod(r1,r2,P,A) 
			distributive polynomial over polynomials over 
			integers, 
polynomial              over integers product udpiprod(P1,P2) univariate 
			dense 
polynomial              over integers pseudo remainder pipsrem(r,P1,P2) 
polynomial              over integers pseudo remainder udpipsrem(P1,P2) 
			univariate dense 
polynomial              over integers putpi(r,P,V) (MACRO) put 
polynomial              over integers quotient and remainder (rekursiv) 
			piqrem(r,P1,P2,pR) 
polynomial              over integers quotient piquot(r,P1,P2) (MACRO) 
polynomial              over integers remainder pirem(r,P1,P2) (MACRO) 
polynomial              over integers resultant, Bezout algorithm 
			piresbez(r,P1,P2) 
polynomial              over integers resultant, Collins algorithm 
			pirescoll(r,P1,P2,n) 
polynomial              over integers resultant, Sylvester algorithm 
			piressylv(r,P1,P2) 
polynomial              over integers sign, base variable pisign(r,P) 
polynomial              over integers squarefree factorization pisfact(r,P) 
polynomial              over integers substitution, main variable 
			pisubst(r,P1,P2) 
polynomial              over integers substitution, specified variable 
			(rekursiv) pisubstsv(r,P1,n,P2) 
polynomial              over integers sum (rekursiv) pisum(r,P1,P2) 
polynomial              over integers sum dipisum(r,P1,P2) distributive 
polynomial              over integers sum norm (rekursiv) pisumnorm(r,P) 
polynomial              over integers sum udpisum(P1,P2) univariate dense 
polynomial              over integers to polynomial over modular integers 
			(rekursiv) pitopmi(r,P,M) 
polynomial              over integers to polynomial over modular singles 
			(rekursiv) pitopms(r,P,m) 
polynomial              over integers to polynomial over p-adic field 
			pitoppf(r,P,p,d) 
polynomial              over integers to polynomial over rationals 
			(rekursiv) pitopr(r,P) 
polynomial              over integers to rational function over the 
			rationals pitorfr(r,P) 
polynomial              over integers to univariate dense polynomial over 
			modular integers udpitoudpmi(P,M) univariate dense 
polynomial              over integers to univariate dense polynomial over 
			p-adic field udpitoudppf(P,p,d) univariate dense 
polynomial              over integers to univariate polynomial over 
			rationals udpitoudpr(P) univariate 
polynomial              over integers translation, all variables (rekursiv) 
			pitransav(r,P,LI) 
polynomial              over integers translation, main variable 
			pitrans(r,P,A) 
polynomial              over integers truncation (rekursiv) pitrunc(r,S,P) 
polynomial              over integers truncation product (rekursiv) 
			pitrprod(r,S,P1,P2) 
polynomial              over integers vecpitvpmpi(r,V,P) vector of 
			polynomials over integers to vector of polynomials 
			modulo 
polynomial              over integers with total degree ordering 
			dipilototdo(r,P) distributive polynomial over 
			integers in lexicographical order to distributive 
polynomial              over integers, Hensel lemma factorization 
			approximation pihlfa(r,p,L,M,S,P) 
polynomial              over integers, Hensel lemma factorization 
			approximation with respect to integer prime 
			upihlfaip(p,P,L,k) univariate 
polynomial              over integers, Hensel lemma initialization 
			upihli(p,P,L) univariate 
polynomial              over integers, Hensel lemma initialization with 
			respect to integer prime upihliip(P,F,L) univariate 
polynomial              over integers, Hensel lemma quadratic step 
			upihlqs(p,p_k,p_l,P,L1,L2,A) univariate 
polynomial              over integers, Hensel lemma quadratic step with 
			respect to integer prime 
			upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
polynomial              over integers, integer product (rekursiv) 
			piiprod(r,P,A) 
polynomial              over integers, integer product dipiiprod(r,P,A) 
			distributive 
polynomial              over integers, integer quotient (rekursiv) 
			piiquot(r,P,A) 
polynomial              over integers, modular ideal, Hensel lemma 
			quadratic step pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) 
polynomial              over integers? (rekursiv) isdpi(r,P) is dense 
polynomial              over modular 2 gf2eltoudpm2(G,a) Galois-field with 
			characteristic 2 element to univariate dense 
polynomial              over modular 2 in special bit-representation ? 
			isudpm2sb(A) is univariate dense 
polynomial              over modular 2 sbtoudpm2(a) (MACRO) special 
			bit-representation to univariate dense 
polynomial              over modular 2 to Galois-field with characteristic 
			2 element udpm2togf2el(G,P) univariate dense 
polynomial              over modular 2 to polynomial over Galois-field with 
			characteristic 2 (rekursiv) pm2topgf2(r,P) 
polynomial              over modular 2 to special bit-representation 
			udpm2tosb(P) univariate dense 
polynomial              over modular 2, irreducible and monic trinomial, 
			generator upm2imtgen(n) univariate 
polynomial              over modular 2, irreducible and monic, generator 
			upm2imgen(n) univariate 
polynomial              over modular integer ? (rekursiv) ispmi(r,m,P) is 
polynomial              over modular integer prime additive valuation 
			upmiaddval(p,P1,P) univariate 
polynomial              over modular integer primes Groebner basis 
			augmentation dipmipgba(r,p,PL,P) distributive 
polynomial              over modular integer primes Groebner basis 
			dipmipgb(r,p,PL) distributive 
polynomial              over modular integer primes Groebner basis 
			recursion dipmipgbr(r,p,PL) distributive 
polynomial              over modular integer primes S-polynomial 
			dipmipsp(r,p,P1,P2) distributive 
polynomial              over modular integer primes difference 
			dipmipdif(r,p,P1,P2) distributive 
polynomial              over modular integer primes in graduated 
			lexicographical order dipmiplotglo(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order to distributive 
polynomial              over modular integer primes in lexicographical 
			order to distributive polynomial over modular 
			integer primes in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive 
polynomial              over modular integer primes in lexicographical 
			order to distributive polynomial over modular 
			integer primes in lexicographical order with 
			inverse exponent vector dipmiplotlio(r,p,P) 
			distributive 
polynomial              over modular integer primes in lexicographical 
			order to distributive polynomial over modular 
			integer primes with total degree ordering 
			dipmiplottdo(r,p,P) distributive 
polynomial              over modular integer primes in lexicographical 
			order with inverse exponent vector 
			dipmiplotlio(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive 
polynomial              over modular integer primes list 
			fgetdipmipl(r,p,VL,pf) file get distributive 
polynomial              over modular integer primes list 
			fputdipmipl(r,p,PL,VL,pf) file put distributive 
polynomial              over modular integer primes list getdipmipl(r,p,VL) 
			(MACRO) get distributive 
polynomial              over modular integer primes list 
			putdipmipl(r,p,PL,VL) (MACRO) put distributive 
polynomial              over modular integer primes monic 
			dipmipmonic(r,p,P) distributive 
polynomial              over modular integer primes negation 
			dipmipneg(r,p,P) distributive 
polynomial              over modular integer primes product 
			dipmipprod(r,p,P1,P2) distributive 
polynomial              over modular integer primes sum 
			dipmipsum(r,p,P1,P2) distributive 
polynomial              over modular integer primes with total degree 
			ordering dipmiplottdo(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical order to distributive 
polynomial              over modular integer primes, modular integer primes 
			product dipmipmiprod(r,p,P,A) distributive 
polynomial              over modular integers (rekursiv) pitopmi(r,P,M) 
			polynomial over integers to 
polynomial              over modular integers (rekursiv) prtopmi(r,P,M) 
			polynomial over rationals to 
polynomial              over modular integers ? (rekursiv) isdpmi(r,m,P) is 
			dense 
polynomial              over modular integers ? isimupmi(p,A) is 
			irreducible, monic, univariate 
polynomial              over modular integers Ben-Or factorization 
			upmibofact(ip,P) univariate 
polynomial              over modular integers Ben-Or factorization, special 
			upmibofacts(ip,P) univariate 
polynomial              over modular integers Berlekamp factorization, last 
			step upmibfls(ip,P,B,d) univariate 
polynomial              over modular integers Bezout-matrix 
			pmibezout(r,m,P1,P2) 
polynomial              over modular integers Jacobi-symbol 
			udpmijacsym(m,P1,P2) univariate dense 
polynomial              over modular integers Jacobi-symbol 
			upmijacsym(m,P1,P2) univariate 
polynomial              over modular integers complete factorization 
			upmicfact(ip,P) univariate 
polynomial              over modular integers derivation udpmideriv(m,P) 
			univariate dense 
polynomial              over modular integers derivation, main variable 
			pmideriv(r,M,P) 
polynomial              over modular integers derivation, specified 
			variable (rekursiv) pmiderivsv(r,m,P,n) 
polynomial              over modular integers difference (rekursiv) 
			dpmidif(r,m,P1,P2) dense 
polynomial              over modular integers difference (rekursiv) 
			pmidif(r,M,P1,P2) 
polynomial              over modular integers difference udpmidif(m,P1,P2) 
			univariate dense 
polynomial              over modular integers discriminant 
			pmidiscr(r,M,P,n) 
polynomial              over modular integers discriminant via Hankel 
			matrix pmidiscrhank(r,M,P) 
polynomial              over modular integers distinct degree factorization 
			upmiddfact(ip,P) univariate 
polynomial              over modular integers evaluation, main variable 
			pmieval(r,M,P,A) 
polynomial              over modular integers evaluation, specified 
			variable (rekursiv) pmievalsv(r,m,P,n,a) 
polynomial              over modular integers exponentiation 
			pmiexp(r,m,P,n) 
polynomial              over modular integers extended greatest common 
			divisor udpmiegcd(m,P1,P2,pPX,pPY) univariate dense 
polynomial              over modular integers extended greatest common 
			divisor upmiegcd(P,P1,P2,pP3,pP4) univariate 
polynomial              over modular integers factorization, Berlekamp 
			algorithm upmibfact(ip,P,d) univariate 
polynomial              over modular integers fgetpmi(r,M,V,pf) file get 
polynomial              over modular integers fputpmi(r,M,P,V,pf) file put 
polynomial              over modular integers getpmi(r,M,V) (MACRO) get 
polynomial              over modular integers greatest common divisor and 
			cofactors (rekursiv) pmigcdcf(r,m,P1,P2,pQ1,pQ2) 
polynomial              over modular integers greatest common divisor 
			udpmigcd(m,P1,P2) univariate dense 
polynomial              over modular integers greatest common divisor 
			upmigcd(ip,P1,P2) univariate 
polynomial              over modular integers greatest squarefree divisor 
			(rekursiv) upmigsd(ip,P) univariate 
polynomial              over modular integers half extended greatest common 
			divisor udpmihegcd(m,P1,P2,pP3) univariate dense 
polynomial              over modular integers half extended greatest common 
			divisor upmihegcd(P,P1,P2,pP3) univariate 
polynomial              over modular integers interpolation (rekursiv) 
			pmiinter(r,m,P1,P2,P3,a,b) 
polynomial              over modular integers mapmitomapmp(r,m,P,M) matrix 
			of polynomials over modular integers to matrix of 
			polynomials modulo 
polynomial              over modular integers modular ideal solution of 
			equation pmimidse(r,M,S,P1,P2,F1,F2,H,pV) 
polynomial              over modular integers modular polynomial 
			exponentiation upmimpexp(ip,K,E,P) univariate 
polynomial              over modular integers monic pmimonic(r,M,P) 
polynomial              over modular integers monic udpmimonic(m,P) 
			univariate dense 
polynomial              over modular integers monic, modular ideal quotient 
			and remainder pmimidqrem(r,M,S,P1,P2,pR) 
polynomial              over modular integers negation (rekursiv) 
			dpmineg(r,m,P) dense 
polynomial              over modular integers negation (rekursiv) 
			pmineg(r,M,P) 
polynomial              over modular integers negation udpmineg(m,P) 
			univariate dense 
polynomial              over modular integers product (rekursiv) 
			dpmiprod(r,M,P1,P2) dense 
polynomial              over modular integers product (rekursiv) 
			pmiprod(r,M,P1,P2) 
polynomial              over modular integers product (rekursiv) 
			pmiupmiprod(r,m,P1,P2) polynomial over modular 
			integers, univariate 
polynomial              over modular integers product udpmiprod(m,P1,P2) 
			univariate dense 
polynomial              over modular integers pseudo remainder 
			pmipsrem(r,m,P1,P2) 
polynomial              over modular integers putpmi(r,m,P,V) (MACRO) put 
polynomial              over modular integers quotient (rekursiv) 
			pmiupmiquot(r,m,P1,P2) polynomial over modular 
			integers, univariate 
polynomial              over modular integers quotient and remainder 
			(rekursiv) pmiqrem(r,M,P1,P2,pR) 
polynomial              over modular integers quotient and remainder 
			udpmiqrem(m,P1,P2,pP3) univariate dense 
polynomial              over modular integers quotient pmiquot(r,M,P1,P2) 
			(MACRO) 
polynomial              over modular integers quotient udpmiquot(m,P1,P2) 
			(MACRO) univariate dense 
polynomial              over modular integers randomize upmirand(ip,m) 
			univariate 
polynomial              over modular integers relative prime factorization 
			upmirelpfact(P,F,Fak,pA2) univariate 
polynomial              over modular integers remainder pmirem(r,M,P1,P2) 
			(MACRO) 
polynomial              over modular integers remainder udpmirem(ip,P,P2) 
			univariate dense 
polynomial              over modular integers remainder upmirem(M,P1,P2) 
			univariate 
polynomial              over modular integers resultant and cofactor of 
			resultant equation upmiresulc(m,P1,P2,pC) 
			univariate 
polynomial              over modular integers resultant pmires(r,m,P1,P2,n) 
polynomial              over modular integers resultant upmires(m,P1,P2) 
			univariate 
polynomial              over modular integers resultant, Collins algorithm 
			(rekursiv) pmirescoll(r,m,P1,P2) 
polynomial              over modular integers separate factor of equal 
			degree upmisfed(ip,G,d) univariate 
polynomial              over modular integers squarefree factorization 
			(rekursiv) upmisfact(ip,P) univariate 
polynomial              over modular integers squarefree part upmisfp(m,P) 
			univariate 
polynomial              over modular integers substitution with respect to 
			a cubic equation bpmisubcubeq(p,P,R) bivariate 
polynomial              over modular integers substitution, main variable 
			pmisubst(r,m,P1,P2) 
polynomial              over modular integers substitution, specified 
			variable (rekursiv) pmisubstsv(r,m,P1,n,P2) 
polynomial              over modular integers sum (rekursiv) 
			dpmisum(r,M,P1,P2) dense 
polynomial              over modular integers sum (rekursiv) 
			pmisum(r,M,P1,P2) 
polynomial              over modular integers sum udpmisum(m,P1,P2) 
			univariate dense 
polynomial              over modular integers to symmetric remainder system 
			(rekursiv) pmitos(r,M,P) 
polynomial              over modular integers transformation 
			pmitransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over modular integers transformation 
			upmitransf(M,P,r,P1) univariate 
polynomial              over modular integers transformation version2 
			upmitransf2(M,P,r,P1) univariate 
polynomial              over modular integers translation, all variables 
			(rekursiv) pmitransav(r,m,P,Lmi) 
polynomial              over modular integers translation, main variable 
			pmitrans(r,m,P,a) 
polynomial              over modular integers udpitoudpmi(P,M) univariate 
			dense polynomial over integers to univariate dense 
polynomial              over modular integers unit? ispmiunit(r,m,P) is 
polynomial              over modular integers univariate content (rekursiv) 
			pmiucont(r,m,P) 
polynomial              over modular integers vecpmitovpmp(r,m,P,V) vector 
			of polynomials over modular integers to vector of 
			polynomials modulo 
polynomial              over modular integers, Berlekamp Q polynomials 
			construction upmibqp(ip,P) univariate 
polynomial              over modular integers, Berlekamp factorization, 
			Zassenhaus method upmibfzm(ip,s,P,G) univariate 
polynomial              over modular integers, complete factorization 
			special upmicfacts(P,F) univariate 
polynomial              over modular integers, modular ideal product 
			pmimidprod(r,M,S,P1,P2) 
polynomial              over modular integers, modular ideal, Hensel lemma 
			quadratic step on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) 
polynomial              over modular integers, modular ideal, Hensel lemma 
			quadratic step 
			pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) 
polynomial              over modular integers, modular integer product 
			udpmimiprod(m,P,a) univariate dense 
polynomial              over modular integers, modular integer quotient 
			(rekursiv) pmimiquot(r,m,P,a) 
polynomial              over modular integers, modular integers product 
			(rekursiv) pmimiprod(r,M,P,A) 
polynomial              over modular integers, monomial, polynomial, 
			remainder upmimprem(ip,K,E,P) univariate 
polynomial              over modular integers, number of irreducible 
			factors upminif(m,P) univariate 
polynomial              over modular integers, root finding (rekursiv) 
			upmirf(ip,P) univariate 
polynomial              over modular integers, root finding, special 
			(rekursiv) upmirfspec(ip,P) univariate 
polynomial              over modular integers, trace function, special 
			upmitfsp(ip,G,d,M) univariate 
polynomial              over modular integers, univariate polynomial over 
			modular integers product (rekursiv) 
			pmiupmiprod(r,m,P1,P2) 
polynomial              over modular integers, univariate polynomial over 
			modular integers quotient (rekursiv) 
			pmiupmiquot(r,m,P1,P2) 
polynomial              over modular single prime quotient 
			cdprfmsp1upq(p,F,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, univariate 
polynomial              over modular single prime, complete factorization 
			special upmscfacts(p,A) univariate 
polynomial              over modular single primes Groebner basis 
			augmentation dipmspgba(r,p,PL,P) distributive 
polynomial              over modular single primes Groebner basis 
			dipmspgb(r,p,PL) distributive 
polynomial              over modular single primes Groebner basis recursion 
			dipmspgbr(r,p,PL) distributive 
polynomial              over modular single primes S-polynomial 
			dipmspsp(r,p,P1,P2) distributive 
polynomial              over modular single primes difference 
			dipmspdif(r,p,P1,P2) distributive 
polynomial              over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, minimal polynomial modulo power of an 
			univariate prime 
polynomial              over modular single primes in graduated 
			lexicographical order dipmsplotglo(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order to distributive 
polynomial              over modular single primes in lexicographical order 
			to distributive polynomial over modular single 
			primes in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive 
polynomial              over modular single primes in lexicographical order 
			to distributive polynomial over modular single 
			primes in lexicographical order with inverse 
			exponent vector dipmsplotlio(r,p,P) distributive 
polynomial              over modular single primes in lexicographical order 
			to distributive polynomial over modular single 
			primes with total degree ordering 
			dipmsplottdo(r,p,P) distributive 
polynomial              over modular single primes in lexicographical order 
			with inverse exponent vector dipmsplotlio(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order to distributive 
polynomial              over modular single primes list 
			fgetdipmspl(r,p,VL,pf) file get distributive 
polynomial              over modular single primes list 
			fputdipmspl(r,p,PL,VL,pf) file put distributive 
polynomial              over modular single primes list getdipmspl(r,p,VL) 
			(MACRO) get distributive 
polynomial              over modular single primes list 
			putdipmspl(r,p,PL,VL) (MACRO) put distributive 
polynomial              over modular single primes monic dipmspmonic(r,p,P) 
			distributive 
polynomial              over modular single primes negation 
			dipmspneg(r,p,P) distributive 
polynomial              over modular single primes product 
			dipmspprod(r,p,P1,P2) distributive 
polynomial              over modular single primes sum dipmspsum(r,p,P1,P2) 
			distributive 
polynomial              over modular single primes with total degree 
			ordering dipmsplottdo(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to distributive 
polynomial              over modular single primes, modular single primes 
			product dipmspmsprod(r,p,P,a) distributive 
polynomial              over modular single trailing base coefficient 
			udpmstbc(m,P) univariate dense 
polynomial              over modular singles (rekursiv) pitopms(r,P,m) 
			polynomial over integers to 
polynomial              over modular singles ? (rekursiv) isdpms(r,m,P) is 
			dense 
polynomial              over modular singles ? (rekursiv) ispms(r,m,P) is 
polynomial              over modular singles ? isimupms(p,A) is 
			irreducible, monic, univariate 
polynomial              over modular singles Berlekamp factorization, last 
			step upmsbfls(m,P,B,d) univariate 
polynomial              over modular singles Bezout-matrix 
			pmsbezout(r,m,P1,P2) 
polynomial              over modular singles Jacobi-symbol 
			udpmsjacsym(m,P1,P2) univariate dense 
polynomial              over modular singles Jacobi-symbol 
			upmsjacsym(m,P1,P2) univariate 
polynomial              over modular singles additive valuation 
			upmsaddval(p,P1,P) univariate 
polynomial              over modular singles complete factorization 
			upmscfact(p,A) univariate 
polynomial              over modular singles derivation udpmsderiv(m,P) 
			univariate dense 
polynomial              over modular singles derivation, main variable 
			pmsderiv(r,m,P) 
polynomial              over modular singles derivation, specified variable 
			(rekursiv) pmsderivsv(r,m,P,n) 
polynomial              over modular singles difference (rekursiv) 
			dpmsdif(r,m,P1,P2) dense 
polynomial              over modular singles difference (rekursiv) 
			pmsdif(r,m,P1,P2) 
polynomial              over modular singles difference udpmsdif(m,P1,P2) 
			univariate dense 
polynomial              over modular singles discriminant pmsdiscr(r,m,P,n) 
polynomial              over modular singles evaluation, main variable 
			pmseval(r,m,P,a) 
polynomial              over modular singles evaluation, specified variable 
			(rekursiv) pmsevalsv(r,m,P,n,a) 
polynomial              over modular singles exponentiation pmsexp(r,m,P,n) 
polynomial              over modular singles extended greatest common 
			divisor udpmsegcd(m,P1,P2,pPX,pPY) univariate dense 
polynomial              over modular singles extended greatest common 
			divisor upmsegcd(m,P1,P2,pP3,pP4) univariate 
polynomial              over modular singles factorization, Berlekamp 
			algorithm upmsbfact(p,A,d) univariate 
polynomial              over modular singles fgetpms(r,m,V,pf) file get 
polynomial              over modular singles fputpms(r,m,P,V,pf) file put 
polynomial              over modular singles getpms(r,m,V) (MACRO) get 
polynomial              over modular singles greatest common divisor and 
			cofactors (rekursiv) pmsgcdcf(r,m,P1,P2,pQ1,pQ2) 
polynomial              over modular singles greatest common divisor 
			udpmsgcd(m,P1,P2) univariate dense 
polynomial              over modular singles greatest common divisor 
			upmsgcd(m,P1,P2) univariate 
polynomial              over modular singles greatest squarefree divisor 
			(rekursiv) upmsgsd(m,P) univariate 
polynomial              over modular singles half extended greatest common 
			divisor udpmshegcd(m,P1,P2,pP3) univariate dense 
polynomial              over modular singles half extended greatest common 
			divisor upmshegcd(m,P1,P2,pP3) univariate 
polynomial              over modular singles interpolation (rekursiv) 
			pmsinter(r,m,P1,P2,P3,a,b) 
polynomial              over modular singles mapmstomapmp(r,m,P,M) matrix 
			of polynomials over modular singles to matrix of 
			polynomials modulo 
polynomial              over modular singles monic pmsmonic(r,m,P) 
polynomial              over modular singles monic udpmsmonic(m,P) 
			univariate dense 
polynomial              over modular singles negation (rekursiv) 
			dpmsneg(r,m,P) dense 
polynomial              over modular singles negation (rekursiv) 
			pmsneg(r,m,P) 
polynomial              over modular singles negation udpmsneg(m,P) 
			univariate dense 
polynomial              over modular singles product (rekursiv) 
			dpmsprod(r,m,P1,P2) dense 
polynomial              over modular singles product (rekursiv) 
			pmsprod(r,m,P1,P2) 
polynomial              over modular singles product (rekursiv) 
			pmsupmsprod(r,m,P1,P2) polynomial over modular 
			singles, univariate 
polynomial              over modular singles product udpmsprod(m,P1,P2) 
			univariate dense 
polynomial              over modular singles pseudo remainder 
			pmspsrem(r,m,P1,P2) 
polynomial              over modular singles putpms(r,m,P,V) (MACRO) put 
polynomial              over modular singles quotient (rekursiv) 
			pmsupmsquot(r,m,P1,P2) polynomial over modular 
			singles, univariate 
polynomial              over modular singles quotient and remainder 
			(rekursiv) pmsqrem(r,m,P1,P2,pR) 
polynomial              over modular singles quotient and remainder 
			udpmsqrem(m,P1,P2,pP3) univariate dense 
polynomial              over modular singles quotient pmsquot(r,m,P1,P2) 
			(MACRO) 
polynomial              over modular singles quotient udpmsquot(m,P1,P2) 
			(MACRO) univariate dense 
polynomial              over modular singles relative prime factorization 
			upmsrelpfact(p,P,Fak,pA2) univariate 
polynomial              over modular singles remainder pmsrem(r,m,P1,P2) 
			(MACRO) 
polynomial              over modular singles remainder udpmsrem(m,P1,P2) 
			univariate dense 
polynomial              over modular singles remainder upmsrem(m,P1,P2) 
			univariate 
polynomial              over modular singles resultant and cofactor of 
			resultant equation upmsresulc(m,P1,P2,pC) 
			univariate 
polynomial              over modular singles resultant pmsres(r,m,P1,P2,n) 
polynomial              over modular singles resultant upmsres(m,P1,P2) 
			univariate 
polynomial              over modular singles resultant, Collins algorithm 
			(rekursiv) pmsrescoll(r,m,P1,P2) 
polynomial              over modular singles square root power series 
			upmssrpser(m,P,i) univariate 
polynomial              over modular singles square root principal part 
			upmssrpp(m,P) univariate 
polynomial              over modular singles squarefree factorization 
			(rekursiv) upmssfact(m,P) univariate 
polynomial              over modular singles squarefree part upmssfp(m,P) 
			univariate 
polynomial              over modular singles substitution, main variable 
			pmssubst(r,m,P1,P2) 
polynomial              over modular singles substitution, specified 
			variable (rekursiv) pmssubstsv(r,m,P1,n,P2) 
polynomial              over modular singles sum (rekursiv) 
			dpmssum(r,m,P1,P2) dense 
polynomial              over modular singles sum (rekursiv) 
			pmssum(r,m,P1,P2) 
polynomial              over modular singles sum udpmssum(m,P1,P2) 
			univariate dense 
polynomial              over modular singles to polynomial over 
			Galois-field with single characteristic (rekursiv) 
			pmstopgfs(r,p,P) 
polynomial              over modular singles to rational function over 
			modular single prime, transcendence degree 1 
			pmstorfmsp1(p,P) (MACRO) 
polynomial              over modular singles transformation 
			pmstransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over modular singles transformation 
			upmstransf(m,P,r,P1) univariate 
polynomial              over modular singles translation, all variables 
			(rekursiv) pmstransav(r,m,P,Lms) 
polynomial              over modular singles translation, main variable 
			pmstrans(r,m,P,a) 
polynomial              over modular singles unit? ispmsunit(r,m,P) is 
polynomial              over modular singles univariate content (rekursiv) 
			pmsucont(r,m,P) 
polynomial              over modular singles vecpmstovpmp(r,m,P,V) vector 
			of polynomials over modular singles to vector of 
			polynomials modulo 
polynomial              over modular singles, Berlekamp Q polynomials 
			construction upmsbqp(p,A) univariate 
polynomial              over modular singles, Berlekamp factorization, 
			Zassenhaus method upmsbfzm(m,s,P,G) univariate 
polynomial              over modular singles, irreducible and monic 
			trinomial, generator upmsimtgen(p,n) univariate 
polynomial              over modular singles, irreducible and monic, 
			generator upmsimgen(p,n) univariate 
polynomial              over modular singles, modular single product 
			(rekursiv) pmsmsprod(r,m,P,a) 
polynomial              over modular singles, modular single product 
			udpmsmsprod(m,P,a) univariate dense 
polynomial              over modular singles, modular single quotient 
			(rekursiv) pmsmsquot(r,m,P,a) 
polynomial              over modular singles, monomial, polynomial, 
			remainder upmsmprem(m,k,T,P) univariate 
polynomial              over modular singles, number of irreducible factors 
			upmsnif(m,P) univariate 
polynomial              over modular singles, root finding (rekursiv) 
			upmsrf(m,P) univariate 
polynomial              over modular singles, summation over Jacobi-symbols 
			udpmssumjs(m,P,n) univariate dense 
polynomial              over modular singles, univariate polynomial over 
			modular singles product (rekursiv) 
			pmsupmsprod(r,m,P1,P2) 
polynomial              over modular singles, univariate polynomial over 
			modular singles quotient (rekursiv) 
			pmsupmsquot(r,m,P1,P2) 
polynomial              over number field (rekursiv) prtopnf(r,P) 
			polynomial over rationals to 
polynomial              over number field Groebner basis augmentation 
			dipnfgba(r,F,PL,P) distributive 
polynomial              over number field Groebner basis dipnfgb(r,F,PL) 
			distributive 
polynomial              over number field Groebner basis recursion 
			dipnfgbr(r,F,PL) distributive 
polynomial              over number field S-polynomial dipnfsp(r,F,P1,P2) 
			distributive 
polynomial              over number field derivation, main variable 
			pnfderiv(r,F,P) 
polynomial              over number field derivation, specified variable 
			(rekursiv) pnfderivsv(r,F,P,n) 
polynomial              over number field difference (rekursiv) 
			pnfdif(r,F,P1,P2) 
polynomial              over number field difference dipnfdif(r,F,P1,P2) 
			distributive 
polynomial              over number field evaluation, main variable 
			pnfeval(r,F,P,a) 
polynomial              over number field evaluation, specified variable 
			(rekursiv) pnfevalsv(r,F,P,n,a) 
polynomial              over number field exponentiation pnfexp(r,F,P,n) 
polynomial              over number field fgetpnf(r,F,V,Vnf,pf) file get 
polynomial              over number field fputpnf(r,F,P,V,Vnf,pf) file put 
polynomial              over number field getpnf(r,F,V,Vnf) (MACRO) get 
polynomial              over number field greatest common divisor and 
			cofactors upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate 
polynomial              over number field greatest common divisor 
			upnfgcd(F,P1,P2) univariate 
polynomial              over number field in graduated lexicographical 
			order dipnflotoglo(r,F,P) distributive polynomial 
			over number field in lexicographical order to 
			distributive 
polynomial              over number field in lexicographical order to 
			distributive polynomial over number field in 
			graduated lexicographical order dipnflotoglo(r,F,P) 
			distributive 
polynomial              over number field in lexicographical order to 
			distributive polynomial over number field in 
			lexicographical order with inverse exponent vector 
			dipnflotolio(r,F,P) distributive 
polynomial              over number field in lexicographical order to 
			distributive polynomial over number field with 
			total degree ordering dipnflototdo(r,F,P) 
			distributive 
polynomial              over number field in lexicographical order with 
			inverse exponent vector dipnflotolio(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order to distributive 
polynomial              over number field list fgetdipnfl(r,F,VL,Vnf,pf) 
			file get distributive 
polynomial              over number field list fputdipnfl(r,F,PL,VL,Vnf,pf) 
			file put distributive 
polynomial              over number field list getdipnfl(r,F,VL,Vnf) 
			(MACRO) get distributive 
polynomial              over number field list putdipnfl(r,F,PL,VL,Vnf) 
			(MACRO) put distributive 
polynomial              over number field mapnftomapmp(r,F,P,M) matrix of 
			polynomials over number field to matrix of 
			polynomials modulo 
polynomial              over number field monic dipnfmonic(r,F,P) 
			distributive 
polynomial              over number field monic pnfmonic(r,F,P) 
polynomial              over number field negation (rekursiv) pnfneg(r,F,P) 
polynomial              over number field negation dipnfneg(r,F,P) 
			distributive 
polynomial              over number field product (rekursiv) 
			pnfprod(r,F,P1,P2) 
polynomial              over number field product dipnfprod(r,F,P1,P2) 
			distributive 
polynomial              over number field putpnf(r,F,P,V,Vnf) (MACRO) put 
polynomial              over number field quotient and remainder (rekursiv) 
			pnfqrem(r,F,P1,P2,pR) 
polynomial              over number field quotient pnfquot(r,F,P1,P2) 
			(MACRO) 
polynomial              over number field remainder pnfrem(r,F,P1,P2) 
			(MACRO) 
polynomial              over number field squarefree factorization 
			upnfsfact(F,P) univariate 
polynomial              over number field sum (rekursiv) pnfsum(r,F,P1,P2) 
polynomial              over number field sum dipnfsum(r,F,P1,P2) 
			distributive 
polynomial              over number field to polynomial over rationals 
			pnftopr(r,P) 
polynomial              over number field transformation 
			pnftransf(r1,F,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over number field vecpnftovpmp(r,F,P,V) vector of 
			polynomials over number field to vector of 
			polynomials modulo 
polynomial              over number field with total degree ordering 
			dipnflototdo(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive 
polynomial              over number field, number field element product 
			(rekursiv) pnfnfprod(r,F,P,a) 
polynomial              over number field, number field element product 
			dipnfnfprod(r,F,P,A) distributive 
polynomial              over number field, number field element quotient 
			(rekursiv) pnfnfquot(r,F,P,a) 
polynomial              over p-adic field ? isdppf(r,p,P) is dense 
polynomial              over p-adic field derivation, main variable 
			(rekursiv) ppfderiv(r,p,P) 
polynomial              over p-adic field derivation, selected variable 
			ppfderivsv(r,p,P,n) 
polynomial              over p-adic field difference ppfdif(r,p,P1,P2) 
polynomial              over p-adic field difference udppfdif(p,P1,P2) 
			univariate dense 
polynomial              over p-adic field evaluation, main variable 
			ppfeval(r,p,P,A) 
polynomial              over p-adic field evaluation, selected variable 
			ppfevalsv(r,p,P,n,A) 
polynomial              over p-adic field exponentiation ppfexp(r,p,P,n) 
polynomial              over p-adic field exponentiation udppfexp(p,P,n) 
			univariate dense 
polynomial              over p-adic field fgetppf(r,p,V,pf) file get 
polynomial              over p-adic field fitting ppffit(r,p,P,d) 
polynomial              over p-adic field fitting udppffit(p,P,Pd) 
			univariate dense 
polynomial              over p-adic field fputppf(r,p,P,V,pf) file put 
polynomial              over p-adic field getppf(r,p,V) get 
polynomial              over p-adic field integer product ppfiprod(r,p,P,i) 
polynomial              over p-adic field negation ppfneg(r,p,P) 
polynomial              over p-adic field negation udppfneg(p,P) univariate 
			dense 
polynomial              over p-adic field order ppford(r,p,P) 
polynomial              over p-adic field p-adic field element product 
			ppfpfprod(r,p,P,b) 
polynomial              over p-adic field p-adic field element product 
			udppfpfprod(p,P,a) univariate dense 
polynomial              over p-adic field pitoppf(r,P,p,d) polynomial over 
			integers to 
polynomial              over p-adic field prime power product 
			ppfpprod(r,p,P,i) 
polynomial              over p-adic field prime power product 
			udppfpprod(p,P,i) univariate dense 
polynomial              over p-adic field product ppfprod(r,p,P1,P2) 
polynomial              over p-adic field product udppfprod(p,P1,P2) 
			univariate dense 
polynomial              over p-adic field prtoppf(r,P,p,d) polynomial over 
			rationals to 
polynomial              over p-adic field putppf(r,p,P,V) put 
polynomial              over p-adic field rational number product 
			(rekursiv) ppfrprod(r,p,P,R) 
polynomial              over p-adic field substitution, main variable 
			ppfsubst(r,p,P1,P2) 
polynomial              over p-adic field substitution, selected variable 
			ppfsubstsv(r,p,P1,n,P2) 
polynomial              over p-adic field sum ppfsum(r,p,P1,P2) 
polynomial              over p-adic field sum udppfsum(p,P1,P2) univariate 
			dense 
polynomial              over p-adic field transformation 
			ppftransf(r1,p,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over p-adic field translation, all variables 
			ppftransav(r,p,P,Lpf) 
polynomial              over p-adic field translation, main variable 
			ppftrans(r,p,P,A) 
polynomial              over p-adic field udpitoudppf(P,p,d) univariate 
			dense polynomial over integers to univariate dense 
polynomial              over p-adic field udprtoudppf(P,p,d) univariate 
			dense polynomial over rationals to univariate dense 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, Dedekind maximality test 
			ouspprmsp1dm(p,P,F) order of an univariate 
			separable 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, Hensel factorization 
			approximation upprmsp1hfa(p,F,P,L,k) univariate 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, Hensel lemma initialization 
			upprmsp1hli(p,F,P,L) univariate 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, Hensel quadratic step 
			upprmsp1hqs(p,F,T,L1,L2,A) univariate 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, algebraic function over 
			modular single prime, transcendence degree 1, 
			evaluation special upprmsp1afes(p,F,P,a) univariate 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, approximation of P-adic 
			factorization uspprmsp1apf(p,P,F,k) univariate 
			separable 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, basis of a local maximal 
			over-order ouspprmsp1bl(p,F,P,Q,pk) order of an 
			univariate separable 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, decomposition law 
			ouspprmsp1dl(p,F,P,k) order of a univariate 
			separable 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, discriminant 
			upprmsp1disc(p,F) univariate 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, reduced discriminant 
			upprmsp1redd(p,F) univariate 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, resultant, Sylvester 
			algorithm pprmsp1ress(r,p,P1,P2) 
polynomial              over polynomial ring over modular single prime, 
			transcendence degree 1, resultant, Sylvester 
			algorithm upprmsp1ress(p,P1,P2) univariate 
polynomial              over polynomials over integers Groebner basis 
			augmentation dippigba(r1,r2,PL,P) distributive 
polynomial              over polynomials over integers Groebner basis 
			dippigb(r1,r2,PL) distributive 
polynomial              over polynomials over integers Groebner basis 
			recursion dippigbr(r1,r2,PL) distributive 
polynomial              over polynomials over integers Groebner system 
			fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file put 
			distributive 
polynomial              over polynomials over integers Groebner system 
			putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) put 
			distributive 
polynomial              over polynomials over integers Groebner test 
			dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) distributive 
polynomial              over polynomials over integers Groebner test 
			fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) file 
			put distributive 
polynomial              over polynomials over integers Groebner test 
			putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) (MACRO) 
			put distributive 
polynomial              over polynomials over integers S-polynomial 
			dippisp(r1,r2,P1,P2) distributive 
polynomial              over polynomials over integers case distinction 
			fgetdippicd(r1,r2,VL1,VL2,fac,pf) file get 
			distributive 
polynomial              over polynomials over integers case distinction 
			getdippicd(r1,r2,VL1,VL2,fac) (MACRO) get 
			distributive 
polynomial              over polynomials over integers comprehensive 
			Groebner basis 
			dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive 
polynomial              over polynomials over integers comprehensive 
			Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put 
			distributive 
polynomial              over polynomials over integers comprehensive 
			Groebner basis putdippicgb(r1,r2,CGBL,i,VL1,VL2) 
			(MACRO) put distributive 
polynomial              over polynomials over integers content and 
			primitive part dippicp(r1,r2,P,pPP) distributive 
polynomial              over polynomials over integers difference 
			dippidif(r1,r2,P1,P2) distributive 
polynomial              over polynomials over integers dimension 
			dippidim(r1,r2,s,PL,CONDS,fac,VL1,VL2,pf) 
			distributive 
polynomial              over polynomials over integers dimension 
			fputdippidim(r1,r2,DIML,VL1,VL2,pf) file put 
			distributive 
polynomial              over polynomials over integers dimension 
			putdippidim(r1,r2,DIML,VL1,VL2) (MACRO) put 
			distributive 
polynomial              over polynomials over integers in graduated 
			lexicographical order dippilotoglo(r1,r2,P) 
			distributive polynomial over polynomials over 
			integers in lexicographical order to distributive 
polynomial              over polynomials over integers in lexicographical 
			order to distributive polynomial over polynomials 
			over integers in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive 
polynomial              over polynomials over integers in lexicographical 
			order to distributive polynomial over polynomials 
			over integers in lexicographical order with inverse 
			exponent vector dippilotolio(r1,r2,P) distributive 
polynomial              over polynomials over integers in lexicographical 
			order to distributive polynomial over polynomials 
			over integers with total degree ordering 
			dippilototdo(r1,r2,P) distributive 
polynomial              over polynomials over integers in lexicographical 
			order with inverse exponent vector 
			dippilotolio(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive 
polynomial              over polynomials over integers list 
			fgetdippil(r1,r2,VL1,VL2,pf) file get distributive 
polynomial              over polynomials over integers list 
			fputdippil(r1,r2,PL,VL1,VL2,pf) file put 
			distributive 
polynomial              over polynomials over integers list 
			getdippil(r1,r2,VL1,VL2) (MACRO) get distributive 
polynomial              over polynomials over integers list 
			putdippil(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive 
polynomial              over polynomials over integers negation 
			dippineg(r1,r2,P) distributive 
polynomial              over polynomials over integers one ? 
			isdippione(r1,r2,P) is distributive 
polynomial              over polynomials over integers parametric ideal 
			membership test dippipim(r1,r2,s,PL,PTL,CONDS,OPL) 
			distributive 
polynomial              over polynomials over integers parametric ideal 
			membership test fputdippipim(r1,r2,NOUT,VL1,VL2,pf) 
			file put distributive 
polynomial              over polynomials over integers parametric ideal 
			membership test putdippipim(r1,r2,NOUT,VL1,VL2) 
			(MACRO) put distributive 
polynomial              over polynomials over integers product 
			dippiprod(r1,r2,P1,P2) distributive 
polynomial              over polynomials over integers quantifier free 
			formula dippiqff(r1,r2,s,PL,CONDS,fac) distributive 
polynomial              over polynomials over integers quantifier free 
			formula fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file 
			put distributive 
polynomial              over polynomials over integers quantifier free 
			formula putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put 
			distributive 
polynomial              over polynomials over integers reduced 
			comprehensive Groebner basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive 
polynomial              over polynomials over integers sum 
			dippisum(r1,r2,P1,P2) distributive 
polynomial              over polynomials over integers with total degree 
			ordering dippilototdo(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive 
polynomial              over polynomials over integers, polynomial over 
			integers product dippipiprod(r1,r2,P,A) 
			distributive 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1 cdprfmsp1fup(p,P) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			univariate 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1 clfcdprfmsp1(P,n) 
			coefficient list from common denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1 sclfuprfmsp1(P,n) special 
			coefficient list from univariate 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1 uprfmsp1fcdp(p,P) univariate 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, from common 
			denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, derivation, main variable 
			prfmsp1deriv(r,p,P) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, difference (rekursiv) 
			prfmsp1dif(r,p,P1,P2) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, extended greatest common 
			divisor uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, from coefficient list 
			cdprfmsp1fcl(L,p) common denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, from common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, from special coefficient 
			list uprfmsp1fscl(L) univariate 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, from univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1 cdprfmsp1fup(p,P) common 
			denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, inverse cdprfmsp1inv(p,F,A) 
			common denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, list from common 
			denominator matrix of rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, negation (rekursiv) 
			prfmsp1neg(r,p,P) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, product (rekursiv) 
			prfmsp1prod(r,p,P1,P2) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, quotient and remainder 
			(rekursiv) prfmsp1qrem(r,p,P1,P2,pR) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, rational function over 
			modular single prime, transcendence degree 1, 
			product (rekursiv) prfmsp1rfprd(r,p,P,a) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, sum (rekursiv) 
			prfmsp1sum(r,p,P1,P2) 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, sum cdprfmsp1sum(p,P1,P2) 
			common denominator 
polynomial              over rational functions over modular single prime, 
			transcendence degree 1, univariate polynomial over 
			modular single prime quotient cdprfmsp1upq(p,F,P) 
			common denominator 
polynomial              over rational functions over modular single primes, 
			transcendence degree 1, module homomorphism 
			cdprfmsp1mh(p,P,M) common denominator 
polynomial              over rational functions over the rationals Groebner 
			basis augmentation diprfrgba(r1,r2,PL,P) 
			distributive 
polynomial              over rational functions over the rationals Groebner 
			basis diprfrgb(r1,r2,PL) distributive 
polynomial              over rational functions over the rationals Groebner 
			basis recursion diprfrgbr(r1,r2,PL) distributive 
polynomial              over rational functions over the rationals 
			S-polynomial diprfrsp(r1,r2,P1,P2) distributive 
polynomial              over rational functions over the rationals 
			difference diprfrdif(r1,r2,P1,P2) distributive 
polynomial              over rational functions over the rationals in 
			graduated lexicographical order 
			diprfrlotglo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive 
polynomial              over rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			graduated lexicographical order 
			diprfrlotglo(r1,r2,P) distributive 
polynomial              over rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			lexicographical order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive 
polynomial              over rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals with 
			total degree ordering diprfrlottdo(r1,r2,P) 
			distributive 
polynomial              over rational functions over the rationals in 
			lexicographical order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive 
polynomial              over rational functions over the rationals list 
			fgetdiprfrl(r1,r2,VL1,VL2,pf) file get distributive 
polynomial              over rational functions over the rationals list 
			fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file put 
			distributive 
polynomial              over rational functions over the rationals list 
			getdiprfrl(r1,r2,VL1,VL2) (MACRO) get distributive 
polynomial              over rational functions over the rationals list 
			putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive 
polynomial              over rational functions over the rationals monic 
			diprfrmonic(r1,r2,P) distributive 
polynomial              over rational functions over the rationals negation 
			diprfrneg(r1,r2,P) distributive 
polynomial              over rational functions over the rationals one ? 
			isdiprfrone(r1,r2,P) is distributive 
polynomial              over rational functions over the rationals product 
			diprfrprod(r1,r2,P1,P2) distributive 
polynomial              over rational functions over the rationals rational 
			function over the rationals product 
			diprfrrfprod(r1,r2,P,A) distributive 
polynomial              over rational functions over the rationals 
			rfrtodiprfr(r1,r2,F) rational function over the 
			rationals to distributive 
polynomial              over rational functions over the rationals sum 
			diprfrsum(r1,r2,P1,P2) distributive 
polynomial              over rational functions over the rationals to 
			rational function over the rationals 
			diprfrtorfr(r1,r2,P) distributive 
polynomial              over rational functions over the rationals with 
			total degree ordering diprfrlottdo(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive 
polynomial              over rationals (rekursiv) pitopr(r,P) polynomial 
			over integers to 
polynomial              over rationals ? (rekursiv) ispr(r,P) is 
polynomial              over rationals ? isiupr(P) is irreducible 
			univariate 
polynomial              over rationals Groebner basis augmentation 
			diprgba(r,PL,P) distributive 
polynomial              over rationals Groebner basis diprgb(r,PL) 
			distributive 
polynomial              over rationals Groebner basis recursion 
			diprgbr(r,PL) distributive 
polynomial              over rationals S-polynomial diprsp(r,P1,P2) 
			distributive 
polynomial              over rationals derivation, main variable 
			prderiv(r,P) 
polynomial              over rationals derivation, specified variable 
			(rekursiv) prderivsv(r,P,n) 
polynomial              over rationals difference (rekursiv) prdif(r,P1,P2) 
polynomial              over rationals difference diprdif(r,P1,P2) 
			distributive 
polynomial              over rationals difference udprdif(P1,P2) univariate 
			dense 
polynomial              over rationals evaluation, main variable 
			preval(r,P,A) 
polynomial              over rationals evaluation, specified variable 
			(rekursiv) prevalsv(r,P,n,A) 
polynomial              over rationals exponentiation prexp(r,P,n) 
polynomial              over rationals factorization uprfact(P) univariate 
polynomial              over rationals fgetpr(r,V,pf) file get 
polynomial              over rationals fputpr(r,P,V,pf) file put 
polynomial              over rationals getpr(r,V) (MACRO) get 
polynomial              over rationals in graduated lexicographical order 
			diprlotoglo(r,P) distributive polynomial over 
			rationals in lexicographical order to distributive 
polynomial              over rationals in lexicographical order to 
			distributive polynomial over rationals in graduated 
			lexicographical order diprlotoglo(r,P) distributive 
polynomial              over rationals in lexicographical order to 
			distributive polynomial over rationals in 
			lexicographical order with inverse exponent vector 
			diprlotolio(r,P) distributive 
polynomial              over rationals in lexicographical order to 
			distributive polynomial over rationals with total 
			degree ordering diprlototdo(r,P) distributive 
polynomial              over rationals in lexicographical order with 
			inverse exponent vector diprlotolio(r,P) 
			distributive polynomial over rationals in 
			lexicographical order to distributive 
polynomial              over rationals integration, main variable 
			printegr(r,P) 
polynomial              over rationals list fgetdiprl(r,VL,pf) file get 
			distributive 
polynomial              over rationals list fputdiprl(r,PL,VL,pf) file put 
			distributive 
polynomial              over rationals list getdiprl(r,VL) (MACRO) get 
			distributive 
polynomial              over rationals list putdiprl(r,PL,VL) (MACRO) put 
			distributive 
polynomial              over rationals maprtompmpr(r,M,P) matrix of 
			polynomials over rationals to matrix of polynomials 
			modulo 
polynomial              over rationals monic diprmonic(r,P) distributive 
polynomial              over rationals negation (rekursiv) prneg(r,P) 
polynomial              over rationals negation diprneg(r,P) distributive 
polynomial              over rationals negation udprneg(P) univariate dense 
polynomial              over rationals nfeltoudpr(a) number field element 
			to univariate dense 
polynomial              over rationals number field element evaluation 
			first variable special version prnfevalfvs(r,F,P) 
polynomial              over rationals number field element evaluation 
			uprnfeval(P,F,a) univariate 
polynomial              over rationals number field element, sparse 
			representation, evaluation uprnfseval(P,F,a) 
			univariate 
polynomial              over rationals one ? isdiprone(r,P) is distributive 
polynomial              over rationals pnftopr(r,P) polynomial over number 
			field to 
polynomial              over rationals product (rekursiv) prprod(r,P1,P2) 
polynomial              over rationals product diprprod(r,P1,P2) 
			distributive 
polynomial              over rationals product udprprod(P1,P2) univariate 
			dense 
polynomial              over rationals putpr(r,P,V) (MACRO) put 
polynomial              over rationals quotient and remainder (rekursiv) 
			prqrem(r,P1,P2,pR) 
polynomial              over rationals quotient and remainder 
			udprqrem(P1,P2,pP3) univariate dense 
polynomial              over rationals quotient prquot(r,P1,P2) (MACRO) 
polynomial              over rationals remainder prrem(r,P1,P2) (MACRO) 
polynomial              over rationals substitution, main variable 
			prsubst(r,P1,P2) 
polynomial              over rationals substitution, specified variable 
			(rekursiv) prsubstsv(r,P1,n,P2) 
polynomial              over rationals sum (rekursiv) prsum(r,P1,P2) 
polynomial              over rationals sum diprsum(r,P1,P2) distributive 
polynomial              over rationals sum udprsum(P1,P2) univariate dense 
polynomial              over rationals to number field element 
			udprtonfel(P) univariate dense 
polynomial              over rationals to number field element 
			uprtonfel(F,P) univariate 
polynomial              over rationals to polynomial over modular integers 
			(rekursiv) prtopmi(r,P,M) 
polynomial              over rationals to polynomial over number field 
			(rekursiv) prtopnf(r,P) 
polynomial              over rationals to polynomial over p-adic field 
			prtoppf(r,P,p,d) 
polynomial              over rationals to univariate dense polynomial over 
			p-adic field udprtoudppf(P,p,d) univariate dense 
polynomial              over rationals translation, all variables 
			(rekursiv) prtransav(r,P,LR) 
polynomial              over rationals translation, main variable 
			prtrans(r,P,A) 
polynomial              over rationals udpitoudpr(P) univariate polynomial 
			over integers to univariate 
polynomial              over rationals vecprtvpmpr(r,V,P) vector of 
			polynomials over rationals to vector of polynomials 
			modulo 
polynomial              over rationals with total degree ordering 
			diprlototdo(r,P) distributive polynomial over 
			rationals in lexicographical order to distributive 
polynomial              over rationals, rational number product (rekursiv) 
			prrprod(r,P,A) 
polynomial              over rationals, rational number product 
			diprrprod(r,P,A) distributive 
polynomial              over rationals, rational number product 
			udprrprod(P,A) univariate dense 
polynomial              over rationals, rational quotient prrquot(r,P,A) 
polynomial              over rationals? (rekursiv) isdpr(r,P) is dense 
polynomial              over the integers approximation of p-adic 
			factorization of the defining polynomial, 
			generators of p-maximal orders of the p-adic 
			divisors of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable 
polynomial              over the integers basis of a local maximal 
			over-order ouspibaslmo(F,p,Q,pk) order of an 
			univariate separable 
polynomial              over the integers basis of a local maximal 
			over-order with respect to integer primes 
			ouspibaslmoi(F,P,Q,pk) order of an univariate 
			separable 
polynomial              over the integers basis of the integral closure ( 
			ORDMAX, Ordmax, ordmax, integral basis ) 
			ouspibasisic(F,pL) order of an univariate separable 
polynomial              over the integers factorization 
			rdiscupifact(rd,c,pL) reduced discriminant and 
			discriminant of an univariate 
polynomial              over the integers from special coefficient list 
			upifscl(L) univariate 
polynomial              over the integers normelpruspi(P,a) norm of an 
			element of the polynomial ring of an univariate 
			separable 
polynomial              over the integers number field element evaluation 
			special upinfeevals(F,P,a) univariate 
polynomial              over the integers rational transformation 
			pirtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) 
polynomial              over the integers reduced discriminant and content 
			of resultant equation upireddiscc(P,pc) univariate 
polynomial              over the integers resultant and cofactor of 
			resultant equation upiresulc(P1,P2,pB) univariate 
polynomial              over the integers resultant, Collins algorithm 
			special pirescspec(r,P1,P2,n) 
polynomial              over the integers sclfupi(P,n) special coefficient 
			list from univariate 
polynomial              over the integers to polynomial over a number field 
			(rekursiv) pitopnf(r,P) 
polynomial              over the integers transformation 
			pitransf(r1,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over the integers vepvelpruspi(F,a,p,k,v) values of 
			the extensions of the p-adic valuation of an 
			element of the polynomial ring of an univariate 
			separable 
polynomial              over the integers, Dedekind maximality test 
			oupidedekmt(M,P) order of an univariate 
polynomial              over the integers, Hensel lemma factorization 
			approximation upihlfa(p,P,L,k) univariate 
polynomial              over the integers, approximation of p-adic 
			factorization uspiapf(p,P,k) univariate separable 
polynomial              over the polynomial ring over modular single prime, 
			transcendence degree 1 nepousppmsp1(p,F,a) norm of 
			an element of the polynomial order of an univariate 
			separable 
polynomial              over the polynomial ring over modular single prime, 
			transcendence degree 1 vepepuspmsp1(p,F,a,P,k,v) 
			values of the extensions of the P-adic valuation of 
			an element of the polynomial order of a univariate 
			separable 
polynomial              over the polynomial ring over modular single prime, 
			transcendence degree 1, integral basis 
			ouspprmsp1ib(p,F,pL) order of an univariate 
			separable 
polynomial              over the rationals Z-module homomorphism 
			cdprzmodhom(P,M) common denominator 
polynomial              over the rationals cdprfupr(P) common denominator 
			polynomial over the rationals from univariate 
polynomial              over the rationals clfcdpr(P,n) coefficient list 
			from common denominator 
polynomial              over the rationals from coefficient list cdprfcl(L) 
			common denominator 
polynomial              over the rationals from common denominator 
			polynomial over the rationals uprfcdpr(PC) 
			univariate 
polynomial              over the rationals from univariate polynomial over 
			the rationals cdprfupr(P) common denominator 
polynomial              over the rationals integer quotient cdpriquot(P,I) 
			common denominator 
polynomial              over the rationals inverse cdprinv(F,A) common 
			denominator 
polynomial              over the rationals list from common denominator 
			matrix of rationals cdprlfcdmar(M) common 
			denominator 
polynomial              over the rationals numerator and denominator 
			prnumden(r,P,pA) 
polynomial              over the rationals rational transformation 
			prrtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) 
polynomial              over the rationals sum cdprsum(P1,P2) common 
			denominator 
polynomial              over the rationals to rational function over the 
			rationals prtorfr(r,P) 
polynomial              over the rationals transformation 
			prtransf(r1,P1,V1,r2,P2,V2,Vn,pV3) 
polynomial              over the rationals uprfcdpr(PC) univariate 
			polynomial over the rationals from common 
			denominator 
polynomial              product by power of main variable ppmvprod(r,P,n) 
polynomial              ptoup(r,P) polynomial to univariate 
polynomial              quotient by power of main variable ppmvquot(r,P,n) 
polynomial              quotient by power of variable (rekursiv) 
			ppvquot(r,P,i,n) 
polynomial              reductum dpred(r,P) dense 
polynomial              reductum pred(r,P) (MACRO) 
polynomial              remainder pgf2expprem(r,G,F,E,M) polynomial over 
			Galois-field with characteristic 2, exponentiation, 
polynomial              remainder pgfsexpprem(r,p,AL,F,E,M) polynomial over 
			Galois-field with single characteristic, 
			exponentiation, 
polynomial              ring of an univariate separable polynomial over the 
			integers normelpruspi(P,a) norm of an element of 
			the 
polynomial              ring of an univariate separable polynomial over the 
			integers vepvelpruspi(F,a,p,k,v) values of the 
			extensions of the p-adic valuation of an element of 
			the 
polynomial              ring over modular single prime, transcendence 
			degree 1 nepousppmsp1(p,F,a) norm of an element of 
			the polynomial order of an univariate separable 
			polynomial over the 
polynomial              ring over modular single prime, transcendence 
			degree 1 vepepuspmsp1(p,F,a,P,k,v) values of the 
			extensions of the P-adic valuation of an element of 
			the polynomial order of a univariate separable 
			polynomial over the 
polynomial              ring over modular single prime, transcendence 
			degree 1, Dedekind maximality test 
			ouspprmsp1dm(p,P,F) order of an univariate 
			separable polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, Hensel factorization approximation 
			upprmsp1hfa(p,F,P,L,k) univariate polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, Hensel lemma initialization 
			upprmsp1hli(p,F,P,L) univariate polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, Hensel quadratic step 
			upprmsp1hqs(p,F,T,L1,L2,A) univariate polynomial 
			over 
polynomial              ring over modular single prime, transcendence 
			degree 1, algebraic function over modular single 
			prime, transcendence degree 1, evaluation special 
			upprmsp1afes(p,F,P,a) univariate polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, approximation of P-adic factorization 
			uspprmsp1apf(p,P,F,k) univariate separable 
			polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, basis from generators oprmsp1basfg(p,F,L) 
			order over 
polynomial              ring over modular single prime, transcendence 
			degree 1, basis of a local maximal over-order 
			ouspprmsp1bl(p,F,P,Q,pk) order of an univariate 
			separable polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, decomposition law ouspprmsp1dl(p,F,P,k) 
			order of a univariate separable polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, discriminant upprmsp1disc(p,F) univariate 
			polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, integral basis ouspprmsp1ib(p,F,pL) order 
			of an univariate separable polynomial over the 
polynomial              ring over modular single prime, transcendence 
			degree 1, reduced discriminant upprmsp1redd(p,F) 
			univariate polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, resultant, Sylvester algorithm 
			pprmsp1ress(r,p,P1,P2) polynomial over 
polynomial              ring over modular single prime, transcendence 
			degree 1, resultant, Sylvester algorithm 
			upprmsp1ress(p,P1,P2) univariate polynomial over 
polynomial              ring over modular single primes, transcendence 
			degree 1, element test modprmsp1elt(B,p,a) module 
			over 
polynomial              special 
			machpolspec(M,det,minusEins,anzahlargs,arg1,...,arg5) 
			matrix characteristic 
polynomial              to dense polynomial (rekursiv) ptodp(r,P) 
polynomial              to distributive polynomial (rekursiv) ptodip(r,P) 
polynomial              to polynomial (rekursiv) diptop(r,P) distributive 
polynomial              to polynomial (rekursiv) dptop(r,P) dense 
polynomial              to univariate polynomial ptoup(r,P) 
polynomial              total degree diptdg(r,P) distributive 
polynomial              trailing base coefficient (rekursiv) ptbc(r,P) 
polynomial              trailing base coefficient udptbc(P) univariate 
			dense 
polynomial              variable list extension pvext(r,P,V,VN) 
polynomial              variable list merge pvmerge(LV,LP,pLP) 
polynomial              variable permutation pvpermut(r,P,PI) 
polynomial              variables pvred(r,P,V,pV) reduction of 
polynomial              with respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and factorization of the 
			defining polynomial or the minimal 
polynomial,             Collins algorithm, version1 nfespecmpc1(F,a) number 
			field element special minimal 
polynomial,             Collins algorithm, version2 nfespecmpc2(F,a) number 
			field element special minimal 
polynomial,             generators of p-maximal orders of the p-adic 
			divisors of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate separable polynomial over 
			the integers approximation of p-adic factorization 
			of the defining 
polynomial,             remainder upgf22pvprem(G,m,P) univariate polynomial 
			over Galois-field with characteristic 2, 2^m-th 
			power of variable, 
polynomial,             remainder upgf2mprem(G,a,T,P) univariate polynomial 
			over Galois-field with characteristic 2, monomial, 
polynomial,             remainder upgfsmieprem(p,AL,a,t,P) univariate 
			polynomial over Galois-field, monomial, integer 
			exponentiation, 
polynomial,             remainder upgfsmprem(p,AL,a,T,P) univariate 
			polynomial over Galois-field, monomial, 
polynomial,             remainder upmimprem(ip,K,E,P) univariate polynomial 
			over modular integers, monomial, 
polynomial,             remainder upmsmprem(m,k,T,P) univariate polynomial 
			over modular singles, monomial, 
polynomials             ? ismadp(r,M) (MACRO) is matrix of dense 
polynomials             ? ismap(r,M) (MACRO) is matrix of 
polynomials             ? isvecdp(r,V) (MACRO) is vector of dense 
polynomials             ? isvecp(r,V) (MACRO) is vector of 
polynomials             bubble sort, special lpbsorts(r,L) list of 
polynomials             construction upgf2bqp(G,P) univariate polynomial 
			over Galois-field with characteristic 2 Berlekamp Q 
polynomials             construction upgfsbqp(p,AL,P) univariate polynomial 
			over Galois-field with single characteristic 
			Berlekamp Q 
polynomials             construction upmibqp(ip,P) univariate polynomial 
			over modular integers, Berlekamp Q 
polynomials             construction upmsbqp(p,A) univariate polynomial 
			over modular singles, Berlekamp Q 
polynomials             ecgf2cdivp(G,a6,m) elliptic curve over Galois-field 
			with characteristic 2, construction of division 
polynomials             ecmpsnfcdivp(P,a4,a6,n) elliptic curve over modular 
			primes, short normal form, construction of division 
polynomials             macup(n,L) matrix of coefficients of univariate 
polynomials             madptomap(r,M) matrix of dense polynomials to 
			matrix of 
polynomials             maptomadp(r,M) matrix of polynomials to matrix of 
			dense 
polynomials             maptomaup(r,M) matrix of polynomials to matrix of 
			univariate 
polynomials             modulo polynomial over Galois-field with single 
			characteristic mpgfstompmp(r,p,AL,P,M) matrix of 
			polynomials over Galois-field with single 
			characteristic to matrix of 
polynomials             modulo polynomial over Galois-field with single 
			characteristic vpgfstovpmp(r,p,AL,P,V) vector of 
			polynomials over Galois-field with single 
			characteristic to vector of 
polynomials             modulo polynomial over integers mapitompmpi(r,M,P) 
			matrix of polynomials over integers to matrix of 
polynomials             modulo polynomial over integers vecpitvpmpi(r,V,P) 
			vector of polynomials over integers to vector of 
polynomials             modulo polynomial over modular integers 
			mapmitomapmp(r,m,P,M) matrix of polynomials over 
			modular integers to matrix of 
polynomials             modulo polynomial over modular integers 
			vecpmitovpmp(r,m,P,V) vector of polynomials over 
			modular integers to vector of 
polynomials             modulo polynomial over modular singles 
			mapmstomapmp(r,m,P,M) matrix of polynomials over 
			modular singles to matrix of 
polynomials             modulo polynomial over modular singles 
			vecpmstovpmp(r,m,P,V) vector of polynomials over 
			modular singles to vector of 
polynomials             modulo polynomial over number field 
			mapnftomapmp(r,F,P,M) matrix of polynomials over 
			number field to matrix of 
polynomials             modulo polynomial over number field 
			vecpnftovpmp(r,F,P,V) vector of polynomials over 
			number field to vector of 
polynomials             modulo polynomial over rationals maprtompmpr(r,M,P) 
			matrix of polynomials over rationals to matrix of 
polynomials             modulo polynomial over rationals vecprtvpmpr(r,V,P) 
			vector of polynomials over rationals to vector of 
polynomials             of the generators ouspiapfgmic(p,P,k) order of an 
			univariate separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal orders 
			of the p-adic divisors of the defining polynomial 
			and p-minimal 
polynomials             over Galois-field with single characteristic ? 
			ismapgfs(r,p,AL,M) (MACRO) is matrix of 
polynomials             over Galois-field with single characteristic ? 
			isvecpgfs(r,p,AL,V) (MACRO) is vector of 
polynomials             over Galois-field with single characteristic 
			characteristic polynomial mapgfschpol(r,p,AL,M) 
			(MACRO) matrix of 
polynomials             over Galois-field with single characteristic 
			construction 1 mapgfscons1(r,p,AL,n) (MACRO) matrix 
			of 
polynomials             over Galois-field with single characteristic 
			determinant mapgfsdet(r,p,AL,M) matrix of 
polynomials             over Galois-field with single characteristic 
			difference mapgfsdif(r,p,AL,M,N) (MACRO) matrix of 
polynomials             over Galois-field with single characteristic 
			difference vecpgfsdif(r,p,AL,U,V) (MACRO) vector of 
polynomials             over Galois-field with single characteristic 
			embedding in field extension mapgfsefe(r,p,ALm,M,g) 
			matrix over 
polynomials             over Galois-field with single characteristic 
			embedding in field extension 
			vecpgfsefe(r,p,ALm,V,g) vector over 
polynomials             over Galois-field with single characteristic 
			exponentiation mapgfsexp(r,p,AL,M,n) matrix of 
polynomials             over Galois-field with single characteristic 
			fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get 
			matrix of 
polynomials             over Galois-field with single characteristic 
			fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) file get vector 
			of 
polynomials             over Galois-field with single characteristic 
			fputmapgfs(r,p,AL,M,V,Vgfs,pf) (MACRO) file put 
			matrix of 
polynomials             over Galois-field with single characteristic 
			fputvpgfs(r,p,AL,W,V,Vgfs,pf) (MACRO) file put 
			vector of 
polynomials             over Galois-field with single characteristic 
			getmapgfs(r,p,AL,V,Vgfs) (MACRO) get matrix of 
polynomials             over Galois-field with single characteristic 
			getvpgfs(r,p,AL,V,Vgfs) (MACRO) get vector of 
polynomials             over Galois-field with single characteristic 
			inverse mapgfsinv(r,p,AL,M) matrix of 
polynomials             over Galois-field with single characteristic linear 
			combination vecpgfslc(r,p,AL,s1,s2,L1,L2) vector of 
polynomials             over Galois-field with single characteristic 
			mpmstompgfs(r,p,M) matrix of polynomials over 
			modular singles to matrix of 
polynomials             over Galois-field with single characteristic 
			negation mapgfsneg(r,p,AL,M) (MACRO) matrix of 
polynomials             over Galois-field with single characteristic 
			negation vecpgfsneg(r,p,AL,V) (MACRO) vector of 
polynomials             over Galois-field with single characteristic 
			product mapgfsprod(r,p,AL,M,N) (MACRO) matrix of 
polynomials             over Galois-field with single characteristic 
			putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) put matrix of 
polynomials             over Galois-field with single characteristic 
			putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) put vector of 
polynomials             over Galois-field with single characteristic scalar 
			multiplication mapgfssmul(r,p,AL,M,el) matrix of 
polynomials             over Galois-field with single characteristic scalar 
			multiplication vecpgfssmul(r,p,AL,V,el) vector of 
polynomials             over Galois-field with single characteristic scalar 
			product vpgfssprod(r,p,AL,V,W) vector of 
polynomials             over Galois-field with single characteristic sum 
			mapgfssum(r,p,AL,M,N) (MACRO) matrix of 
polynomials             over Galois-field with single characteristic sum 
			vecpgfssum(r,p,AL,U,V) (MACRO) vector of 
polynomials             over Galois-field with single characteristic to 
			matrix of polynomials modulo polynomial over 
			Galois-field with single characteristic 
			mpgfstompmp(r,p,AL,P,M) matrix of 
polynomials             over Galois-field with single characteristic to 
			vector of polynomials modulo polynomial over 
			Galois-field with single characteristic 
			vpgfstovpmp(r,p,AL,P,V) vector of 
polynomials             over Galois-field with single characteristic 
			transformation 
			mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) matrix 
			of 
polynomials             over Galois-field with single characteristic 
			transformation 
			vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) vector 
			of 
polynomials             over Galois-field with single characteristic vector 
			multiplication mapgfsvmul(r,p,AL,A,x) (MACRO) 
			matrix of 
polynomials             over Galois-field with single characteristic 
			vpmstovpgfs(r,p,V) vector of polynomials over 
			modular singles to vector of 
polynomials             over integers ? ismadpi(r,M) (MACRO) is matrix of 
			dense 
polynomials             over integers ? ismapi(r,M) (MACRO) is matrix of 
polynomials             over integers ? isvecdpi(r,V) (MACRO) is vector of 
			dense 
polynomials             over integers ? isvecpi(r,V) (MACRO) is vector of 
polynomials             over integers Galois-field with single 
			characteristic element evaluation first variable 
			special version mapigfsevfvs(r,p,AL,M) matrix over 
polynomials             over integers Galois-field with single 
			characteristic element evaluation first variable 
			special version vecpigfsefvs(r,p,AL,V) vector over 
polynomials             over integers Groebner basis augmentation 
			dippigba(r1,r2,PL,P) distributive polynomial over 
polynomials             over integers Groebner basis dippigb(r1,r2,PL) 
			distributive polynomial over 
polynomials             over integers Groebner basis recursion 
			dippigbr(r1,r2,PL) distributive polynomial over 
polynomials             over integers Groebner system 
			fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file put 
			distributive polynomial over 
polynomials             over integers Groebner system 
			putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) put 
			distributive polynomial over 
polynomials             over integers Groebner test 
			dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) distributive 
			polynomial over 
polynomials             over integers Groebner test 
			fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) file 
			put distributive polynomial over 
polynomials             over integers Groebner test 
			putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) (MACRO) 
			put distributive polynomial over 
polynomials             over integers S-polynomial dippisp(r1,r2,P1,P2) 
			distributive polynomial over 
polynomials             over integers case distinction 
			fgetdippicd(r1,r2,VL1,VL2,fac,pf) file get 
			distributive polynomial over 
polynomials             over integers case distinction 
			getdippicd(r1,r2,VL1,VL2,fac) (MACRO) get 
			distributive polynomial over 
polynomials             over integers characteristic polynomial 
			mapichpol(r,M) (MACRO) matrix of 
polynomials             over integers comprehensive Groebner basis 
			dippicgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over 
polynomials             over integers comprehensive Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file put 
			distributive polynomial over 
polynomials             over integers comprehensive Groebner basis 
			putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) put 
			distributive polynomial over 
polynomials             over integers construction 1 mapicons1(r,n) (MACRO) 
			matrix of 
polynomials             over integers content and primitive part 
			dippicp(r1,r2,P,pPP) distributive polynomial over 
polynomials             over integers determinant mapidet(r,M) matrix of 
polynomials             over integers difference dippidif(r1,r2,P1,P2) 
			distributive polynomial over 
polynomials             over integers difference mapidif(r,M,N) (MACRO) 
			matrix of 
polynomials             over integers difference vecpidif(r,U,V) (MACRO) 
			vector of 
polynomials             over integers dimension 
			dippidim(r1,r2,s,PL,CONDS,fac,VL1,VL2,pf) 
			distributive polynomial over 
polynomials             over integers dimension 
			fputdippidim(r1,r2,DIML,VL1,VL2,pf) file put 
			distributive polynomial over 
polynomials             over integers dimension 
			putdippidim(r1,r2,DIML,VL1,VL2) (MACRO) put 
			distributive polynomial over 
polynomials             over integers exponentiation mapiexp(r,M,n) matrix 
			of 
polynomials             over integers fgetmapi(r,V,pf) (MACRO) file get 
			matrix of 
polynomials             over integers fgetvecpi(r,VL,pf) (MACRO) file get 
			vector of 
polynomials             over integers fputlpi(r,L,V,pf) file put list of 
polynomials             over integers fputmapi(r,M,V,pf) (MACRO) file put 
			matrix of 
polynomials             over integers fputvecpi(r,V,VL,pf) (MACRO) file put 
			vector of 
polynomials             over integers getmapi(r,V) (MACRO) get matrix of 
polynomials             over integers getvecpi(r,VL) (MACRO) get vector of 
polynomials             over integers in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over 
polynomials             over integers in lexicographical order to 
			distributive polynomial over polynomials over 
			integers in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
polynomials             over integers in lexicographical order to 
			distributive polynomial over polynomials over 
			integers in lexicographical order with inverse 
			exponent vector dippilotolio(r1,r2,P) distributive 
			polynomial over 
polynomials             over integers in lexicographical order to 
			distributive polynomial over polynomials over 
			integers with total degree ordering 
			dippilototdo(r1,r2,P) distributive polynomial over 
polynomials             over integers in lexicographical order with inverse 
			exponent vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over 
polynomials             over integers inverse mapiinv(r,M) matrix of 
polynomials             over integers linear combination 
			vecpilc(r,P1,P2,V1,V2) vector of 
polynomials             over integers list fgetdippil(r1,r2,VL1,VL2,pf) 
			file get distributive polynomial over 
polynomials             over integers list fputdippil(r1,r2,PL,VL1,VL2,pf) 
			file put distributive polynomial over 
polynomials             over integers list getdippil(r1,r2,VL1,VL2) (MACRO) 
			get distributive polynomial over 
polynomials             over integers list putdippil(r1,r2,PL,VL1,VL2) 
			(MACRO) put distributive polynomial over 
polynomials             over integers maitomapi(r,M) matrix of integers to 
			matrix of 
polynomials             over integers negation dippineg(r1,r2,P) 
			distributive polynomial over 
polynomials             over integers negation mapineg(r,M) (MACRO) matrix 
			of 
polynomials             over integers negation vecpineg(r,V) (MACRO) vector 
			of 
polynomials             over integers number field element evaluation first 
			variable special version mapinfevlfvs(r,F,M) matrix 
			of 
polynomials             over integers number field element evaluation first 
			variable special version vpinfevalfvs(r,F,V) vector 
			of 
polynomials             over integers one ? isdippione(r1,r2,P) is 
			distributive polynomial over 
polynomials             over integers parametric ideal membership test 
			dippipim(r1,r2,s,PL,PTL,CONDS,OPL) distributive 
			polynomial over 
polynomials             over integers parametric ideal membership test 
			fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put 
			distributive polynomial over 
polynomials             over integers parametric ideal membership test 
			putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put 
			distributive polynomial over 
polynomials             over integers product dippiprod(r1,r2,P1,P2) 
			distributive polynomial over 
polynomials             over integers product mapiprod(r,M,N) (MACRO) 
			matrix of 
polynomials             over integers putmapi(r,M,V) (MACRO) put matrix of 
polynomials             over integers putvecpi(r,V,VL) (MACRO) put vector 
			of 
polynomials             over integers quantifier free formula 
			dippiqff(r1,r2,s,PL,CONDS,fac) distributive 
			polynomial over 
polynomials             over integers quantifier free formula 
			fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file put 
			distributive polynomial over 
polynomials             over integers quantifier free formula 
			putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put 
			distributive polynomial over 
polynomials             over integers reduced comprehensive Groebner basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over 
polynomials             over integers scalar multiplication mapismul(r,M,P) 
			matrix of 
polynomials             over integers scalar multiplication 
			vecpismul(r,P,V) vector of 
polynomials             over integers scalar product vecpisprod(r,V,W) 
			vector of 
polynomials             over integers sum dippisum(r1,r2,P1,P2) 
			distributive polynomial over 
polynomials             over integers sum mapisum(r,M,N) (MACRO) matrix of 
polynomials             over integers sum vecpisum(r,U,V) (MACRO) vector of 
polynomials             over integers to matrix of polynomials modulo 
			polynomial over integers mapitompmpi(r,M,P) matrix 
			of 
polynomials             over integers to matrix of polynomials over modular 
			integers mapitomapmi(r,M,m) matrix of 
polynomials             over integers to matrix of polynomials over modular 
			singles mapitomapms(r,M,m) matrix of 
polynomials             over integers to matrix of polynomials over number 
			field mapitomapnf(r,M) matrix of 
polynomials             over integers to matrix of rational functions over 
			rationals mapitomarfr(r,M) matrix of 
polynomials             over integers to matrix of univariate dense 
			polynomials over modular integers mudpitudpmi(M,m) 
			matrix of univariate dense 
polynomials             over integers to matrix of univariate dense 
			polynomials over rationals mudpitmudpr(M) matrix of 
			univariate dense 
polynomials             over integers to vector of polynomials modulo 
			polynomial over integers vecpitvpmpi(r,V,P) vector 
			of 
polynomials             over integers to vector of polynomials over modular 
			integers vecpitovpmi(r,V,m) vector of 
polynomials             over integers to vector of polynomials over modular 
			singles vecpitovpms(r,V,m) vector of 
polynomials             over integers to vector of polynomials over number 
			field vecpitovpnf(r,V) vector of 
polynomials             over integers to vector of polynomials over 
			rationals vecpitovpr(V) vector of 
polynomials             over integers to vector of rational functions over 
			rationals vecpitovrfr(r,V) vector of 
polynomials             over integers to vector of univariate dense 
			polynomials over modular integers vudpitudpmi(V,M) 
			vector of univariate dense 
polynomials             over integers to vector of univariate dense 
			polynomials over rationals vudpitvudpr(V) vector of 
			univariate dense 
polynomials             over integers vecitovecpi(r,V) vector of integers 
			to vector of 
polynomials             over integers vector multiplication 
			mapivecmul(r,A,x) (MACRO) matrix of 
polynomials             over integers with total degree ordering 
			dippilototdo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over 
polynomials             over integers, polynomial over integers product 
			dippipiprod(r1,r2,P,A) distributive polynomial over 
polynomials             over modular integer primes Euklid- Gauss- step for 
			columns maupmipegsc(p,M,A,B) matrix of univariate 
polynomials             over modular integer primes Euklid- Gauss- step for 
			rows maupmipegsr(p,M,A,B) matrix of univariate 
polynomials             over modular integer primes elementary divisor form 
			and cofactors maupmipedfcf(p,M,pA,pB) matrix of 
			univariate 
polynomials             over modular integers ? ismapmi(r,m,M) (MACRO) is 
			matrix of 
polynomials             over modular integers characteristic polynomial 
			mapmichpol(r,m,M) (MACRO) matrix of 
polynomials             over modular integers construction 1 
			mapmicons1(r,m,n) (MACRO) matrix of 
polynomials             over modular integers determinant mapmidet(r,m,M) 
			matrix of 
polynomials             over modular integers difference mapmidif(r,m,M,N) 
			(MACRO) matrix of 
polynomials             over modular integers difference vecpmidif(r,m,U,V) 
			(MACRO) vector of 
polynomials             over modular integers exponentiation 
			mapmiexp(r,m,M,n) matrix of 
polynomials             over modular integers fgetmapmi(r,m,V,pf) (MACRO) 
			file get matrix of 
polynomials             over modular integers fgetvecpmi(r,m,VL,pf) (MACRO) 
			file get vector of 
polynomials             over modular integers fputmapmi(r,m,M,V,pf) (MACRO) 
			file put matrix of 
polynomials             over modular integers fputvecpmi(r,m,V,VL,pf) 
			(MACRO) file put vector of 
polynomials             over modular integers getmapmi(r,m,V) (MACRO) get 
			matrix of 
polynomials             over modular integers getvecpmi(r,m,VL) (MACRO) get 
			vector of 
polynomials             over modular integers inverse mapmiinv(r,m,M) 
			matrix of 
polynomials             over modular integers linear combination 
			vecpmilc(r,m,P1,P2,V1,V2) vector of 
polynomials             over modular integers mapitomapmi(r,M,m) matrix of 
			polynomials over integers to matrix of 
polynomials             over modular integers maprtomapmi(r,M,m) matrix of 
			polynomials over rationals to matrix of 
polynomials             over modular integers mudpitudpmi(M,m) matrix of 
			univariate dense polynomials over integers to 
			matrix of univariate dense 
polynomials             over modular integers negation mapmineg(r,m,M) 
			(MACRO) matrix of 
polynomials             over modular integers negation vecpmineg(r,m,V) 
			(MACRO) vector of 
polynomials             over modular integers product mapmiprod(r,m,M,N) 
			(MACRO) matrix of 
polynomials             over modular integers putmapmi(r,m,M,V) (MACRO) put 
			matrix of 
polynomials             over modular integers putvecpmi(r,m,V,VL) (MACRO) 
			put vector of 
polynomials             over modular integers scalar multiplication 
			mapmismul(r,m,M,P) matrix of 
polynomials             over modular integers scalar multiplication 
			vecpmismul(r,m,P,V) vector of 
polynomials             over modular integers scalar product 
			vecpmisprod(r,m,V,W) vector of 
polynomials             over modular integers sum mapmisum(r,m,M,N) (MACRO) 
			matrix of 
polynomials             over modular integers sum vecpmisum(r,m,U,V) 
			(MACRO) vector of 
polynomials             over modular integers to matrix of polynomials 
			modulo polynomial over modular integers 
			mapmitomapmp(r,m,P,M) matrix of 
polynomials             over modular integers to vector of polynomials 
			modulo polynomial over modular integers 
			vecpmitovpmp(r,m,P,V) vector of 
polynomials             over modular integers transformation 
			mapmitransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
polynomials             over modular integers transformation 
			vpmitransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
polynomials             over modular integers vecpitovpmi(r,V,m) vector of 
			polynomials over integers to vector of 
polynomials             over modular integers vecprtovpmi(r,V,m) vector of 
			polynomials over rationals to vector of 
polynomials             over modular integers vector multiplication 
			mapmivecmul(r,m,A,x) (MACRO) matrix of 
polynomials             over modular integers vudpitudpmi(V,M) vector of 
			univariate dense polynomials over integers to 
			vector of univariate dense 
polynomials             over modular single prime unimodular transformation 
			vecupmsunimt(p,V,W,i,pV1,pW1) vector of univariate 
polynomials             over modular single primes Euklid- Gauss- step for 
			columns maupmspegsc(p,M,A,B) matrix of univariate 
polynomials             over modular single primes Euklid- Gauss- step for 
			rows maupmspegsr(p,M,A,B) matrix of univariate 
polynomials             over modular single primes elementary divisor form 
			and cofactors maupmspedfcf(p,M,pA,pB) matrix of 
			univariate 
polynomials             over modular single primes hermitian reduction, 
			special maupmshermsp(p,M,r,pD) matrix of univariate 
polynomials             over modular singles ? ismadpms(r,m,M) (MACRO) is 
			matrix of dense 
polynomials             over modular singles ? ismapms(r,m,M) (MACRO) is 
			matrix of 
polynomials             over modular singles ? isvecdpms(r,m,V) (MACRO) is 
			vector of dense 
polynomials             over modular singles ? isvecpms(r,m,V) (MACRO) is 
			vector of 
polynomials             over modular singles characteristic polynomial 
			mapmschpol(r,m,M) (MACRO) matrix of 
polynomials             over modular singles construction 1 
			mapmscons1(r,m,n) (MACRO) matrix of 
polynomials             over modular singles determinant mapmsdet(r,m,M) 
			matrix of 
polynomials             over modular singles difference mapmsdif(r,m,M,N) 
			(MACRO) matrix of 
polynomials             over modular singles difference vecpmsdif(r,m,U,V) 
			(MACRO) vector of 
polynomials             over modular singles exponentiation 
			mapmsexp(r,m,M,n) matrix of 
polynomials             over modular singles fgetmapms(r,m,V,pf) (MACRO) 
			file get matrix of 
polynomials             over modular singles fgetvecpms(r,m,VL,pf) (MACRO) 
			file get vector of 
polynomials             over modular singles fputmapms(r,m,M,V,pf) (MACRO) 
			file put matrix of 
polynomials             over modular singles fputvecpms(r,m,V,VL,pf) 
			(MACRO) file put vector of 
polynomials             over modular singles getmapms(r,m,V) (MACRO) get 
			matrix of 
polynomials             over modular singles getvecpms(r,m,VL) (MACRO) get 
			vector of 
polynomials             over modular singles inverse mapmsinv(r,m,M) matrix 
			of 
polynomials             over modular singles linear combination 
			vecpmslc(r,m,P1,P2,V1,V2) vector of 
polynomials             over modular singles mapitomapms(r,M,m) matrix of 
			polynomials over integers to matrix of 
polynomials             over modular singles negation mapmsneg(r,m,M) 
			(MACRO) matrix of 
polynomials             over modular singles negation vecpmsneg(r,m,V) 
			(MACRO) vector of 
polynomials             over modular singles product mapmsprod(r,m,M,N) 
			(MACRO) matrix of 
polynomials             over modular singles putmapms(r,m,M,V) (MACRO) put 
			matrix of 
polynomials             over modular singles putvecpms(r,m,V,VL) (MACRO) 
			put vector of 
polynomials             over modular singles scalar multiplication 
			mapmssmul(r,m,M,P) matrix of 
polynomials             over modular singles scalar multiplication 
			vecpmssmul(r,m,P,V) vector of 
polynomials             over modular singles scalar product 
			vecpmssprod(r,m,V,W) vector of 
polynomials             over modular singles sum mapmssum(r,m,M,N) (MACRO) 
			matrix of 
polynomials             over modular singles sum vecpmssum(r,m,U,V) (MACRO) 
			vector of 
polynomials             over modular singles to matrix of polynomials 
			modulo polynomial over modular singles 
			mapmstomapmp(r,m,P,M) matrix of 
polynomials             over modular singles to matrix of polynomials over 
			Galois-field with single characteristic 
			mpmstompgfs(r,p,M) matrix of 
polynomials             over modular singles to matrix of rational 
			functions over modular single primes, transcendence 
			degree 1 mpmstmrfmsp1(p,M) matrix of 
polynomials             over modular singles to vector of polynomials 
			modulo polynomial over modular singles 
			vecpmstovpmp(r,m,P,V) vector of 
polynomials             over modular singles to vector of polynomials over 
			Galois-field with single characteristic 
			vpmstovpgfs(r,p,V) vector of 
polynomials             over modular singles to vector of rational 
			functions over modular single primes, transcendence 
			degree 1 vpmstvrfmsp1(p,V) vector of 
polynomials             over modular singles transformation 
			mapmstransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
polynomials             over modular singles transformation 
			vpmstransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
polynomials             over modular singles vecpitovpms(r,V,m) vector of 
			polynomials over integers to vector of 
polynomials             over modular singles vector multiplication 
			mapmsvecmul(r,m,A,x) (MACRO) matrix of 
polynomials             over number field characteristic polynomial 
			mapnfchpol(r,F,M) (MACRO) matrix of 
polynomials             over number field construction 1 mapnfcons1(r,F,n) 
			(MACRO) matrix of 
polynomials             over number field determinant mapnfdet(r,F,M) 
			matrix of 
polynomials             over number field difference mapnfdif(r,F,M,N) 
			(MACRO) matrix of 
polynomials             over number field difference vecpnfdif(r,F,U,V) 
			(MACRO) vector of 
polynomials             over number field exponentiation mapnfexp(r,F,M,n) 
			matrix of 
polynomials             over number field fgetmapnf(r,F,V,Vnf,pf) (MACRO) 
			file get matrix of 
polynomials             over number field fgetvecpnf(r,F,VL,VLnf,pf) 
			(MACRO) file get vector of 
polynomials             over number field fputmapnf(r,F,M,V,Vnf,pf) (MACRO) 
			file put matrix of 
polynomials             over number field fputvecpnf(r,F,W,VL,VLnf,pf) 
			(MACRO) file put vector of 
polynomials             over number field getmapnf(r,F,V,Vnf) (MACRO) get 
			matrix of 
polynomials             over number field getvecpnf(r,F,VL,VLnf) (MACRO) 
			get vector of 
polynomials             over number field inverse mapnfinv(r,F,M) matrix of 
polynomials             over number field linear combination 
			vecpnflc(r,F,s1,s2,L1,L2) vector of 
polynomials             over number field mapitomapnf(r,M) matrix of 
			polynomials over integers to matrix of 
polynomials             over number field maprtomapnf(r,M) matrix of 
			polynomials over rationals to matrix of 
polynomials             over number field negation mapnfneg(r,F,M) (MACRO) 
			matrix of 
polynomials             over number field negation vecpnfneg(r,F,U) (MACRO) 
			vector of 
polynomials             over number field product mapnfprod(r,F,M,N) 
			(MACRO) matrix of 
polynomials             over number field putmapnf(r,F,M,V,Vnf) (MACRO) put 
			matrix of 
polynomials             over number field putvecpnf(r,F,W,VL,VLnf) (MACRO) 
			put vector of 
polynomials             over number field scalar multiplication 
			mapnfsmul(r,F,M,el) matrix of 
polynomials             over number field scalar multiplication 
			vecpnfsmul(r,F,U,el) vector of 
polynomials             over number field scalar product vpnfsprod(r,F,V,W) 
			vector of 
polynomials             over number field sum mapnfsum(r,F,M,N) (MACRO) 
			matrix of 
polynomials             over number field sum vecpnfsum(r,F,U,V) (MACRO) 
			vector of 
polynomials             over number field to matrix of polynomials modulo 
			polynomial over number field mapnftomapmp(r,F,P,M) 
			matrix of 
polynomials             over number field to matrix of polynomials over 
			rationals mapnftomapr(r,M) matrix of 
polynomials             over number field to vector of polynomials modulo 
			polynomial over number field vecpnftovpmp(r,F,P,V) 
			vector of 
polynomials             over number field to vector of polynomials over 
			rationals vecpnftovpr(r,V) vector of 
polynomials             over number field transformation 
			mapnftransf(r1,F,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
polynomials             over number field transformation 
			vpnftransf(r1,F,W1,V1,r2,P2,V2,Vn,pV3) vector of 
polynomials             over number field vecpitovpnf(r,V) vector of 
			polynomials over integers to vector of 
polynomials             over number field vecprtovpnf(r,V) vector of 
			polynomials over rationals to vector of 
polynomials             over number field vector multiplication 
			mapnfvecmul(r,F,A,x) (MACRO) matrix of 
polynomials             over rationals ? ismadpr(r,M) (MACRO) is matrix of 
			dense 
polynomials             over rationals ? ismapr(r,M) (MACRO) is matrix of 
polynomials             over rationals ? isvecdpr(r,V) (MACRO) is vector of 
			dense 
polynomials             over rationals ? isvecpr(r,V) (MACRO) is vector of 
polynomials             over rationals Euklid- Gauss- step for columns 
			maupregsc(M,A,B) matrix of univariate 
polynomials             over rationals Euklid- Gauss- step for rows 
			maupregsr(M,A,B) matrix of univariate 
polynomials             over rationals characteristic polynomial 
			maprchpol(r,M) (MACRO) matrix of 
polynomials             over rationals construction 1 maprcons1(r,n) 
			(MACRO) matrix of 
polynomials             over rationals determinant maprdet(r,M) matrix of 
polynomials             over rationals difference maprdif(r,M,N) (MACRO) 
			matrix of 
polynomials             over rationals difference vecprdif(r,U,V) (MACRO) 
			vector of 
polynomials             over rationals elementary divisor form and 
			cofactors maupredfcf(M,pA,pB) matrix of univariate 
polynomials             over rationals exponentiation maprexp(r,M,n) matrix 
			of 
polynomials             over rationals fgetmapr(r,V,pf) (MACRO) file get 
			matrix of 
polynomials             over rationals fgetvecpr(r,VL,pf) (MACRO) file get 
			vector of 
polynomials             over rationals fputlpr(r,L,V,pf) file put list of 
polynomials             over rationals fputmapr(r,M,V,pf) (MACRO) file put 
			matrix of 
polynomials             over rationals fputvecpr(r,V,VL,pf) (MACRO) file 
			put vector of 
polynomials             over rationals getmapr(r,V) (MACRO) get matrix of 
polynomials             over rationals getvecpr(r,VL) (MACRO) get vector of 
polynomials             over rationals inverse maprinv(r,M) matrix of 
polynomials             over rationals linear combination 
			vecprlc(r,P1,P2,V1,V2) vector of 
polynomials             over rationals manftomudpr(F,M) matrix of number 
			field elements to matrix of univariate dense 
polynomials             over rationals mapnftomapr(r,M) matrix of 
			polynomials over number field to matrix of 
polynomials             over rationals martomapr(r,M) matrix of rationals 
			to matrix of 
polynomials             over rationals mudpitmudpr(M) matrix of univariate 
			dense polynomials over integers to matrix of 
			univariate dense 
polynomials             over rationals negation maprneg(r,M) (MACRO) matrix 
			of 
polynomials             over rationals negation vecprneg(r,V) (MACRO) 
			vector of 
polynomials             over rationals number field element evaluation 
			first variable special version maprnfevlfvs(r,F,M) 
			matrix of 
polynomials             over rationals number field element evaluation 
			first variable special version vprnfevalfvs(r,F,V) 
			vector of 
polynomials             over rationals product maprprod(r,M,N) (MACRO) 
			matrix of 
polynomials             over rationals putmapr(r,M,V) (MACRO) put matrix of 
polynomials             over rationals putvecpr(r,V,VL) (MACRO) put vector 
			of 
polynomials             over rationals scalar multiplication 
			maprsmul(r,M,P) matrix of 
polynomials             over rationals scalar multiplication 
			vecprsmul(r,P,V) vector of 
polynomials             over rationals scalar product vecprsprod(r,V,W) 
			vector of 
polynomials             over rationals sum maprsum(r,M,N) (MACRO) matrix of 
polynomials             over rationals sum vecprsum(r,U,V) (MACRO) vector 
			of 
polynomials             over rationals to matrix of number field elements 
			maudprtomnf(M) matrix of univariate dense 
polynomials             over rationals to matrix of polynomials modulo 
			polynomial over rationals maprtompmpr(r,M,P) matrix 
			of 
polynomials             over rationals to matrix of polynomials over 
			modular integers maprtomapmi(r,M,m) matrix of 
polynomials             over rationals to matrix of polynomials over number 
			field maprtomapnf(r,M) matrix of 
polynomials             over rationals to matrix of rational functions over 
			rationals maprtomarfr(r,M) matrix of 
polynomials             over rationals to vector of number field elements 
			vudprtovnf(V) vector of univariate dense 
polynomials             over rationals to vector of polynomials modulo 
			polynomial over rationals vecprtvpmpr(r,V,P) vector 
			of 
polynomials             over rationals to vector of polynomials over 
			modular integers vecprtovpmi(r,V,m) vector of 
polynomials             over rationals to vector of polynomials over number 
			field vecprtovpnf(r,V) vector of 
polynomials             over rationals to vector of rational functions over 
			rationals vecprtovrfr(r,V) vector of 
polynomials             over rationals vecpitovpr(V) vector of polynomials 
			over integers to vector of 
polynomials             over rationals vecpnftovpr(r,V) vector of 
			polynomials over number field to vector of 
polynomials             over rationals vecrtovecpr(r,V) vector of rationals 
			to vector of 
polynomials             over rationals vector multiplication 
			maprvecmul(r,A,x) (MACRO) matrix of 
polynomials             over rationals vnftovudpr(F,V) vector of number 
			field elements to vector of univariate dense 
polynomials             over rationals vudpitvudpr(V) vector of univariate 
			dense polynomials over integers to vector of 
			univariate dense 
polynomials             over the integers transformation 
			mapitransf(r1,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
polynomials             over the integers transformation 
			vecpitransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of 
polynomials             over the rationals transformation 
			maprtransf(r1,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
polynomials             over the rationals transformation 
			vecprtransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of 
polynomials             to matrix of dense polynomials maptomadp(r,M) 
			matrix of 
polynomials             to matrix of polynomials madptomap(r,M) matrix of 
			dense 
polynomials             to matrix of univariate polynomials maptomaup(r,M) 
			matrix of 
polynomials             to vector of dense polynomials vecptovecdp(r,V) 
			vector of 
polynomials             to vector of polynomials vecdptovecp(r,V) vector of 
			dense 
polynomials             to vector of univariate polynomials 
			vecptovecup(r,V) vector of 
polynomials             variable permutation mavpermut(r,M,PI) matrix of 
polynomials             variable permutation vecvpermut(r,V,PI) vector of 
polynomials             vecdptovecp(r,V) vector of dense polynomials to 
			vector of 
polynomials             vecptovecdp(r,V) vector of polynomials to vector of 
			dense 
polynomials             vecptovecup(r,V) vector of polynomials to vector of 
			univariate 
positive                definite binary quadratic forms iprpdbqf(D,h1,h2) 
			integer primitive reduced 
positive                degree upgfsrandpd(p,AL,m) univariate polynomial 
			over Galois-field with single characteristic 
			randomize, 
positive                entries ) maihermltpe(A) (MACRO) matrix of integers 
			Hermite normal form ( lower triangular form with 
power                   flpow(f,g) floating point 
power                   maximum lipairspmax(L) list of integer pairs 
power                   of 2 divisibility imp2d(A) integer maximal 
power                   of 2 ecgf2npmp2(G,a6,c,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a 
power                   of 2 product ip2prod(A,n) integer 
power                   of 2 quotient ip2quot(A,n) integer 
power                   of 2 rp2(n) rational number 
power                   of a prime ? isspprime(a,pc) is single 
power                   of an univariate prime polynomial over modular 
			single primes iafmsp1mpmpp(p,F,a,P,e,Q) integral 
			algebraic function over modular single primes, 
			transcendence degree 1, minimal polynomial modulo 
power                   of main variable ppmvprod(r,P,n) polynomial product 
			by 
power                   of main variable ppmvquot(r,P,n) polynomial 
			quotient by 
power                   of prime ideal homomorphism zero? 
			isqnfppihom0(D,P,k,pi,z,a) is quadratic number 
			field element 
power                   of variable (rekursiv) ppvquot(r,P,i,n) polynomial 
			quotient by 
power                   of variable, polynomial, remainder 
			upgf22pvprem(G,m,P) univariate polynomial over 
			Galois-field with characteristic 2, 2^m-th 
power                   product pfpprod(p,a,i) p-adic field element prime 
power                   product ppfpprod(r,p,P,i) polynomial over p-adic 
			field prime 
power                   product udppfpprod(p,P,i) univariate dense 
			polynomial over p-adic field prime 
power                   series upmssrpser(m,P,i) univariate polynomial over 
			modular singles square root 
power                   square root mppsqrt(p,n,r,xk,k) modular prime 
ppfderiv(r,p,P)         polynomial over p-adic field derivation, main 
			variable (rekursiv) 
ppfderivsv(r,p,P,n)     polynomial over p-adic field derivation, selected 
			variable 
ppfdif(r,p,P1,P2)       polynomial over p-adic field difference 
ppfeval(r,p,P,A)        polynomial over p-adic field evaluation, main 
			variable 
ppfevalsv(r,p,P,n,A)    polynomial over p-adic field evaluation, selected 
			variable 
ppfexp(r,p,P,n)         polynomial over p-adic field exponentiation 
ppffit(r,p,P,d)         polynomial over p-adic field fitting 
ppfiprod(r,p,P,i)       polynomial over p-adic field integer product 
ppfneg(r,p,P)           polynomial over p-adic field negation 
ppford(r,p,P)           polynomial over p-adic field order 
ppfpfprod(r,p,P,b)      polynomial over p-adic field p-adic field element 
			product 
ppfpprod(r,p,P,i)       polynomial over p-adic field prime power product 
ppfprod(r,p,P1,P2)      polynomial over p-adic field product 
ppfrprod(r,p,P,R)       polynomial over p-adic field rational number 
			product (rekursiv) 
ppfsubst(r,p,P1,P2)     polynomial over p-adic field substitution, main 
			variable 
ppfsubstsv(r,p,P1,n,P2) polynomial over p-adic field substitution, selected 
			variable 
ppfsum(r,p,P1,P2)       polynomial over p-adic field sum 
ppftrans(r,p,P,A)       polynomial over p-adic field translation, main 
			variable 
ppftransav(r,p,P,Lpf)   polynomial over p-adic field translation, all 
			variables 
ppftransf(r1,p,P1,V1,r2,P2,V2,Vn,pV3) polynomial over p-adic field 
			transformation 
ppmvprod(r,P,n)         polynomial product by power of main variable 
ppmvquot(r,P,n)         polynomial quotient by power of main variable 
pprmsp1ress(r,p,P1,P2)  polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, resultant, Sylvester 
			algorithm 
ppvquot(r,P,i,n)        polynomial quotient by power of variable (rekursiv) 
prderiv(r,P)            polynomial over rationals derivation, main variable 
prderivsv(r,P,n)        polynomial over rationals derivation, specified 
			variable (rekursiv) 
prdif(r,P1,P2)          polynomial over rationals difference (rekursiv) 
precision               bubble sort lsbsort(L) list of single 
precision               flsetprec(k,N) floating point set 
precision               fputsi(n,pf) file put single 
precision               getsi() (MACRO) get single 
precision               integer prime divisor search dpipds(a,N) double 
precision               putsi(n) (MACRO) put single 
precisions              bubble merge sort lsbmsort(L) list of single 
precisions              insert lsins(n,L) list of single 
precisions              merge lsmerge(L1,L2) list of single 
pred(r,P)               (MACRO) polynomial reductum 
preval(r,P,A)           polynomial over rationals evaluation, main variable 
prevalsv(r,P,n,A)       polynomial over rationals evaluation, specified 
			variable (rekursiv) 
prexp(r,P,n)            polynomial over rationals exponentiation 
prfmsp1deriv(r,p,P)     polynomial over rational functions over modular 
			single prime, transcendence degree 1, derivation, 
			main variable 
prfmsp1dif(r,p,P1,P2)   polynomial over rational functions over modular 
			single prime, transcendence degree 1, difference 
			(rekursiv) 
prfmsp1neg(r,p,P)       polynomial over rational functions over modular 
			single prime, transcendence degree 1, negation 
			(rekursiv) 
prfmsp1prod(r,p,P1,P2)  polynomial over rational functions over modular 
			single prime, transcendence degree 1, product 
			(rekursiv) 
prfmsp1qrem(r,p,P1,P2,pR) polynomial over rational functions over modular 
			single prime, transcendence degree 1, quotient and 
			remainder (rekursiv) 
prfmsp1rfprd(r,p,P,a)   polynomial over rational functions over modular 
			single prime, transcendence degree 1, rational 
			function over modular single prime, transcendence 
			degree 1, product (rekursiv) 
prfmsp1sum(r,p,P1,P2)   polynomial over rational functions over modular 
			single prime, transcendence degree 1, sum 
			(rekursiv) 
primality               test (rekursiv) igkapt(n,msg) integer Goldwasser 
			Kilian Atkin 
primality               test iecpt(n,m,lp,a,b,anz) integer elliptic curve 
primality               test iftpt(n,L,anz) integer Fermat's theorem 
primality               test ispt(M,M1,F) integer Selfridge 
prime                   ? isipprime(n,a) is integer pseudo 
prime                   ? isiprime(n) is integer 
prime                   ? isispprime(n,k) is integer strong pseudo 
prime                   ? isspprime(a,pc) is single power of a 
prime                   ? issprime(a,pc) is single 
prime                   Jacobi-symbol ( Legendre-symbol ) ipjacsym(a,p) 
			integer 
prime                   abnfrelclmp(m,q,g) abelian number field relative 
			class number modulo 
prime                   additive valuation upmiaddval(p,P1,P) univariate 
			polynomial over modular integer 
prime                   construction iprimeconstr(bits,f,pL,n) integer 
prime                   construction, transcendence degree 1 
			rfmsp1cons(p,P1,P2) rational function over modular 
			single 
prime                   decomposition law nfipdeclaw(F,P) number field, 
			integer 
prime                   decomposition law nfspdeclaw(F,p) number field, 
			single 
prime                   determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
			modular primes, short normal form, number of points 
			modulo a single 
prime                   determined with the Schoof algorithm, version 1 
			ecgf2npmspv1(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a single 
prime                   determined with the Schoof algorithm, version 2 
			ecgf2npmspv2(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a single 
prime                   difference, transcendence degree 1 
			rfmsp1dif(p,R1,R2) rational function over modular 
			single 
prime                   divisor search dpipds(a,N) double precision integer 
prime                   divisor search ilpds(N,A,B,pP,pN1) integer large 
prime                   divisor search impds(N,A,B,pP,pQ) integer medium 
prime                   divisor search imspds(N,a,b) integer medium single 
prime                   divisor search sum 
			elcpdssum(N,x1,y1,x2,y2,px3,py3,a) elliptic curve 
prime                   divisors ( lists only ) ispd_lo(N,pM) integer small 
prime                   divisors search ispd(N,pM) integer small 
prime                   eciminbrtmp(E,p,n) elliptic curve with integer 
			coefficients, minimal model, bad reduction type 
			modulo 
prime                   eciminmrtmp(E,p) elliptic curve with integer 
			coefficients, minimal model, multiplicative 
			reduction type modulo 
prime                   factorization upgfsrelpfac(p,AL,P,Fak,pA2) 
			univariate polynomial over Galois-field with single 
			characteristic relative 
prime                   factorization upmirelpfact(P,F,Fak,pA2) univariate 
			polynomial over modular integers relative 
prime                   factorization upmsrelpfact(p,P,Fak,pA2) univariate 
			polynomial over modular singles relative 
prime                   find non square mipfnsquare(p) modular integer 
prime                   find square mipfsquare(p) modular integer 
prime                   generator ipgen(u,o) integer 
prime                   generator spgen(a,b) single 
prime                   ideal factorization of the discriminant 
			ecqnfacpifdi(E) elliptic curve over quadratic 
			number field, actual model, 
prime                   ideal factorization qnfpifact(D,a) quadratic number 
			field element 
prime                   ideal factorization, special version 
			qnfielpifacts(D,a,L) quadratic number field 
			integral element 
prime                   ideal homomorphism qnfpihom(D,P,pi,z,a) quadratic 
			number field 
prime                   ideal homomorphism zero? isqnfppihom0(D,P,k,pi,z,a) 
			is quadratic number field element power of 
prime                   ideal order qnfielpiord(D,P,pi,z,a) quadratic 
			number field, integral element, 
prime                   ideal order qnfpiord(D,P,pi,z,a) quadratic number 
			field element 
prime                   ideal qnfsysrmodpi(D,P,pi,z,k) quadratic number 
			field system of representatives modulo a 
prime                   ilkprime() integer largest known 
prime                   irandprime(a1,a2,n) integer random 
prime                   negation, transcendence degree 1 rfmsp1neg(p,R) 
			rational function over modular single 
prime                   polynomial over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, minimal polynomial modulo power of an 
			univariate 
prime                   power product pfpprod(p,a,i) p-adic field element 
prime                   power product ppfpprod(r,p,P,i) polynomial over 
			p-adic field 
prime                   power product udppfpprod(p,P,i) univariate dense 
			polynomial over p-adic field 
prime                   power square root mppsqrt(p,n,r,xk,k) modular 
prime                   product, transcendence degree 1 rfmsp1prod(p,R1,R2) 
			rational function over modular single 
prime                   quotient cdprfmsp1upq(p,F,P) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, univariate 
			polynomial over modular single 
prime                   quotient, transcendence degree 1 
			rfmsp1quot(p,R1,R2) rational function over modular 
			single 
prime                   representation as a norm in an imaginary quadratic 
			field iprniqf(p,D) integer 
prime                   square root mipsqrt(p,r) modular integer 
prime                   sum, transcendence degree 1 rfmsp1sum(p,R1,R2) 
			rational function over modular single 
prime                   unimodular transformation 
			vecupmsunimt(p,V,W,i,pV1,pW1) vector of univariate 
			polynomials over modular single 
prime                   upihlfaip(p,P,L,k) univariate polynomial over 
			integers, Hensel lemma factorization approximation 
			with respect to integer 
prime                   upihliip(P,F,L) univariate polynomial over 
			integers, Hensel lemma initialization with respect 
			to integer 
prime                   upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over integers, Hensel lemma quadratic 
			step with respect to integer 
prime,                  complete factorization special upmscfacts(p,A) 
			univariate polynomial over modular single 
prime,                  number of points ecmspnp(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular single 
prime,                  printing messages isiprimemsg(n) (MACRO) is integer 
prime,                  transcendence degree 1 ? isrfmsp1(p,R) is rational 
			function over modular single 
prime,                  transcendence degree 1 cdprfmsp1fup(p,P) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			univariate polynomial over rational functions over 
			modular single 
prime,                  transcendence degree 1 cdprfmsp1lfm(M,p) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, list 
			from common denominator matrix of rational 
			functions over modular single 
prime,                  transcendence degree 1 clfcdprfmsp1(P,n) 
			coefficient list from common denominator polynomial 
			over rational functions over modular single 
prime,                  transcendence degree 1 fputrfmsp1(p,R,V,pf) (MACRO) 
			file put rational function over modular single 
prime,                  transcendence degree 1 nepousppmsp1(p,F,a) norm of 
			an element of the polynomial order of an univariate 
			separable polynomial over the polynomial ring over 
			modular single 
prime,                  transcendence degree 1 pmstorfmsp1(p,P) (MACRO) 
			polynomial over modular singles to rational 
			function over modular single 
prime,                  transcendence degree 1 putrfmsp1(p,R,V) (MACRO) put 
			rational function over modular single 
prime,                  transcendence degree 1 sclfuprfmsp1(P,n) special 
			coefficient list from univariate polynomial over 
			rational functions over modular single 
prime,                  transcendence degree 1 uprfmsp1fcdp(p,P) univariate 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, from common 
			denominator polynomial over rational functions over 
			modular single 
prime,                  transcendence degree 1 vepepuspmsp1(p,F,a,P,k,v) 
			values of the extensions of the P-adic valuation of 
			an element of the polynomial order of a univariate 
			separable polynomial over the polynomial ring over 
			modular single 
prime,                  transcendence degree 1, Dedekind maximality test 
			ouspprmsp1dm(p,P,F) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single 
prime,                  transcendence degree 1, Hensel factorization 
			approximation upprmsp1hfa(p,F,P,L,k) univariate 
			polynomial over polynomial ring over modular single 
prime,                  transcendence degree 1, Hensel lemma initialization 
			upprmsp1hli(p,F,P,L) univariate polynomial over 
			polynomial ring over modular single 
prime,                  transcendence degree 1, Hensel quadratic step 
			upprmsp1hqs(p,F,T,L1,L2,A) univariate polynomial 
			over polynomial ring over modular single 
prime,                  transcendence degree 1, P-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial afmsp1pptf(p,F,P,Q,Pp,a0,z) 
			algebraic function over modular single 
prime,                  transcendence degree 1, P-star valuation 
			iafmsp1psval(p,P,A) integral algebraic function 
			over modular single 
prime,                  transcendence degree 1, algebraic function over 
			modular single prime, transcendence degree 1, 
			evaluation special upprmsp1afes(p,F,P,a) univariate 
			polynomial over polynomial ring over modular single 
prime,                  transcendence degree 1, approximation of P-adic 
			factorization uspprmsp1apf(p,P,F,k) univariate 
			separable polynomial over polynomial ring over 
			modular single 
prime,                  transcendence degree 1, basis from generators 
			oprmsp1basfg(p,F,L) order over polynomial ring over 
			modular single 
prime,                  transcendence degree 1, basis of a local maximal 
			over-order ouspprmsp1bl(p,F,P,Q,pk) order of an 
			univariate separable polynomial over polynomial 
			ring over modular single 
prime,                  transcendence degree 1, decomposition law 
			affmsp1decl(p,F,P) algebraic function field over 
			modular single 
prime,                  transcendence degree 1, decomposition law 
			ouspprmsp1dl(p,F,P,k) order of a univariate 
			separable polynomial over polynomial ring over 
			modular single 
prime,                  transcendence degree 1, derivation, main variable 
			prfmsp1deriv(r,p,P) polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, difference (rekursiv) 
			prfmsp1dif(r,p,P1,P2) polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, discriminant 
			upprmsp1disc(p,F) univariate polynomial over 
			polynomial ring over modular single 
prime,                  transcendence degree 1, evaluation special 
			upprmsp1afes(p,F,P,a) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, algebraic function over 
			modular single 
prime,                  transcendence degree 1, exponentiation special 
			afmsp1expsp(p,F,a,e,M) algebraic function over 
			modular single 
prime,                  transcendence degree 1, extended greatest common 
			divisor uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate 
			polynomial over rational functions over modular 
			single 
prime,                  transcendence degree 1, from coefficient list 
			cdprfmsp1fcl(L,p) common denominator polynomial 
			over rational functions over modular single 
prime,                  transcendence degree 1, from common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular single 
prime,                  transcendence degree 1, from special coefficient 
			list uprfmsp1fscl(L) univariate polynomial over 
			rational functions over modular single 
prime,                  transcendence degree 1, from univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1 cdprfmsp1fup(p,P) common 
			denominator polynomial over rational functions over 
			modular single 
prime,                  transcendence degree 1, hermitian reduction 
			cdmarfmsp1hr(p,M) common denominator matrix of 
			rational functions over modular single 
prime,                  transcendence degree 1, identity construction 
			cdmarfmsp1id(n) common denominator matrix of 
			rational functions over modular single 
prime,                  transcendence degree 1, integral basis 
			ouspprmsp1ib(p,F,pL) order of an univariate 
			separable polynomial over the polynomial ring over 
			modular single 
prime,                  transcendence degree 1, inverse cdprfmsp1inv(p,F,A) 
			common denominator polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, list from common 
			denominator matrix of rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over modular single 
prime,                  transcendence degree 1, negation (rekursiv) 
			prfmsp1neg(r,p,P) polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, product (rekursiv) 
			prfmsp1prod(r,p,P1,P2) polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, product (rekursiv) 
			prfmsp1rfprd(r,p,P,a) polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, rational function over modular single 
prime,                  transcendence degree 1, product special 
			afmsp1prodsp(p,F,a,b,M) algebraic function over 
			modular single 
prime,                  transcendence degree 1, quotient and remainder 
			(rekursiv) prfmsp1qrem(r,p,P1,P2,pR) polynomial 
			over rational functions over modular single 
prime,                  transcendence degree 1, rational function over 
			modular single prime, transcendence degree 1, 
			product (rekursiv) prfmsp1rfprd(r,p,P,a) polynomial 
			over rational functions over modular single 
prime,                  transcendence degree 1, reduced discriminant 
			upprmsp1redd(p,F) univariate polynomial over 
			polynomial ring over modular single 
prime,                  transcendence degree 1, resultant, Sylvester 
			algorithm pprmsp1ress(r,p,P1,P2) polynomial over 
			polynomial ring over modular single 
prime,                  transcendence degree 1, resultant, Sylvester 
			algorithm upprmsp1ress(p,P1,P2) univariate 
			polynomial over polynomial ring over modular single 
prime,                  transcendence degree 1, sum (rekursiv) 
			prfmsp1sum(r,p,P1,P2) polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, sum cdprfmsp1sum(p,P1,P2) 
			common denominator polynomial over rational 
			functions over modular single 
prime,                  transcendence degree 1, univariate polynomial over 
			modular single prime quotient cdprfmsp1upq(p,F,P) 
			common denominator polynomial over rational 
			functions over modular single 
primes                  ? iselecmp(p,a1,a2,a3,a4,a6,P) is element of an 
			elliptic curve over modular 
primes                  Euklid- Gauss- step for columns 
			maupmipegsc(p,M,A,B) matrix of univariate 
			polynomials over modular integer 
primes                  Euklid- Gauss- step for columns 
			maupmspegsc(p,M,A,B) matrix of univariate 
			polynomials over modular single 
primes                  Euklid- Gauss- step for rows maupmipegsr(p,M,A,B) 
			matrix of univariate polynomials over modular 
			integer 
primes                  Euklid- Gauss- step for rows maupmspegsr(p,M,A,B) 
			matrix of univariate polynomials over modular 
			single 
primes                  Groebner basis augmentation dipmipgba(r,p,PL,P) 
			distributive polynomial over modular integer 
primes                  Groebner basis augmentation dipmspgba(r,p,PL,P) 
			distributive polynomial over modular single 
primes                  Groebner basis dipmipgb(r,p,PL) distributive 
			polynomial over modular integer 
primes                  Groebner basis dipmspgb(r,p,PL) distributive 
			polynomial over modular single 
primes                  Groebner basis recursion dipmipgbr(r,p,PL) 
			distributive polynomial over modular integer 
primes                  Groebner basis recursion dipmspgbr(r,p,PL) 
			distributive polynomial over modular single 
primes                  S-polynomial dipmipsp(r,p,P1,P2) distributive 
			polynomial over modular integer 
primes                  S-polynomial dipmspsp(r,p,P1,P2) distributive 
			polynomial over modular single 
primes                  Tate's values b2, b4, b6 
			ecmptavb6(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular 
primes                  Tate's values b2, b4, b6, b8 
			ecmptavb8(p,a1,a2,a3,a4,a6) elliptic curve over 
			modular 
primes                  Tate's values c4, c6 ecmptavc6(p,a1,a2,a3,a4,a6) 
			elliptic curve over modular 
primes                  difference dipmipdif(r,p,P1,P2) distributive 
			polynomial over modular integer 
primes                  difference dipmspdif(r,p,P1,P2) distributive 
			polynomial over modular single 
primes                  elementary divisor form and cofactors 
			maupmipedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over modular integer 
primes                  elementary divisor form and cofactors 
			maupmspedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over modular single 
primes                  equal ? isppecmpeq(p,P1,P2) is projective point of 
			an elliptic curve over modular 
primes                  hermitian reduction, special maupmshermsp(p,M,r,pD) 
			matrix of univariate polynomials over modular 
			single 
primes                  iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, minimal polynomial modulo power of an 
			univariate prime polynomial over modular single 
primes                  in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular integer 
primes                  in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular single 
primes                  in lexicographical order to distributive polynomial 
			over modular integer primes in graduated 
			lexicographical order dipmiplotglo(r,p,P) 
			distributive polynomial over modular integer 
primes                  in lexicographical order to distributive polynomial 
			over modular integer primes in lexicographical 
			order with inverse exponent vector 
			dipmiplotlio(r,p,P) distributive polynomial over 
			modular integer 
primes                  in lexicographical order to distributive polynomial 
			over modular integer primes with total degree 
			ordering dipmiplottdo(r,p,P) distributive 
			polynomial over modular integer 
primes                  in lexicographical order to distributive polynomial 
			over modular single primes in graduated 
			lexicographical order dipmsplotglo(r,p,P) 
			distributive polynomial over modular single 
primes                  in lexicographical order to distributive polynomial 
			over modular single primes in lexicographical order 
			with inverse exponent vector dipmsplotlio(r,p,P) 
			distributive polynomial over modular single 
primes                  in lexicographical order to distributive polynomial 
			over modular single primes with total degree 
			ordering dipmsplottdo(r,p,P) distributive 
			polynomial over modular single 
primes                  in lexicographical order with inverse exponent 
			vector dipmiplotlio(r,p,P) distributive polynomial 
			over modular integer primes in lexicographical 
			order to distributive polynomial over modular 
			integer 
primes                  in lexicographical order with inverse exponent 
			vector dipmsplotlio(r,p,P) distributive polynomial 
			over modular single primes in lexicographical order 
			to distributive polynomial over modular single 
primes                  infempmppip(F,a,p,e,Q) integral number field 
			element minimal polynomial modulo p-power with 
			respect to integer 
primes                  infepptfip(F,p,Q,ppot,a0,z) integral number field 
			element p-primality test and factorization of the 
			defining polynomial or the minimal polynomial with 
			respect to integer 
primes                  infepstarvip(P,A) integral number field element 
			p-star valuation with respect to integer 
primes                  ippnfecalip(F,P,Q,mp) integral P-primary number 
			field element, core algorithm with respect to 
			integer 
primes                  ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
			denominator of the p-star value with respect to 
			integer 
primes                  ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field element regulation with 
			respect to integer 
primes                  list fgetdipmipl(r,p,VL,pf) file get distributive 
			polynomial over modular integer 
primes                  list fgetdipmspl(r,p,VL,pf) file get distributive 
			polynomial over modular single 
primes                  list fputdipmipl(r,p,PL,VL,pf) file put 
			distributive polynomial over modular integer 
primes                  list fputdipmspl(r,p,PL,VL,pf) file put 
			distributive polynomial over modular single 
primes                  list getdipmipl(r,p,VL) (MACRO) get distributive 
			polynomial over modular integer 
primes                  list getdipmspl(r,p,VL) (MACRO) get distributive 
			polynomial over modular single 
primes                  list putdipmipl(r,p,PL,VL) (MACRO) put distributive 
			polynomial over modular integer 
primes                  list putdipmspl(r,p,PL,VL) (MACRO) put distributive 
			polynomial over modular single 
primes                  monic dipmipmonic(r,p,P) distributive polynomial 
			over modular integer 
primes                  monic dipmspmonic(r,p,P) distributive polynomial 
			over modular single 
primes                  multiplication-map ecmpmul(p,a1,a2,a3,a4,a6,n,P1) 
			elliptic curve over modular 
primes                  negation dipmipneg(r,p,P) distributive polynomial 
			over modular integer 
primes                  negation dipmspneg(r,p,P) distributive polynomial 
			over modular single 
primes                  negative point ecmpneg(p,a1,a2,a3,a4,a6,P) elliptic 
			curve over modular 
primes                  ouspibaslmoi(F,P,Q,pk) order of an univariate 
			separable polynomial over the integers basis of a 
			local maximal over-order with respect to integer 
primes                  point at infinity ? isppecmppai(p,P) is projective 
			point of an elliptic curve over modular 
primes                  product dipmipmiprod(r,p,P,A) distributive 
			polynomial over modular integer primes, modular 
			integer 
primes                  product dipmipprod(r,p,P1,P2) distributive 
			polynomial over modular integer 
primes                  product dipmspmsprod(r,p,P,a) distributive 
			polynomial over modular single primes, modular 
			single 
primes                  product dipmspprod(r,p,P1,P2) distributive 
			polynomial over modular single 
primes                  short normal form number of points special version 
			ecmipsnfnpsv(p,a4,a6) elliptic curve over modular 
			integer 
primes                  square root mpsqrt(p,a) modular 
primes                  sum dipmipsum(r,p,P1,P2) distributive polynomial 
			over modular integer 
primes                  sum dipmspsum(r,p,P1,P2) distributive polynomial 
			over modular single 
primes                  to short normal form ecmptosnf(p,a1,a2,a3,a4,a6) 
			elliptic curve over modular 
primes                  transcendence degree 1, determinant 
			marfmsp1det(p,M) matrix of rational functions over 
			modular single 
primes                  transcendence degree 1, difference 
			marfmsp1dif(p,M,N) (MACRO) matrix of rational 
			functions over modular single 
primes                  with total degree ordering dipmiplottdo(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order to distributive polynomial 
			over modular integer 
primes                  with total degree ordering dipmsplottdo(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order to distributive polynomial 
			over modular single 
primes,                 birational transformation of coefficients 
			ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) elliptic curve 
			over modular 
primes,                 discriminant ecmpdisc(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular 
primes,                 find point ecmpfp(p,a1,a2,a3,a4,a6) elliptic curve 
			over modular 
primes,                 j-invariant ecmpjinv(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular 
primes,                 line through points ecmplp(p,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over modular 
primes,                 modular integer primes product 
			dipmipmiprod(r,p,P,A) distributive polynomial over 
			modular integer 
primes,                 modular single primes product dipmspmsprod(r,p,P,a) 
			distributive polynomial over modular single 
primes,                 short normal form ? iselecmpsnf(p,a,b,P) is element 
			of an elliptic curve over modular 
primes,                 short normal form, Shanks' algorithm 
			ecmspsnfsha(p,a4,a6) (MACRO) elliptic curve over 
			modular single 
primes,                 short normal form, combined Schoof- Shanks- 
			algorithm ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic 
			curve over modular 
primes,                 short normal form, construction of division 
			polynomials ecmpsnfcdivp(P,a4,a6,n) elliptic curve 
			over modular 
primes,                 short normal form, discriminant 
			ecmpsnfdisc(p,a4,a6) elliptic curve over modular 
primes,                 short normal form, find point ecmpsnffp(p,a4,a6) 
			elliptic curve over modular 
primes,                 short normal form, finding a multiple of the order 
			of a point with the Pollard Lambda method 
			ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
			modular 
primes,                 short normal form, finding a multiple of the order 
			of a point with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular 
primes,                 short normal form, j-invariant ecmpsnfjinv(p,a4,a6) 
			elliptic curve over modular 
primes,                 short normal form, line through points 
			ecmpsnflp(p,a4,a6,P1,P2) elliptic curve over 
			modular 
primes,                 short normal form, modified Shanks' algorithm, 
			first part ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) 
			elliptic curve over modular 
primes,                 short normal form, multiple of the order of a point 
			to exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular 
primes,                 short normal form, multiplication-map 
			ecmpsnfmul(p,a4,a6,n,P1) elliptic curve over 
			modular 
primes,                 short normal form, multiplication-map, special 
			version ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve 
			over modular 
primes,                 short normal form, negative point 
			ecmpsnfneg(p,a4,a6,P) elliptic curve over modular 
primes,                 short normal form, number of points 
			ecmspsnfnp(p,a4,a6) elliptic curve over modular 
			single 
primes,                 short normal form, number of points modulo 2 
			ecmpsnfnpm2(P,a4,a6) elliptic curve over modular 
primes,                 short normal form, number of points modulo a single 
			prime determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
			modular 
primes,                 short normal form, number of points modulo an 
			integer determined with the Schoof algorithm 
			ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve over 
			modular 
primes,                 short normal form, sum of points 
			ecmpsnfsum(p,a4,a6,P1,P2) elliptic curve over 
			modular 
primes,                 short normal form, sum of points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve 
			over modular 
primes,                 standard representation of projective point 
			ecmpsrpp(p,P) elliptic curve over modular 
primes,                 sum of points ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) 
			elliptic curve over modular 
primes,                 transcendence degree 1 ? ismarfmsp1(p,M) (MACRO) is 
			matrix of rational functions over modular single 
primes,                 transcendence degree 1 ? isvecrfmsp1(p,V) (MACRO) 
			is vector of rational functions over modular single 
primes,                 transcendence degree 1 fgetmarfmsp1(p,V,pf) (MACRO) 
			file get matrix of rational functions over modular 
			single 
primes,                 transcendence degree 1 fgetrfmsp1(p,V,pf) file get 
			rational function over modular single 
primes,                 transcendence degree 1 fgetvrfmsp1(p,VL,pf) (MACRO) 
			file get vector of rational functions over modular 
			single 
primes,                 transcendence degree 1 fputmarfmsp1(p,M,V,pf) 
			(MACRO) file put matrix of rational functions over 
			modular single 
primes,                 transcendence degree 1 fputvrfmsp1(p,V,VL,pf) 
			(MACRO) file put vector of rational functions over 
			modular single 
primes,                 transcendence degree 1 getmarfmsp1(p,V) (MACRO) get 
			matrix of rational functions over modular single 
primes,                 transcendence degree 1 getrfmsp1(p,V) (MACRO) get 
			rational function over modular single 
primes,                 transcendence degree 1 getvecrfmsp1(p,VL) (MACRO) 
			get vector of rational functions over modular 
			single 
primes,                 transcendence degree 1 mpmstmrfmsp1(p,M) matrix of 
			polynomials over modular singles to matrix of 
			rational functions over modular single 
primes,                 transcendence degree 1 putmarfmsp1(p,M,V) (MACRO) 
			put matrix of rational functions over modular 
			single 
primes,                 transcendence degree 1 putvecrfmsp1(p,V,VL) (MACRO) 
			put vector of rational functions over modular 
			single 
primes,                 transcendence degree 1 vpmstvrfmsp1(p,V) vector of 
			polynomials over modular singles to vector of 
			rational functions over modular single 
primes,                 transcendence degree 1, construction 1 
			marfmsp1c1(p,n) (MACRO) matrix of rational 
			functions over modular single 
primes,                 transcendence degree 1, core algorithm 
			afmsp1coreal(p,F,P,Q,mp) algebraic function over 
			modular single 
primes,                 transcendence degree 1, difference 
			vecrfmsp1dif(p,U,V) (MACRO) vector of rational 
			functions over modular single 
primes,                 transcendence degree 1, element test 
			modprmsp1elt(B,p,a) module over polynomial ring 
			over modular single 
primes,                 transcendence degree 1, exponentiation 
			marfmsp1exp(p,M,n) matrix of rational functions 
			over modular single 
primes,                 transcendence degree 1, increasing the denominator 
			of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over modular single 
primes,                 transcendence degree 1, inverse marfmsp1inv(p,M) 
			matrix of rational functions over modular single 
primes,                 transcendence degree 1, inverse rfmsp1inv(p,R) 
			rational function over modular single 
primes,                 transcendence degree 1, linear combination 
			vecrfmsp1lc(p,F1,F2,V1,V2) vector of rational 
			functions over modular single 
primes,                 transcendence degree 1, minimal polynomial 
			afmsp1minpol(p,F,a) algebraic function over modular 
			single 
primes,                 transcendence degree 1, minimal polynomial 
			iafmsp1mpol(p,F,a,Q) integral algebraic function 
			over modular single 
primes,                 transcendence degree 1, minimal polynomial modulo 
			power of an univariate prime polynomial over 
			modular single primes iafmsp1mpmpp(p,F,a,P,e,Q) 
			integral algebraic function over modular single 
primes,                 transcendence degree 1, module homomorphism 
			cdprfmsp1mh(p,P,M) common denominator polynomial 
			over rational functions over modular single 
primes,                 transcendence degree 1, negation marfmsp1neg(p,M) 
			(MACRO) matrix of rational functions over modular 
			single 
primes,                 transcendence degree 1, negation vecrfmsp1neg(p,V) 
			(MACRO) vector of rational functions over modular 
			single 
primes,                 transcendence degree 1, null space basis 
			marfmsp1nsb(p,M) matrix of rational functions over 
			modular single 
primes,                 transcendence degree 1, product marfmsp1prod(p,M,N) 
			(MACRO) matrix of rational functions over modular 
			single 
primes,                 transcendence degree 1, rank marfmsp1rk(p,M) matrix 
			of rational functions over modular single 
primes,                 transcendence degree 1, regulation 
			afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) algebraic 
			function over modular single 
primes,                 transcendence degree 1, scalar multiplication 
			marfmsp1smul(p,M,F) matrix of rational functions 
			over modular single 
primes,                 transcendence degree 1, scalar multiplication 
			vecrfmsp1sm(p,F,V) vector of rational functions 
			over modular single 
primes,                 transcendence degree 1, scalar product 
			vecrfmsp1sp(p,V,W) vector of rational functions 
			over modular single 
primes,                 transcendence degree 1, solution of a system of 
			linear equations marfmsp1ssle(p,A,b,pX,pN) matrix 
			of rational functions over modular single 
primes,                 transcendence degree 1, sum marfmsp1sum(p,M,N) 
			(MACRO) matrix of rational functions over modular 
			single 
primes,                 transcendence degree 1, sum vecrfmsp1sum(p,U,V) 
			(MACRO) vector of rational functions over modular 
			single 
primes,                 transcendence degree 1, vector multiplication 
			marfmsp1vmul(p,A,x) (MACRO) matrix of rational 
			functions over modular single 
primitive               ideal product qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over modular singles 
primitive               ideal product qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over modular singles, 
			sparse representation, 
primitive               ideal product, special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles 
primitive               ideal product, special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, 
primitive               ideal qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic 
			function field over modular singles, imaginary 
			case, sparse representation, reduction of a 
primitive               ideal qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic 
			function field over modular singles, real case, 
			reduction of a 
primitive               ideal qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic 
			function field over modular singles, real case, 
			sparse representation, reduction of a 
primitive               ideal reduction qffmsipidred(m,D,Q,P,pQr,pPr) 
			quadratic function field over modular singles, 
			imaginary case, 
primitive               ideal square qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic 
			function field over modular singles 
primitive               ideal square qffmsspidsqu(m,D,Q1,P1,pQ,pP) 
			quadratic function field over modular singles, 
			sparse representation, 
primitive               ideal square, special version 
			qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles 
primitive               ideal square, special version 
			qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, sparse representation, 
primitive               part dipicp(r,P,pPP) distributive polynomial over 
			integers content and 
primitive               part dippicp(r1,r2,P,pPP) distributive polynomial 
			over polynomials over integers content and 
primitive               part picontpp(r,P,pPP) polynomial over integers 
			content and 
primitive               part piprimpart(r,P) (MACRO) polynomial over 
			integers 
primitive               part udpicontpp(P,pPP) univariate dense polynomial 
			over integers content and 
primitive               reduced positive definite binary quadratic forms 
			iprpdbqf(D,h1,h2) integer 
primitive               root miproot(Q) modular integer 
principal               ideal generating element, real case, 
			qffmspidgenr(m,D,Q,P,G,pB) quadratic function field 
			over modular singles, 
principal               part upmssrpp(m,P) univariate polynomial over 
			modular singles square root 
print                   formated fprintf(pf,format[,arg]...) (MACRO) file 
print                   formated printf(format[,arg]...) (MACRO) 
print                   time stoptime(a) stop and 
printegr(r,P)           polynomial over rationals integration, main 
			variable 
printf(format[,arg]...) (MACRO) print formated 
printing                messages isiprimemsg(n) (MACRO) is integer prime, 
prneg(r,P)              polynomial over rationals negation (rekursiv) 
prnfevalfvs(r,F,P)      polynomial over rationals number field element 
			evaluation first variable special version 
prnumden(r,P,pA)        polynomial over the rationals numerator and 
			denominator 
product                 (rekursiv) dpmiprod(r,M,P1,P2) dense polynomial 
			over modular integers 
product                 (rekursiv) dpmsprod(r,m,P1,P2) dense polynomial 
			over modular singles 
product                 (rekursiv) pgf2gf2prod(r,G,P,a) polynomial over 
			Galois-field with characteristic 2, Galois-field 
			with characteristic 2 element 
product                 (rekursiv) pgf2prod(r,G,P1,P2) polynomial over 
			Galois-field with characteristic 2 
product                 (rekursiv) pgfsgfsprod(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic, 
			Galois-field with single characteristic element 
product                 (rekursiv) pgfsprod(r,p,AL,P1,P2) polynomial over 
			Galois-field with single characteristic 
product                 (rekursiv) piiprod(r,P,A) polynomial over integers, 
			integer 
product                 (rekursiv) piprod(r,P1,P2) polynomial over integers 
product                 (rekursiv) pitrprod(r,S,P1,P2) polynomial over 
			integers truncation 
product                 (rekursiv) pmimiprod(r,M,P,A) polynomial over 
			modular integers, modular integers 
product                 (rekursiv) pmiprod(r,M,P1,P2) polynomial over 
			modular integers 
product                 (rekursiv) pmiupmiprod(r,m,P1,P2) polynomial over 
			modular integers, univariate polynomial over 
			modular integers 
product                 (rekursiv) pmsmsprod(r,m,P,a) polynomial over 
			modular singles, modular single 
product                 (rekursiv) pmsprod(r,m,P1,P2) polynomial over 
			modular singles 
product                 (rekursiv) pmsupmsprod(r,m,P1,P2) polynomial over 
			modular singles, univariate polynomial over modular 
			singles 
product                 (rekursiv) pnfnfprod(r,F,P,a) polynomial over 
			number field, number field element 
product                 (rekursiv) pnfprod(r,F,P1,P2) polynomial over 
			number field 
product                 (rekursiv) ppfrprod(r,p,P,R) polynomial over p-adic 
			field rational number 
product                 (rekursiv) prfmsp1prod(r,p,P1,P2) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, 
product                 (rekursiv) prfmsp1rfprd(r,p,P,a) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, rational function over 
			modular single prime, transcendence degree 1, 
product                 (rekursiv) prprod(r,P1,P2) polynomial over 
			rationals 
product                 (rekursiv) prrprod(r,P,A) polynomial over 
			rationals, rational number 
product                 as function miprodf(M,A,B) modular integer 
product                 by power of main variable ppmvprod(r,P,n) 
			polynomial 
product                 ciprod(v,i) complex integer 
product                 cprod(v,w) complex 
product                 dipgfsgfprod(r,p,AL,P,a) distributive polynomial 
			over Galois-field with single characteristic, 
			Galois-field with single characteristic element 
product                 dipgfsprod(r,p,AL,P1,P2) distributive polynomial 
			over Galois-field with single characteristic 
product                 dipiiprod(r,P,A) distributive polynomial over 
			integers, integer 
product                 dipiprod(r,P1,P2) distributive polynomial over 
			integers 
product                 dipmipmiprod(r,p,P,A) distributive polynomial over 
			modular integer primes, modular integer primes 
product                 dipmipprod(r,p,P1,P2) distributive polynomial over 
			modular integer primes 
product                 dipmspmsprod(r,p,P,a) distributive polynomial over 
			modular single primes, modular single primes 
product                 dipmspprod(r,p,P1,P2) distributive polynomial over 
			modular single primes 
product                 dipnfnfprod(r,F,P,A) distributive polynomial over 
			number field, number field element 
product                 dipnfprod(r,F,P1,P2) distributive polynomial over 
			number field 
product                 dippipiprod(r1,r2,P,A) distributive polynomial over 
			polynomials over integers, polynomial over integers 
product                 dippiprod(r1,r2,P1,P2) distributive polynomial over 
			polynomials over integers 
product                 diprfrprod(r1,r2,P1,P2) distributive polynomial 
			over rational functions over the rationals 
product                 diprfrrfprod(r1,r2,P,A) distributive polynomial 
			over rational functions over the rationals rational 
			function over the rationals 
product                 diprprod(r,P1,P2) distributive polynomial over 
			rationals 
product                 diprrprod(r,P,A) distributive polynomial over 
			rationals, rational number 
product                 flprod(f,g) floating point 
product                 gf2prod(G,a,b) Galois-field with characteristic 2 
product                 gfsprod(p,AL,a,b) Galois-field with single 
			characteristic 
product                 i22prod(A,B) integer 2x2 
product                 iecpprod(p,E,P,a) integer elliptic curve point 
product                 ifelprod(a,b) integer factor exponent list 
product                 ip2prod(A,n) integer power of 2 
product                 iprod(A,B) integer 
product                 isprod(A,b) integer single-precision 
product                 liprod(L1,L2) list of integers 
product                 magfsprod(p,AL,M,N) (MACRO) matrix of Galois-field 
			with single characteristic elements 
product                 maiprod(M,N) (MACRO) matrix of integers 
product                 mamiprod(m,M,N) (MACRO) matrix of modular integers 
product                 mamsprod(m,M,N) (MACRO) matrix of modular singles 
product                 manfprod(F,M,N) (MACRO) matrix of number field 
			elements 
product                 manfsprod(F,M,N) (MACRO) matrix of number field 
			elements, sparse representation, 
product                 mapgfsprod(r,p,AL,M,N) (MACRO) matrix of 
			polynomials over Galois-field with single 
			characteristic 
product                 mapiprod(r,M,N) (MACRO) matrix of polynomials over 
			integers 
product                 mapmiprod(r,m,M,N) (MACRO) matrix of polynomials 
			over modular integers 
product                 mapmsprod(r,m,M,N) (MACRO) matrix of polynomials 
			over modular singles 
product                 mapnfprod(r,F,M,N) (MACRO) matrix of polynomials 
			over number field 
product                 maprod(M,N,prod,sum,anzahlargs,arg1,arg2) matrix 
product                 maprprod(r,M,N) (MACRO) matrix of polynomials over 
			rationals 
product                 marfmsp1prod(p,M,N) (MACRO) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, 
product                 marfrprod(r,M,N) (MACRO) matrix of rational 
			functions over rationals 
product                 marprod(M,N) (MACRO) matrix of rationals 
product                 miprod(M,A,B) modular integer 
product                 msprod(m,a,b) modular single 
product                 nfeliprod(F,a,i) number field element integer 
product                 nfelrprod(F,a,R) number field element rational 
			number 
product                 nfprod(F,a,b) number field element 
product                 nfsprod(F,a,b) number field, sparse representation, 
product                 over all c_p- values ecrprodcp(E) elliptic curve 
			over the rationals, 
product                 over all entries liprodoe(L) list of integers 
product                 pfeliprod(p,a,i) p-adic field element integer 
product                 pfelrprod(p,a,R) p-adic field element rational 
			number 
product                 pfpprod(p,a,i) p-adic field element prime power 
product                 pfprod(p,a,b) p-adic field element 
product                 pimidprod(r,S,P1,P2) polynomial over integers 
			modular ideal 
product                 pmimidprod(r,M,S,P1,P2) polynomial over modular 
			integers, modular ideal 
product                 ppfiprod(r,p,P,i) polynomial over p-adic field 
			integer 
product                 ppfpfprod(r,p,P,b) polynomial over p-adic field 
			p-adic field element 
product                 ppfpprod(r,p,P,i) polynomial over p-adic field 
			prime power 
product                 ppfprod(r,p,P1,P2) polynomial over p-adic field 
product                 qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles primitive ideal 
product                 qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, primitive ideal 
product                 qnfidprod(D,A,B) quadratic number field ideal 
product                 qnfiprod(D,a,b) quadratic number field element, 
			integer, 
product                 qnfprod(D,a,b) quadratic number field element 
product                 qnfrprod(D,a,b) quadratic number field element, 
			rational number, 
product                 rfrprod(r,R1,R2) rational function over the 
			rationals 
product                 rprod(R,S) rational number 
product                 special afmsp1prodsp(p,F,a,b,M) algebraic function 
			over modular single prime, transcendence degree 1, 
product                 special 
			maprodspec(M,N,prod,sum,anzahlargs,arg1,...,arg5) 
			matrix 
product                 special nfeprodspec(F,a,b,M) number field element 
product                 special sxprods(a,b) single XOR 
product                 sprod(a,b,pc,pd) single-precision 
product                 sxprod(a,b,pc,pd) single XOR 
product                 udpiiprod(P,A) univariate dense polynomial over 
			integers integer 
product                 udpiprod(P1,P2) univariate dense polynomial over 
			integers 
product                 udpmimiprod(m,P,a) univariate dense polynomial over 
			modular integers, modular integer 
product                 udpmiprod(m,P1,P2) univariate dense polynomial over 
			modular integers 
product                 udpmsmsprod(m,P,a) univariate dense polynomial over 
			modular singles, modular single 
product                 udpmsprod(m,P1,P2) univariate dense polynomial over 
			modular singles 
product                 udppfpfprod(p,P,a) univariate dense polynomial over 
			p-adic field p-adic field element 
product                 udppfpprod(p,P,i) univariate dense polynomial over 
			p-adic field prime power 
product                 udppfprod(p,P1,P2) univariate dense polynomial over 
			p-adic field 
product                 udprprod(P1,P2) univariate dense polynomial over 
			rationals 
product                 udprrprod(P,A) univariate dense polynomial over 
			rationals, rational number 
product                 vecgf2sprod(G,V,W) vector of Galois-field with 
			characteristic 2 elements scalar 
product                 vecgfssprod(p,AL,V,W) vector of Galois-field with 
			single characteristic elements scalar 
product                 vecisprod(V,W) vector of integers scalar 
product                 vecmisprod(M,V,W) vector of modular integers scalar 
product                 vecmssprod(m,V,W) vector of modular singles scalar 
product                 vecnfsprod(F,V,W) vector of number field elements 
			scalar 
product                 vecnfssprod(F,V,W) vector of number field elements, 
			sparse representation, scalar 
product                 vecpisprod(r,V,W) vector of polynomials over 
			integers scalar 
product                 vecpmisprod(r,m,V,W) vector of polynomials over 
			modular integers scalar 
product                 vecpmssprod(r,m,V,W) vector of polynomials over 
			modular singles scalar 
product                 vecprsprod(r,V,W) vector of polynomials over 
			rationals scalar 
product                 vecrfmsp1sp(p,V,W) vector of rational functions 
			over modular single primes, transcendence degree 1, 
			scalar 
product                 vecrfrsprod(r,V,W) vector of rational functions 
			over rationals scalar 
product                 vecrsprod(V,W) vector of rationals scalar 
product                 vpgfssprod(r,p,AL,V,W) vector of polynomials over 
			Galois-field with single characteristic scalar 
product                 vpnfsprod(r,F,V,W) vector of polynomials over 
			number field scalar 
product                 with arithmetic list gf2prodAL(AL,a,b) Galois-field 
			with characteristic 2 
product,                lists only iprod_lo(A,B) integer 
product,                special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles primitive ideal 
product,                special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, primitive ideal 
product,                transcendence degree 1 rfmsp1prod(p,R1,R2) rational 
			function over modular single prime 
projective              point ecgf2srpp(G,P) elliptic curve over 
			Galois-field with characteristic 2, standard 
			representation of 
projective              point ecmpsrpp(p,P) elliptic curve over modular 
			primes, standard representation of 
projective              point ecnfsrpp(F,P) elliptic curve over number 
			field standard representation of 
projective              point of an elliptic curve over Galois-field with 
			characteristic 2 equal ? isppecgf2eq(p,P1,P2) is 
projective              point of an elliptic curve over Galois-field with 
			characteristic 2 point at infinity ? 
			isppecgf2pai(G,P) is 
projective              point of an elliptic curve over modular primes 
			equal ? isppecmpeq(p,P1,P2) is 
projective              point of an elliptic curve over modular primes 
			point at infinity ? isppecmppai(p,P) is 
projective              point of an elliptic curve over number field equal? 
			isppecnfeq(F,P1,P2) is 
projective              point of an elliptic curve over number field point 
			at infinity ? isppecnfpai(P) is 
projective              representation ecrptoproj(P) elliptic curve over 
			rational numbers, point to 
prprod(r,P1,P2)         polynomial over rationals product (rekursiv) 
prqrem(r,P1,P2,pR)      polynomial over rationals quotient and remainder 
			(rekursiv) 
prquot(r,P1,P2)         (MACRO) polynomial over rationals quotient 
prrem(r,P1,P2)          (MACRO) polynomial over rationals remainder 
prrprod(r,P,A)          polynomial over rationals, rational number product 
			(rekursiv) 
prrquot(r,P,A)          polynomial over rationals, rational quotient 
prrtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) polynomial over the rationals rational 
			transformation 
prsubst(r,P1,P2)        polynomial over rationals substitution, main 
			variable 
prsubstsv(r,P1,n,P2)    polynomial over rationals substitution, specified 
			variable (rekursiv) 
prsum(r,P1,P2)          polynomial over rationals sum (rekursiv) 
prtopmi(r,P,M)          polynomial over rationals to polynomial over 
			modular integers (rekursiv) 
prtopnf(r,P)            polynomial over rationals to polynomial over number 
			field (rekursiv) 
prtoppf(r,P,p,d)        polynomial over rationals to polynomial over p-adic 
			field 
prtorfr(r,P)            polynomial over the rationals to rational function 
			over the rationals 
prtrans(r,P,A)          polynomial over rationals translation, main 
			variable 
prtransav(r,P,LR)       polynomial over rationals translation, all 
			variables (rekursiv) 
prtransf(r1,P1,V1,r2,P2,V2,Vn,pV3) polynomial over the rationals 
			transformation 
pseudo                  prime ? isipprime(n,a) is integer 
pseudo                  prime ? isispprime(n,k) is integer strong 
pseudo                  remainder pipsrem(r,P1,P2) polynomial over integers 
pseudo                  remainder pmipsrem(r,m,P1,P2) polynomial over 
			modular integers 
pseudo                  remainder pmspsrem(r,m,P1,P2) polynomial over 
			modular singles 
pseudo                  remainder udpipsrem(P1,P2) univariate dense 
			polynomial over integers 
pseudoprimes            (rekursiv) ifactpp(N) integer factorization into 
psylvester(r,P1,P2)     polynomial Sylvester matrix 
ptbc(r,P)               polynomial trailing base coefficient (rekursiv) 
ptodip(r,P)             polynomial to distributive polynomial (rekursiv) 
ptodp(r,P)              polynomial to dense polynomial (rekursiv) 
ptol(pc)                (MACRO) pointer to list 
ptoup(r,P)              polynomial to univariate polynomial 
pure                    divisor search elcpds(N,a,z) elliptic curve 
put                     Galois-field with characteristic 2 element 
			fputgf2el(G,a,V,pf) file 
put                     Galois-field with characteristic 2 element 
			putgf2el(G,a,V) (MACRO) 
put                     Galois-field with single characteristic element 
			fputgfsel(p,AL,a,V,pf) file 
put                     Galois-field with single characteristic element 
			putgfsel(p,AL,a,V) (MACRO) 
put                     atom fputa(a,pf) file 
put                     atom puta(a) (MACRO) 
put                     atom sputa(a,str) (MACRO) string 
put                     bits fputbits(s,pf) file 
put                     bits putbits(s) (MACRO) 
put                     character fputc(c,pf) (MACRO) file 
put                     character putc(c,pf) (MACRO) 
put                     character putchar(c) (MACRO) 
put                     complex number fputcn(a,v,n,pf) file 
put                     complex number putcn(a,v,n) (MACRO) 
put                     distributive polynomial dimension 
			fputdipdim(r,dim,S,M,VL,pf) file 
put                     distributive polynomial dimension 
			putdipdim(r,dim,S,M,VL) (MACRO) 
put                     distributive polynomial over Galois-field with 
			single characteristic list 
			fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file 
put                     distributive polynomial over Galois-field with 
			single characteristic list 
			putdipgfsl(r,p,AL,PL,VL,Vgfs) (MACRO) 
put                     distributive polynomial over integers list 
			fputdipil(r,PL,VL,pf) file 
put                     distributive polynomial over integers list 
			putdipil(r,PL,VL) (MACRO) 
put                     distributive polynomial over modular integer primes 
			list fputdipmipl(r,p,PL,VL,pf) file 
put                     distributive polynomial over modular integer primes 
			list putdipmipl(r,p,PL,VL) (MACRO) 
put                     distributive polynomial over modular single primes 
			list fputdipmspl(r,p,PL,VL,pf) file 
put                     distributive polynomial over modular single primes 
			list putdipmspl(r,p,PL,VL) (MACRO) 
put                     distributive polynomial over number field list 
			fputdipnfl(r,F,PL,VL,Vnf,pf) file 
put                     distributive polynomial over number field list 
			putdipnfl(r,F,PL,VL,Vnf) (MACRO) 
put                     distributive polynomial over polynomials over 
			integers Groebner system 
			fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file 
put                     distributive polynomial over polynomials over 
			integers Groebner system 
			putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) 
put                     distributive polynomial over polynomials over 
			integers Groebner test 
			fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) file 
put                     distributive polynomial over polynomials over 
			integers Groebner test 
			putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) (MACRO) 
put                     distributive polynomial over polynomials over 
			integers comprehensive Groebner basis 
			fputdippicgb(r1,r2,CGBL,i,VL1,VL2,pf) file 
put                     distributive polynomial over polynomials over 
			integers comprehensive Groebner basis 
			putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) 
put                     distributive polynomial over polynomials over 
			integers dimension 
			fputdippidim(r1,r2,DIML,VL1,VL2,pf) file 
put                     distributive polynomial over polynomials over 
			integers dimension putdippidim(r1,r2,DIML,VL1,VL2) 
			(MACRO) 
put                     distributive polynomial over polynomials over 
			integers list fputdippil(r1,r2,PL,VL1,VL2,pf) file 
put                     distributive polynomial over polynomials over 
			integers list putdippil(r1,r2,PL,VL1,VL2) (MACRO) 
put                     distributive polynomial over polynomials over 
			integers parametric ideal membership test 
			fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file 
put                     distributive polynomial over polynomials over 
			integers parametric ideal membership test 
			putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) 
put                     distributive polynomial over polynomials over 
			integers quantifier free formula 
			fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) file 
put                     distributive polynomial over polynomials over 
			integers quantifier free formula 
			putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) 
put                     distributive polynomial over rational functions 
			over the rationals list 
			fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file 
put                     distributive polynomial over rational functions 
			over the rationals list 
			putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) 
put                     distributive polynomial over rationals list 
			fputdiprl(r,PL,VL,pf) file 
put                     distributive polynomial over rationals list 
			putdiprl(r,PL,VL) (MACRO) 
put                     elliptic curve fputecr(E,pf) file 
put                     elliptic curve over rational numbers putecr(E) 
			(MACRO) 
put                     elliptic curve over rational numbers, actual curve 
			fputecrac(E,pf) file 
put                     elliptic curve over rational numbers, actual curve 
			putecrac(E) (MACRO) 
put                     elliptic curve over rational numbers, list of 
			points putecrlistp(P,modus) (MACRO) 
put                     elliptic curve over rational numbers, point 
			fputecrp(P,pf) file 
put                     elliptic curve over rational numbers, point 
			putecrp(P) (MACRO) 
put                     elliptic curve over the rational numbers, 
			invariants fputecrinv(E,pf) file 
put                     elliptic curve over the rational numbers, 
			invariants putecrinv(E) (MACRO) 
put                     elliptic curve over the rational numbers, list of 
			points fputecrlistp(P,modus,pf) file 
put                     elliptic curve with integer coefficients, minimal 
			model fputecimin(E,pf) file 
put                     elliptic curve with integer coefficients, minimal 
			model putecimin(E) (MACRO) 
put                     elliptic curve with integer coefficients, short 
			normal form fputecisnf(E,*pf) file 
put                     elliptic curve with integer coefficients, short 
			normal form putecisnf(E) (MACRO) 
put                     factor list fputfactl(L,pf) file 
put                     factor list putfactl(L) (MACRO) 
put                     floating point by fix point fputflfx(f,vk,nk,pf) 
			file 
put                     floating point by fix point putflfx(f,vk,nk) 
			(MACRO) 
put                     floating point fputfl(f,n,pf) file 
put                     floating point putfl(f,n) (MACRO) 
put                     floating point special version sputflsp(prec,f,str) 
			string 
put                     integer factor exponent list fputifel(L,pf) file 
put                     integer factor exponent list putifel(L) (MACRO) 
put                     integer fputi(A,pf) file 
put                     integer puti(A) (MACRO) 
put                     integer sputi(A,str) string 
put                     list (rekursiv) fputl(L,pf) file 
put                     list of integers fputli(L,pf) file 
put                     list of integers putli(L) (MACRO) 
put                     list of polynomials over integers fputlpi(r,L,V,pf) 
			file 
put                     list of polynomials over rationals 
			fputlpr(r,L,V,pf) file 
put                     list of rationals fputlr(L,pf) file 
put                     list putl(L) (MACRO) 
put                     list sputl(l,str) string 
put                     list structure (rekursiv) fputlstruct(L,pf) file 
put                     list structure putlstruct(L) (MACRO) 
put                     matrix 
			fputma(M,pf,fputfkt,anzahlargs,arg1,arg2,arg3) file 
put                     matrix of Galois-field with single characteristic 
			elements fputmagfs(p,AL,M,V,pf) (MACRO) file 
put                     matrix of Galois-field with single characteristic 
			elements putmagfs(p,AL,M,V) (MACRO) 
put                     matrix of floatings by fix point 
			fputmaflfx(M,v,n,pf) file 
put                     matrix of floatings by fix point putmaflfx(M,v,n) 
			(MACRO) 
put                     matrix of integers fputmai(M,pf) (MACRO) file 
put                     matrix of integers putmai(M) (MACRO) 
put                     matrix of modular integers fputmami(m,M,pf) (MACRO) 
			file 
put                     matrix of modular integers putmami(m,M) (MACRO) 
put                     matrix of modular singles fputmams(m,M,pf) (MACRO) 
			file 
put                     matrix of modular singles putmams(m,M) (MACRO) 
put                     matrix of number field elements fputmanf(F,M,VL,pf) 
			(MACRO) file 
put                     matrix of number field elements putmanf(F,M,VL) 
			(MACRO) 
put                     matrix of number field elements, sparse 
			representation fputmanfs(F,M,VL,pf) (MACRO) file 
put                     matrix of number field elements, sparse 
			representation putmanfs(F,M,VL) (MACRO) 
put                     matrix of polynomials over Galois-field with single 
			characteristic fputmapgfs(r,p,AL,M,V,Vgfs,pf) 
			(MACRO) file 
put                     matrix of polynomials over Galois-field with single 
			characteristic putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) 
put                     matrix of polynomials over integers 
			fputmapi(r,M,V,pf) (MACRO) file 
put                     matrix of polynomials over integers putmapi(r,M,V) 
			(MACRO) 
put                     matrix of polynomials over modular integers 
			fputmapmi(r,m,M,V,pf) (MACRO) file 
put                     matrix of polynomials over modular integers 
			putmapmi(r,m,M,V) (MACRO) 
put                     matrix of polynomials over modular singles 
			fputmapms(r,m,M,V,pf) (MACRO) file 
put                     matrix of polynomials over modular singles 
			putmapms(r,m,M,V) (MACRO) 
put                     matrix of polynomials over number field 
			fputmapnf(r,F,M,V,Vnf,pf) (MACRO) file 
put                     matrix of polynomials over number field 
			putmapnf(r,F,M,V,Vnf) (MACRO) 
put                     matrix of polynomials over rationals 
			fputmapr(r,M,V,pf) (MACRO) file 
put                     matrix of polynomials over rationals putmapr(r,M,V) 
			(MACRO) 
put                     matrix of rational functions over modular single 
			primes, transcendence degree 1 
			fputmarfmsp1(p,M,V,pf) (MACRO) file 
put                     matrix of rational functions over modular single 
			primes, transcendence degree 1 putmarfmsp1(p,M,V) 
			(MACRO) 
put                     matrix of rational functions over rationals 
			fputmarfr(r,M,V,pf) (MACRO) file 
put                     matrix of rational functions over rationals 
			putmarfr(r,M,V) (MACRO) 
put                     matrix of rationals fputmar(M,pf) (MACRO) file 
put                     matrix of rationals putmar(M) (MACRO) 
put                     matrix of singles fputmas(M) file 
put                     matrix special 
			fputmaspec(M,pf,fputfkt,anzahlargs,arg1,...,arg8) 
			file 
put                     modular integer fputmi(M,A,pf) file 
put                     modular integer putmi(M,A) (MACRO) 
put                     modular single fputms(m,a,pf) file 
put                     modular single putms(m,a) (MACRO) 
put                     number field element fputnfel(F,a,V,pf) file 
put                     number field element putnfel(F,a,V) (MACRO) 
put                     number field element, sparse representation 
			fputnfels(F,a,V,pf) file 
put                     number field element, sparse representation 
			putnfels(F,a,V) (MACRO) 
put                     object fputo(a,pf) (MACRO) file 
put                     object puto(a) (MACRO) 
put                     original number field element fputonfel(F,a,V,pf) 
			file 
put                     original number field element putonfel(F,a,V) 
			(MACRO) 
put                     p-adic field element fputpfel(p,a,pf) file 
put                     p-adic field element putpfel(p,a) (MACRO) 
put                     polynomial over Galois-field 
			fputpgfs(r,p,AL,P,V,Vgfs,pf) file 
put                     polynomial over Galois-field 
			putpgfs(r,p,AL,P,V,Vgfs) (MACRO) 
put                     polynomial over Galois-field with characteristic 2 
			fputpgf2(r,G,P,V,Vgf2,pf) file 
put                     polynomial over Galois-field with characteristic 2 
			putpgf2(r,G,P,V,Vgf2) (MACRO) 
put                     polynomial over integers fputpi(r,P,V,pf) file 
put                     polynomial over integers putpi(r,P,V) (MACRO) 
put                     polynomial over modular integers 
			fputpmi(r,M,P,V,pf) file 
put                     polynomial over modular integers putpmi(r,m,P,V) 
			(MACRO) 
put                     polynomial over modular singles fputpms(r,m,P,V,pf) 
			file 
put                     polynomial over modular singles putpms(r,m,P,V) 
			(MACRO) 
put                     polynomial over number field 
			fputpnf(r,F,P,V,Vnf,pf) file 
put                     polynomial over number field putpnf(r,F,P,V,Vnf) 
			(MACRO) 
put                     polynomial over p-adic field fputppf(r,p,P,V,pf) 
			file 
put                     polynomial over p-adic field putppf(r,p,P,V) 
put                     polynomial over rationals fputpr(r,P,V,pf) file 
put                     polynomial over rationals putpr(r,P,V) (MACRO) 
put                     quadratic number field element factor exponent list 
			fputqnffel(D,L,pf) file 
put                     quadratic number field element factor exponent list 
			putqnffel(D,L) (MACRO) 
put                     quadratic number field element fputqnfel(D,a,pf) 
			file 
put                     quadratic number field element putqnfel(D,a) 
			(MACRO) 
put                     quadratic number field ideal fputqnfid(D,A,pf) file 
put                     quadratic number field ideal putqnfid(D,A) (MACRO) 
put                     rational function over modular single prime, 
			transcendence degree 1 fputrfmsp1(p,R,V,pf) (MACRO) 
			file 
put                     rational function over modular single prime, 
			transcendence degree 1 putrfmsp1(p,R,V) (MACRO) 
put                     rational function over rationals fputrfr(r,R,V,pf) 
			file 
put                     rational function over rationals putrfr(r,R,V) 
			(MACRO) 
put                     rational number decimal fputrd(R,n,pf) file 
put                     rational number decimal putrd(R,n) (MACRO) 
put                     rational number fputr(R,pf) file 
put                     rational number putr(R) (MACRO) 
put                     rational number sputr(R,str) string 
put                     single precision fputsi(n,pf) file 
put                     single precision putsi(n) (MACRO) 
put                     special p-adic field element fputspfel(p,a,pf) file 
put                     special p-adic field element putspfel(p,a) (MACRO) 
put                     string fputs(s,pf) (MACRO) file 
put                     string puts(s) (MACRO) 
put                     vector 
			fputvec(V,pf,fputfkt,anzahlargs,arg1,arg2,arg3) 
			file 
put                     vector of Galois-field with single characteristic 
			elements fputvecgfs(p,AL,V,VL,pf) (MACRO) file 
put                     vector of Galois-field with single characteristic 
			elements putvecgfs(p,AL,V,VL) (MACRO) 
put                     vector of integers fputveci(V,pf) (MACRO) file 
put                     vector of integers putveci(V) (MACRO) 
put                     vector of modular integers fputvecmi(m,V,pf) 
			(MACRO) file 
put                     vector of modular integers putvecmi(m,V) (MACRO) 
put                     vector of modular singles fputvecms(m,V,pf) (MACRO) 
			file 
put                     vector of modular singles putvecms(m,V) (MACRO) 
put                     vector of number field elements 
			fputvecnf(F,V,VL,pf) (MACRO) file 
put                     vector of number field elements putvecnf(F,V,VL) 
			(MACRO) 
put                     vector of number field elements, sparse 
			representation fputvecnfs(F,V,VL,pf) (MACRO) file 
put                     vector of number field elements, sparse 
			representation putvecnfs(F,V,VL) (MACRO) 
put                     vector of polynomials over Galois-field with single 
			characteristic fputvpgfs(r,p,AL,W,V,Vgfs,pf) 
			(MACRO) file 
put                     vector of polynomials over Galois-field with single 
			characteristic putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) 
put                     vector of polynomials over integers 
			fputvecpi(r,V,VL,pf) (MACRO) file 
put                     vector of polynomials over integers 
			putvecpi(r,V,VL) (MACRO) 
put                     vector of polynomials over modular integers 
			fputvecpmi(r,m,V,VL,pf) (MACRO) file 
put                     vector of polynomials over modular integers 
			putvecpmi(r,m,V,VL) (MACRO) 
put                     vector of polynomials over modular singles 
			fputvecpms(r,m,V,VL,pf) (MACRO) file 
put                     vector of polynomials over modular singles 
			putvecpms(r,m,V,VL) (MACRO) 
put                     vector of polynomials over number field 
			fputvecpnf(r,F,W,VL,VLnf,pf) (MACRO) file 
put                     vector of polynomials over number field 
			putvecpnf(r,F,W,VL,VLnf) (MACRO) 
put                     vector of polynomials over rationals 
			fputvecpr(r,V,VL,pf) (MACRO) file 
put                     vector of polynomials over rationals 
			putvecpr(r,V,VL) (MACRO) 
put                     vector of rational functions over modular single 
			primes, transcendence degree 1 
			fputvrfmsp1(p,V,VL,pf) (MACRO) file 
put                     vector of rational functions over modular single 
			primes, transcendence degree 1 putvecrfmsp1(p,V,VL) 
			(MACRO) 
put                     vector of rational functions over rationals 
			fputvecrfr(r,V,VL,pf) (MACRO) file 
put                     vector of rational functions over rationals 
			putvecrfr(r,V,VL) (MACRO) 
put                     vector of rationals fputvecr(V,pf) (MACRO) file 
put                     vector of rationals putvecr(V) (MACRO) 
put                     vector special 
			fputvecspec(V,pf,fputfkt,anzahlargs,arg1,...,arg8) 
			file 
puta(a)                 (MACRO) put atom 
putbits(s)              (MACRO) put bits 
putc(c,pf)              (MACRO) put character 
putchar(c)              (MACRO) put character 
putcn(a,v,n)            (MACRO) put complex number 
putdipdim(r,dim,S,M,VL) (MACRO) put distributive polynomial dimension 
putdipgfsl(r,p,AL,PL,VL,Vgfs) (MACRO) put distributive polynomial over 
			Galois-field with single characteristic list 
putdipil(r,PL,VL)       (MACRO) put distributive polynomial over integers 
			list 
putdipmipl(r,p,PL,VL)   (MACRO) put distributive polynomial over modular 
			integer primes list 
putdipmspl(r,p,PL,VL)   (MACRO) put distributive polynomial over modular 
			single primes list 
putdipnfl(r,F,PL,VL,Vnf) (MACRO) put distributive polynomial over number 
			field list 
putdippicgb(r1,r2,CGBL,i,VL1,VL2) (MACRO) put distributive polynomial over 
			polynomials over integers comprehensive Groebner 
			basis 
putdippidim(r1,r2,DIML,VL1,VL2) (MACRO) put distributive polynomial over 
			polynomials over integers dimension 
putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) put distributive polynomial over 
			polynomials over integers Groebner system 
putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) (MACRO) put distributive polynomial 
			over polynomials over integers Groebner test 
putdippil(r1,r2,PL,VL1,VL2) (MACRO) put distributive polynomial over 
			polynomials over integers list 
putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put distributive polynomial over 
			polynomials over integers parametric ideal 
			membership test 
putdippiqff(r1,r2,QFFL,VL1,VL2) (MACRO) put distributive polynomial over 
			polynomials over integers quantifier free formula 
putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) put distributive polynomial over 
			rational functions over the rationals list 
putdiprl(r,PL,VL)       (MACRO) put distributive polynomial over rationals 
			list 
putecimin(E)            (MACRO) put elliptic curve with integer 
			coefficients, minimal model 
putecisnf(E)            (MACRO) put elliptic curve with integer 
			coefficients, short normal form 
putecr(E)               (MACRO) put elliptic curve over rational numbers 
putecrac(E)             (MACRO) put elliptic curve over rational numbers, 
			actual curve 
putecrinv(E)            (MACRO) put elliptic curve over the rational 
			numbers, invariants 
putecrlistp(P,modus)    (MACRO) put elliptic curve over rational numbers, 
			list of points 
putecrp(P)              (MACRO) put elliptic curve over rational numbers, 
			point 
putfactl(L)             (MACRO) put factor list 
putfl(f,n)              (MACRO) put floating point 
putflfx(f,vk,nk)        (MACRO) put floating point by fix point 
putgf2el(G,a,V)         (MACRO) put Galois-field with characteristic 2 
			element 
putgfsel(p,AL,a,V)      (MACRO) put Galois-field with single characteristic 
			element 
puti(A)                 (MACRO) put integer 
putifel(L)              (MACRO) put integer factor exponent list 
putl(L)                 (MACRO) put list 
putli(L)                (MACRO) put list of integers 
putlstruct(L)           (MACRO) put list structure 
putmaflfx(M,v,n)        (MACRO) put matrix of floatings by fix point 
putmagfs(p,AL,M,V)      (MACRO) put matrix of Galois-field with single 
			characteristic elements 
putmai(M)               (MACRO) put matrix of integers 
putmami(m,M)            (MACRO) put matrix of modular integers 
putmams(m,M)            (MACRO) put matrix of modular singles 
putmanf(F,M,VL)         (MACRO) put matrix of number field elements 
putmanfs(F,M,VL)        (MACRO) put matrix of number field elements, sparse 
			representation 
putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) put matrix of polynomials over 
			Galois-field with single characteristic 
putmapi(r,M,V)          (MACRO) put matrix of polynomials over integers 
putmapmi(r,m,M,V)       (MACRO) put matrix of polynomials over modular 
			integers 
putmapms(r,m,M,V)       (MACRO) put matrix of polynomials over modular 
			singles 
putmapnf(r,F,M,V,Vnf)   (MACRO) put matrix of polynomials over number field 
putmapr(r,M,V)          (MACRO) put matrix of polynomials over rationals 
putmar(M)               (MACRO) put matrix of rationals 
putmarfmsp1(p,M,V)      (MACRO) put matrix of rational functions over 
			modular single primes, transcendence degree 1 
putmarfr(r,M,V)         (MACRO) put matrix of rational functions over 
			rationals 
putmi(M,A)              (MACRO) put modular integer 
putms(m,a)              (MACRO) put modular single 
putnfel(F,a,V)          (MACRO) put number field element 
putnfels(F,a,V)         (MACRO) put number field element, sparse 
			representation 
puto(a)                 (MACRO) put object 
putonfel(F,a,V)         (MACRO) put original number field element 
putpfel(p,a)            (MACRO) put p-adic field element 
putpgf2(r,G,P,V,Vgf2)   (MACRO) put polynomial over Galois-field with 
			characteristic 2 
putpgfs(r,p,AL,P,V,Vgfs) (MACRO) put polynomial over Galois-field 
putpi(r,P,V)            (MACRO) put polynomial over integers 
putpmi(r,m,P,V)         (MACRO) put polynomial over modular integers 
putpms(r,m,P,V)         (MACRO) put polynomial over modular singles 
putpnf(r,F,P,V,Vnf)     (MACRO) put polynomial over number field 
putppf(r,p,P,V)         put polynomial over p-adic field 
putpr(r,P,V)            (MACRO) put polynomial over rationals 
putqnfel(D,a)           (MACRO) put quadratic number field element 
putqnffel(D,L)          (MACRO) put quadratic number field element factor 
			exponent list 
putqnfid(D,A)           (MACRO) put quadratic number field ideal 
putr(R)                 (MACRO) put rational number 
putrd(R,n)              (MACRO) put rational number decimal 
putrfmsp1(p,R,V)        (MACRO) put rational function over modular single 
			prime, transcendence degree 1 
putrfr(r,R,V)           (MACRO) put rational function over rationals 
puts(s)                 (MACRO) put string 
putsi(n)                (MACRO) put single precision 
putspfel(p,a)           (MACRO) put special p-adic field element 
putvecgfs(p,AL,V,VL)    (MACRO) put vector of Galois-field with single 
			characteristic elements 
putveci(V)              (MACRO) put vector of integers 
putvecmi(m,V)           (MACRO) put vector of modular integers 
putvecms(m,V)           (MACRO) put vector of modular singles 
putvecnf(F,V,VL)        (MACRO) put vector of number field elements 
putvecnfs(F,V,VL)       (MACRO) put vector of number field elements, sparse 
			representation 
putvecpi(r,V,VL)        (MACRO) put vector of polynomials over integers 
putvecpmi(r,m,V,VL)     (MACRO) put vector of polynomials over modular 
			integers 
putvecpms(r,m,V,VL)     (MACRO) put vector of polynomials over modular 
			singles 
putvecpnf(r,F,W,VL,VLnf) (MACRO) put vector of polynomials over number field 
putvecpr(r,V,VL)        (MACRO) put vector of polynomials over rationals 
putvecr(V)              (MACRO) put vector of rationals 
putvecrfmsp1(p,V,VL)    (MACRO) put vector of rational functions over 
			modular single primes, transcendence degree 1 
putvecrfr(r,V,VL)       (MACRO) put vector of rational functions over 
			rationals 
putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) put vector of polynomials over 
			Galois-field with single characteristic 
pvext(r,P,V,VN)         polynomial variable list extension 
pvinsert(r,P,k)         polynomial insertion of new variables (rekursiv) 
pvmerge(LV,LP,pLP)      polynomial variable list merge 
pvpermut(r,P,PI)        polynomial variable permutation 
pvred(r,P,V,pV)         reduction of polynomial variables 
qffmsdcn(m,P)           quadratic function field over modular singles 
			divisor class number 
qffmsdcns1(m,P)         quadratic function field over modular singles 
			divisor class number subroutine 1 
qffmsdcns2(m,P)         quadratic function field over modular singles 
			divisor class number subroutine 2 
qffmsdcns3(m,P)         quadratic function field over modular singles 
			divisor class number subroutine 3 
qffmsfubs(m,D)          quadratic function field over modular singles 
			fundamental unit, baby step version 
qffmsfuobs(m,D)         quadratic function field over modular singles 
			fundamental unit, original version 
qffmsicggii(m,D,H,L,pIT) quadratic function field over modular singles ideal 
			class group generators and isomorphy type, 
			imaginary case 
qffmsicggir(m,D,d,H,L,pIT) quadratic function field over modular singles 
			ideal class group generators and isomorphy type, 
			real case 
qffmsicgrep(m,D,pHid)   quadratic function field over modular singles ideal 
			class group system of representatives 
qffmsicgri(m,D,pHid)    quadratic function field over modular singles ideal 
			class group system of representatives, imaginary 
			case 
qffmsicgrr(m,D,d)       quadratic function field over modular singles ideal 
			class group system of representatives, real case 
qffmsicgsti(m,D,L)      quadratic function field over modular singles ideal 
			class group structure, imaginary case 
qffmsicgstr(m,D,d,LG,pHid) quadratic function field over modular singles 
			ideal class group structure, real case 
qffmsicn(m,P)           quadratic function field over modular singles ideal 
			class number 
qffmsipidred(m,D,Q,P,pQr,pPr) quadratic function field over modular singles, 
			imaginary case, primitive ideal reduction 
qffmsiselic(m,D,L,Q,P)  quadratic function field over modular singles is 
			element of an ideal class 
qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic function field over modular singles 
			is equal ideal special 
qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic function field over modular singles, 
			imaginary case, sparse representation, reduction of 
			a primitive ideal 
qffmsordsici(m,D,Q,P,OS) quadratic function field over modular singles order 
			of one single ideal class, imaginary case 
qffmsordsicr(m,D,d,LE,ID,OS) quadratic function field over modular singles 
			order of one single ideal class, real case 
qffmspidgenr(m,D,Q,P,G,pB) quadratic function field over modular singles, 
			principal ideal generating element, real case, 
qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic function field over modular 
			singles primitive ideal product 
qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic function field over modular 
			singles primitive ideal product, special version 
qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic function field over modular singles 
			primitive ideal square 
qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic function field over modular 
			singles primitive ideal square, special version 
qffmsreg(m,P)           quadratic function field over modular singles 
			regulator 
qffmsregbg(m,D)         quadratic function field over modular singles 
			regulator, baby step - giant step version 
qffmsregbg1(m,D,s)      quadratic function field over modular singles 
			regulator, baby step - giant step version, first 
			case 
qffmsregbg2(m,D,s)      quadratic function field over modular singles 
			regulator, baby step - giant step version, second 
			case 
qffmsregbg3(m,D,s)      quadratic function field over modular singles 
			regulator, baby step - giant step version, third 
			case 
qffmsregbg4(m,D,s)      quadratic function field over modular singles 
			regulator, baby step - giant step version, fourth 
			case 
qffmsregbs(m,D)         quadratic function field over modular singles 
			regulator, baby step version 
qffmsregobg(m,D)        quadratic function field over modular singles 
			regulator, original baby step - giant step version 
qffmsregobs(m,D)        quadratic function field over modular singles 
			regulator, original baby step version 
qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function field over modular 
			singles, real case, reduction of a primitive ideal 
qffmsrqired(m,D,d,Q,P,pPr) quadratic function field over modular singles 
			reduction of a real quadratic irrational 
qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function field over modular 
			singles, real case, sparse representation, 
			reduction of a primitive ideal 
qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic function field over modular 
			singles, sparse representation, primitive ideal 
			product 
qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic function field over modular 
			singles, sparse representation, primitive ideal 
			product, special version 
qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function field over modular 
			singles, sparse representation, primitive ideal 
			square, special version 
qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic function field over modular singles, 
			sparse representation, primitive ideal square 
qffmssrqired(m,D,d,Q,P,pPr) quadratic function field over modular singles, 
			sparse representation, reduction of a real 
			quadratic irrational 
qffmszcgiti(m,D,LG,IT)  quadratic function field over modular singles zero 
			class group isomorphy type, imaginary case 
qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function field over modular singles 
			zero class group isomorphy type, real case 
qnfaval(D,p,a)          quadratic number field additive valuation 
qnfconj(D,a)            quadratic number field conjugate element 
qnfdegrescf(D,p)        quadratic number field degrees of the residue class 
			fields 
qnfdif(D,a,b)           (MACRO) quadratic number field element difference 
qnfdirchar(D,z)         quadratic number field Dirichlet character 
qnfdisc(D)              quadratic number field discriminant 
qnfelcomp(D,A,B)        quadratic number field element comparison 
qnfexp(D,a,e)           quadratic number field element exponentiation 
qnfidcomp(D,A,B)        quadratic number field ideal comparison 
qnfidexp(D,A,e)         quadratic number field ideal exponentiation 
qnfidif(D,a,b)          (MACRO) quadratic number field element, integer, 
			difference 
qnfidone(D)             (MACRO) quadratic number field ideal one 
qnfidprod(D,A,B)        quadratic number field ideal product 
qnfidsquare(D,A)        quadratic number field ideal square 
qnfielpifacts(D,a,L)    quadratic number field integral element prime ideal 
			factorization, special version 
qnfielpiord(D,P,pi,z,a) quadratic number field, integral element, prime 
			ideal order 
qnfintbas(D)            quadratic number field integral basis 
qnfinv(D,a)             quadratic number field element inverse element 
qnfiprod(D,a,b)         quadratic number field element, integer, product 
qnfiquot(D,a,b)         quadratic number field element, integer, quotient 
qnfisum(D,a,b)          quadratic number field element, integer, sum 
qnfminrep(D,a)          quadratic number field element minimal 
			representation 
qnfneg(D,a,b)           quadratic number field element negation 
qnfnorm(D,a)            quadratic number field norm of an element 
qnfpifact(D,a)          quadratic number field element prime ideal 
			factorization 
qnfpihom(D,P,pi,z,a)    quadratic number field prime ideal homomorphism 
qnfpiord(D,P,pi,z,a)    quadratic number field element prime ideal order 
qnfprod(D,a,b)          quadratic number field element product 
qnfquot(D,a,b)          (MACRO) quadratic number field element quotient 
qnframind(D,p)          quadratic number field ramification indices 
qnfrdif(D,a,b)          (MACRO) quadratic number field element, rational 
			number, difference 
qnfrprod(D,a,b)         quadratic number field element, rational number, 
			product 
qnfrquot(D,a,b)         (MACRO) quadratic number field element, rational 
			number, quotient 
qnfrsum(D,a,b)          quadratic number field element, rational number, 
			sum 
qnfsquare(D,a)          quadratic number field element square 
qnfsum(D,a,b)           quadratic number field element sum 
qnfsysrmodpi(D,P,pi,z,k) quadratic number field system of representatives 
			modulo a prime ideal 
qnftrace(D,a)           quadratic number field trace of an element 
qnfunit(D)              quadratic number field unit group 
quadratic               field iprniqf(p,D) integer prime representation as 
			a norm in an imaginary 
quadratic               forms iprpdbqf(D,h1,h2) integer primitive reduced 
			positive definite binary 
quadratic               function field over modular singles divisor class 
			number qffmsdcn(m,P) 
quadratic               function field over modular singles divisor class 
			number subroutine 1 qffmsdcns1(m,P) 
quadratic               function field over modular singles divisor class 
			number subroutine 2 qffmsdcns2(m,P) 
quadratic               function field over modular singles divisor class 
			number subroutine 3 qffmsdcns3(m,P) 
quadratic               function field over modular singles fundamental 
			unit, baby step version qffmsfubs(m,D) 
quadratic               function field over modular singles fundamental 
			unit, original version qffmsfuobs(m,D) 
quadratic               function field over modular singles ideal class 
			group generators and isomorphy type, imaginary case 
			qffmsicggii(m,D,H,L,pIT) 
quadratic               function field over modular singles ideal class 
			group generators and isomorphy type, real case 
			qffmsicggir(m,D,d,H,L,pIT) 
quadratic               function field over modular singles ideal class 
			group structure, imaginary case qffmsicgsti(m,D,L) 
quadratic               function field over modular singles ideal class 
			group structure, real case 
			qffmsicgstr(m,D,d,LG,pHid) 
quadratic               function field over modular singles ideal class 
			group system of representatives 
			qffmsicgrep(m,D,pHid) 
quadratic               function field over modular singles ideal class 
			group system of representatives, imaginary case 
			qffmsicgri(m,D,pHid) 
quadratic               function field over modular singles ideal class 
			group system of representatives, real case 
			qffmsicgrr(m,D,d) 
quadratic               function field over modular singles ideal class 
			number qffmsicn(m,P) 
quadratic               function field over modular singles is element of 
			an ideal class qffmsiselic(m,D,L,Q,P) 
quadratic               function field over modular singles is equal ideal 
			special qffmsiseqids(m,D,Q1,P1,Q2,P2) 
quadratic               function field over modular singles order of one 
			single ideal class, imaginary case 
			qffmsordsici(m,D,Q,P,OS) 
quadratic               function field over modular singles order of one 
			single ideal class, real case 
			qffmsordsicr(m,D,d,LE,ID,OS) 
quadratic               function field over modular singles primitive ideal 
			product qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) 
quadratic               function field over modular singles primitive ideal 
			product, special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) 
quadratic               function field over modular singles primitive ideal 
			square qffmspidsqu(m,D,Q1,P1,pQ,pP) 
quadratic               function field over modular singles primitive ideal 
			square, special version 
			qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) 
quadratic               function field over modular singles reduction of a 
			real quadratic irrational 
			qffmsrqired(m,D,d,Q,P,pPr) 
quadratic               function field over modular singles regulator 
			qffmsreg(m,P) 
quadratic               function field over modular singles regulator, baby 
			step - giant step version qffmsregbg(m,D) 
quadratic               function field over modular singles regulator, baby 
			step - giant step version, first case 
			qffmsregbg1(m,D,s) 
quadratic               function field over modular singles regulator, baby 
			step - giant step version, fourth case 
			qffmsregbg4(m,D,s) 
quadratic               function field over modular singles regulator, baby 
			step - giant step version, second case 
			qffmsregbg2(m,D,s) 
quadratic               function field over modular singles regulator, baby 
			step - giant step version, third case 
			qffmsregbg3(m,D,s) 
quadratic               function field over modular singles regulator, baby 
			step version qffmsregbs(m,D) 
quadratic               function field over modular singles regulator, 
			original baby step - giant step version 
			qffmsregobg(m,D) 
quadratic               function field over modular singles regulator, 
			original baby step version qffmsregobs(m,D) 
quadratic               function field over modular singles zero class 
			group isomorphy type, imaginary case 
			qffmszcgiti(m,D,LG,IT) 
quadratic               function field over modular singles zero class 
			group isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) 
quadratic               function field over modular singles, imaginary 
			case, primitive ideal reduction 
			qffmsipidred(m,D,Q,P,pQr,pPr) 
quadratic               function field over modular singles, imaginary 
			case, sparse representation, reduction of a 
			primitive ideal qffmsispidrd(m,D,Q,P,pQr,pPr) 
quadratic               function field over modular singles, principal 
			ideal generating element, real case, 
			qffmspidgenr(m,D,Q,P,G,pB) 
quadratic               function field over modular singles, real case, 
			reduction of a primitive ideal 
			qffmsrpidred(m,D,d,Q,P,pQr,pPr) 
quadratic               function field over modular singles, real case, 
			sparse representation, reduction of a primitive 
			ideal qffmsrspidrd(m,D,d,Q,P,pQr,pPr) 
quadratic               function field over modular singles, sparse 
			representation, primitive ideal product 
			qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) 
quadratic               function field over modular singles, sparse 
			representation, primitive ideal product, special 
			version qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) 
quadratic               function field over modular singles, sparse 
			representation, primitive ideal square 
			qffmsspidsqu(m,D,Q1,P1,pQ,pP) 
quadratic               function field over modular singles, sparse 
			representation, primitive ideal square, special 
			version qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) 
quadratic               function field over modular singles, sparse 
			representation, reduction of a real quadratic 
			irrational qffmssrqired(m,D,d,Q,P,pPr) 
quadratic               irrational qffmsrqired(m,D,d,Q,P,pPr) quadratic 
			function field over modular singles reduction of a 
			real 
quadratic               irrational qffmssrqired(m,D,d,Q,P,pPr) quadratic 
			function field over modular singles, sparse 
			representation, reduction of a real 
quadratic               number field Dirichlet character qnfdirchar(D,z) 
quadratic               number field additive valuation qnfaval(D,p,a) 
quadratic               number field conjugate element qnfconj(D,a) 
quadratic               number field degrees of the residue class fields 
			qnfdegrescf(D,p) 
quadratic               number field discriminant qnfdisc(D) 
quadratic               number field element comparison qnfelcomp(D,A,B) 
quadratic               number field element difference qnfdif(D,a,b) 
			(MACRO) 
quadratic               number field element exponentiation qnfexp(D,a,e) 
quadratic               number field element factor exponent list 
			fputqnffel(D,L,pf) file put 
quadratic               number field element factor exponent list 
			putqnffel(D,L) (MACRO) put 
quadratic               number field element fgetqnfel(D,pf) file get 
quadratic               number field element fputqnfel(D,a,pf) file put 
quadratic               number field element getqnfel(D) (MACRO) get 
quadratic               number field element integer? isqnfint(D,a) (MACRO) 
			is 
quadratic               number field element integral element? 
			isqnfiel(D,a) is 
quadratic               number field element inverse element qnfinv(D,a) 
quadratic               number field element itoqnf(D,a) (MACRO) integer to 
quadratic               number field element minimal representation 
			qnfminrep(D,a) 
quadratic               number field element negation qnfneg(D,a,b) 
quadratic               number field element one? isqnfone(D,a) (MACRO) is 
quadratic               number field element power of prime ideal 
			homomorphism zero? isqnfppihom0(D,P,k,pi,z,a) is 
quadratic               number field element prime ideal factorization 
			qnfpifact(D,a) 
quadratic               number field element prime ideal order 
			qnfpiord(D,P,pi,z,a) 
quadratic               number field element product qnfprod(D,a,b) 
quadratic               number field element putqnfel(D,a) (MACRO) put 
quadratic               number field element quotient qnfquot(D,a,b) 
			(MACRO) 
quadratic               number field element rational isqnfrat(D,a) (MACRO) 
			is 
quadratic               number field element rtoqnf(D,A) (MACRO) rational 
			number to 
quadratic               number field element square qnfsquare(D,a) 
quadratic               number field element sum qnfsum(D,a,b) 
quadratic               number field element, difference iqnfdif(D,a,b) 
			(MACRO) integer, 
quadratic               number field element, difference rqnfdif(D,a,b) 
			(MACRO) rational number, 
quadratic               number field element, integer, difference 
			qnfidif(D,a,b) (MACRO) 
quadratic               number field element, integer, product 
			qnfiprod(D,a,b) 
quadratic               number field element, integer, quotient 
			qnfiquot(D,a,b) 
quadratic               number field element, integer, sum qnfisum(D,a,b) 
quadratic               number field element, quotient iqnfquot(D,a,b) 
			integer, 
quadratic               number field element, quotient rqnfquot(D,a,b) 
			rational number, 
quadratic               number field element, rational number, difference 
			qnfrdif(D,a,b) (MACRO) 
quadratic               number field element, rational number, product 
			qnfrprod(D,a,b) 
quadratic               number field element, rational number, quotient 
			qnfrquot(D,a,b) (MACRO) 
quadratic               number field element, rational number, sum 
			qnfrsum(D,a,b) 
quadratic               number field fundamental unit rqnffu(D,pl) real 
quadratic               number field ideal comparison qnfidcomp(D,A,B) 
quadratic               number field ideal exponentiation qnfidexp(D,A,e) 
quadratic               number field ideal fputqnfid(D,A,pf) file put 
quadratic               number field ideal one qnfidone(D) (MACRO) 
quadratic               number field ideal one? isqnfidone(D,A) is 
quadratic               number field ideal product qnfidprod(D,A,B) 
quadratic               number field ideal putqnfid(D,A) (MACRO) put 
quadratic               number field ideal square qnfidsquare(D,A) 
quadratic               number field integral basis qnfintbas(D) 
quadratic               number field integral element prime ideal 
			factorization, special version qnfielpifacts(D,a,L) 
quadratic               number field norm of an element qnfnorm(D,a) 
quadratic               number field prime ideal homomorphism 
			qnfpihom(D,P,pi,z,a) 
quadratic               number field ramification indices qnframind(D,p) 
quadratic               number field system of representatives modulo a 
			prime ideal qnfsysrmodpi(D,P,pi,z,k) 
quadratic               number field to elliptic curve with integral 
			coefficients ecqnftoeci(D,L) elliptic curve over 
quadratic               number field trace of an element qnftrace(D,a) 
quadratic               number field unit group qnfunit(D) 
quadratic               number field, Tate's algorithm 
			ecqnftatealg(D,LC,LTV,P,pi,z,n) elliptic curve over 
quadratic               number field, actual model, Tate value b2 
			ecqnfacb2(E) elliptic curve over 
quadratic               number field, actual model, Tate value b4 
			ecqnfacb4(E) elliptic curve over 
quadratic               number field, actual model, Tate value b6 
			ecqnfacb6(E) elliptic curve over 
quadratic               number field, actual model, Tate value b8 
			ecqnfacb8(E) elliptic curve over 
quadratic               number field, actual model, Tate value c4 
			ecqnfacc4(E) elliptic curve over 
quadratic               number field, actual model, Tate value c6 
			ecqnfacc6(E) elliptic curve over 
quadratic               number field, actual model, discriminant 
			ecqnfacdisc(E) elliptic curve over 
quadratic               number field, actual model, factorization of the 
			norm of the discriminant ecqnfacfndisc(E) elliptic 
			curve over 
quadratic               number field, actual model, norm of the 
			discriminant ecqnfacndisc(E) elliptic curve over 
quadratic               number field, actual model, prime ideal 
			factorization of the discriminant ecqnfacpifdi(E) 
			elliptic curve over 
quadratic               number field, conductor ecqnfcond(E) elliptic curve 
			over 
quadratic               number field, field discriminant ecqnfflddisc(E) 
			(MACRO) elliptic curve over 
quadratic               number field, field discriminant modulo 4 
			ecqnfdmod4(E) (MACRO) elliptic curve over 
quadratic               number field, initialization 
			ecqnfinit(D,a1,a2,a3,a4,a6) elliptic curve over 
quadratic               number field, integral element, prime ideal order 
			qnfielpiord(D,P,pi,z,a) 
quadratic               number field, j-invariant ecqnfjinv(E) elliptic 
			curve over 
quadratic               step on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
			modular integers, modular ideal, Hensel lemma 
quadratic               step pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial 
			over integers, modular ideal, Hensel lemma 
quadratic               step pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) 
			polynomial over modular integers, modular ideal, 
			Hensel lemma 
quadratic               step upihlqs(p,p_k,p_l,P,L1,L2,A) univariate 
			polynomial over integers, Hensel lemma 
quadratic               step upprmsp1hqs(p,F,T,L1,L2,A) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Hensel 
quadratic               step with respect to integer prime 
			upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over integers, Hensel lemma 
quantifier              free formula dippiqff(r1,r2,s,PL,CONDS,fac) 
			distributive polynomial over polynomials over 
			integers 
quantifier              free formula fputdippiqff(r1,r2,QFFL,VL1,VL2,pf) 
			file put distributive polynomial over polynomials 
			over integers 
quantifier              free formula putdippiqff(r1,r2,QFFL,VL1,VL2) 
			(MACRO) put distributive polynomial over 
			polynomials over integers 
quotient                (rekursiv) pgfsgfsquot(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic, 
			Galois-field with single characteristic element 
quotient                (rekursiv) piiquot(r,P,A) polynomial over integers, 
			integer 
quotient                (rekursiv) pmimiquot(r,m,P,a) polynomial over 
			modular integers, modular integer 
quotient                (rekursiv) pmiupmiquot(r,m,P1,P2) polynomial over 
			modular integers, univariate polynomial over 
			modular integers 
quotient                (rekursiv) pmsmsquot(r,m,P,a) polynomial over 
			modular singles, modular single 
quotient                (rekursiv) pmsupmsquot(r,m,P1,P2) polynomial over 
			modular singles, univariate polynomial over modular 
			singles 
quotient                (rekursiv) pnfnfquot(r,F,P,a) polynomial over 
			number field, number field element 
quotient                and remainder (rekursiv) pgf2qrem(r,G,P1,P2,pR) 
			polynomial over Galois-field with characteristic 2 
quotient                and remainder (rekursiv) pgfsqrem(r,p,AL,P1,P2,pR) 
			polynomial over Galois-field with single 
			characteristic 
quotient                and remainder (rekursiv) piqrem(r,P1,P2,pR) 
			polynomial over integers 
quotient                and remainder (rekursiv) pmiqrem(r,M,P1,P2,pR) 
			polynomial over modular integers 
quotient                and remainder (rekursiv) pmsqrem(r,m,P1,P2,pR) 
			polynomial over modular singles 
quotient                and remainder (rekursiv) pnfqrem(r,F,P1,P2,pR) 
			polynomial over number field 
quotient                and remainder (rekursiv) prfmsp1qrem(r,p,P1,P2,pR) 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, 
quotient                and remainder (rekursiv) prqrem(r,P1,P2,pR) 
			polynomial over rationals 
quotient                and remainder flqrem(A,B,pQ,pR) floating 
quotient                and remainder iqrem(A,B,pQ,pR) integer 
quotient                and remainder isqrem(A,b,pQ,pr) integer 
			single-precision 
quotient                and remainder pmimidqrem(r,M,S,P1,P2,pR) polynomial 
			over modular integers monic, modular ideal 
quotient                and remainder special version 3 iqrem_3(A,B,pQ,pR) 
			integer 
quotient                and remainder sqrem(a,b,d,pq,pr) single-precision 
quotient                and remainder udpmiqrem(m,P1,P2,pP3) univariate 
			dense polynomial over modular integers 
quotient                and remainder udpmsqrem(m,P1,P2,pP3) univariate 
			dense polynomial over modular singles 
quotient                and remainder udprqrem(P1,P2,pP3) univariate dense 
			polynomial over rationals 
quotient                and remainder, lists only iqrem_lo(A,B,pQ,pR) 
			integer 
quotient                and remainder, old version iqrem_2(A,B,pQ,pR) 
			integer 
quotient                by power of main variable ppmvquot(r,P,n) 
			polynomial 
quotient                by power of variable (rekursiv) ppvquot(r,P,i,n) 
			polynomial 
quotient                cdprfmsp1upq(p,F,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, univariate polynomial over 
			modular single prime 
quotient                cdpriquot(P,I) common denominator polynomial over 
			the rationals integer 
quotient                ciquot(v,i) complex integer 
quotient                cquot(v,w) complex 
quotient                flquot(f,g) floating point 
quotient                flsquot(f,n) floating point single 
quotient                gf2quot(G,a,b) Galois-field with characteristic 2 
quotient                gfsquot(p,AL,a,b) Galois-field with single 
			characteristic 
quotient                ip2quot(A,n) integer power of 2 
quotient                iqnfquot(D,a,b) integer, quadratic number field 
			element, 
quotient                iquot(A,B) (MACRO) integer 
quotient                isquot(A,b) (MACRO) integer single-precision 
quotient                miquot(M,A,B) (MACRO) modular integer 
quotient                msquot(m,a,b) (MACRO) modular single 
quotient                nfquot(F,a,b) number field 
quotient                nfsquot(F,a,b) number field, sparse representation, 
quotient                pfquot(p,a,b) p-adic field 
quotient                pgf2quot(r,G,P1,P2) (MACRO) polynomial over 
			Galois-field with characteristic 2 
quotient                pgfsquot(r,p,AL,P1,P2) (MACRO) polynomial over 
			Galois-field with single characteristic 
quotient                piquot(r,P1,P2) (MACRO) polynomial over integers 
quotient                pmiquot(r,M,P1,P2) (MACRO) polynomial over modular 
			integers 
quotient                pmsquot(r,m,P1,P2) (MACRO) polynomial over modular 
			singles 
quotient                pnfquot(r,F,P1,P2) (MACRO) polynomial over number 
			field 
quotient                prquot(r,P1,P2) (MACRO) polynomial over rationals 
quotient                prrquot(r,P,A) polynomial over rationals, rational 
quotient                qnfiquot(D,a,b) quadratic number field element, 
			integer, 
quotient                qnfquot(D,a,b) (MACRO) quadratic number field 
			element 
quotient                qnfrquot(D,a,b) (MACRO) quadratic number field 
			element, rational number, 
quotient                rfrquot(r,R1,R2) rational function over the 
			rationals 
quotient                rqnfquot(D,a,b) rational number, quadratic number 
			field element, 
quotient                rquot(R,S) (MACRO) rational number 
quotient                udpmiquot(m,P1,P2) (MACRO) univariate dense 
			polynomial over modular integers 
quotient                udpmsquot(m,P1,P2) (MACRO) univariate dense 
			polynomial over modular singles 
quotient,               transcendence degree 1 rfmsp1quot(p,R1,R2) rational 
			function over modular single prime 
rabs(R)                 (MACRO) rational number absolute value 
rabsheight(r)           rational number absolute height 
ramification            indices qnframind(D,p) quadratic number field 
random                  divisor search (rekursiv) irds(n,G,p) integer 
random                  generator upgf2gen(G,m) univariate polynomial over 
			Galois-field with characteristic 2, 
random                  permutation lsrandperm(n) list of singles 
random                  prime irandprime(a1,a2,n) integer 
randomize               gf2elrand(G) Galois-field with characteristic 2 
			element 
randomize               gfselrand(p,AL) Galois-field with single 
			characteristic, element 
randomize               irand(G) integer 
randomize               masrand(m,n,grenze) matrix of singles 
randomize               upgfsrand(p,AL,m) univariate polynomial over 
			Galois-field with single characteristic 
randomize               upmirand(ip,m) univariate polynomial over modular 
			integers 
randomize,              alternative version irand_2(u) integer 
randomize,              positive degree upgfsrandpd(p,AL,m) univariate 
			polynomial over Galois-field with single 
			characteristic 
rank                    ecrrank(E) elliptic curve over the rationals, 
rank                    magfsrk(p,AL,M) matrix of Galois-field with single 
			characteristic elements 
rank                    manfrk(F,M) matrix of number field elements 
rank                    manfsrk(F,M) matrix of number field elements, 
			sparse representation, 
rank                    marfmsp1rk(p,M) matrix of rational functions over 
			modular single primes, transcendence degree 1, 
rank                    marfrrk(r,M) matrix of rational functions over 
			rationals 
rank                    marrk(M) matrix of rationals 
rational                ) model eciminbtac(E) elliptic curve with integer 
			coefficients, minimal model, birational 
			transformation to actual ( 
rational                ) model ecisnfbtac(E) elliptic curve with integer 
			coefficients, short normal form, birational 
			transformation to actual ( 
rational                additive m-adic value raval(m,R) 
rational                additive value with respect to integer 
			ravalint(M,R) 
rational                function over modular single prime construction, 
			transcendence degree 1 rfmsp1cons(p,P1,P2) 
rational                function over modular single prime difference, 
			transcendence degree 1 rfmsp1dif(p,R1,R2) 
rational                function over modular single prime negation, 
			transcendence degree 1 rfmsp1neg(p,R) 
rational                function over modular single prime product, 
			transcendence degree 1 rfmsp1prod(p,R1,R2) 
rational                function over modular single prime quotient, 
			transcendence degree 1 rfmsp1quot(p,R1,R2) 
rational                function over modular single prime sum, 
			transcendence degree 1 rfmsp1sum(p,R1,R2) 
rational                function over modular single prime, transcendence 
			degree 1 ? isrfmsp1(p,R) is 
rational                function over modular single prime, transcendence 
			degree 1 fputrfmsp1(p,R,V,pf) (MACRO) file put 
rational                function over modular single prime, transcendence 
			degree 1 pmstorfmsp1(p,P) (MACRO) polynomial over 
			modular singles to 
rational                function over modular single prime, transcendence 
			degree 1 putrfmsp1(p,R,V) (MACRO) put 
rational                function over modular single prime, transcendence 
			degree 1, product (rekursiv) prfmsp1rfprd(r,p,P,a) 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, 
rational                function over modular single primes, transcendence 
			degree 1 fgetrfmsp1(p,V,pf) file get 
rational                function over modular single primes, transcendence 
			degree 1 getrfmsp1(p,V) (MACRO) get 
rational                function over modular single primes, transcendence 
			degree 1, inverse rfmsp1inv(p,R) 
rational                function over rationals fgetrfr(r,V,pf) file get 
rational                function over rationals fputrfr(r,R,V,pf) file put 
rational                function over rationals getrfr(r,V) (MACRO) get 
rational                function over rationals one isrfrone(r,A) is 
rational                function over rationals putrfr(r,R,V) (MACRO) put 
rational                function over rationals rtorfr(r,R) rational number 
			to 
rational                function over the rationals ? isrfr(r,R) is 
rational                function over the rationals construction 
			rfrcons(r,P1,P2) 
rational                function over the rationals difference 
			rfrdif(r,R1,R2) 
rational                function over the rationals diprfrtorfr(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals to 
rational                function over the rationals inverse rfrinv(r,R) 
rational                function over the rationals negation rfrneg(r,R) 
rational                function over the rationals pitorfr(r,P) polynomial 
			over integers to 
rational                function over the rationals product 
			diprfrrfprod(r1,r2,P,A) distributive polynomial 
			over rational functions over the rationals 
rational                function over the rationals product 
			rfrprod(r,R1,R2) 
rational                function over the rationals prtorfr(r,P) polynomial 
			over the rationals to 
rational                function over the rationals quotient 
			rfrquot(r,R1,R2) 
rational                function over the rationals sum rfrsum(r,R1,R2) 
rational                function over the rationals to distributive 
			polynomial over rational functions over the 
			rationals rfrtodiprfr(r1,r2,F) 
rational                function over the rationals transformation 
			rfrtransf(r1,R1,V1,r2,R2,V2,Vn,pV3) 
rational                functions over modular single prime, transcendence 
			degree 1 cdprfmsp1fup(p,P) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, from 
			univariate polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1 cdprfmsp1lfm(M,p) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, list from 
			common denominator matrix of 
rational                functions over modular single prime, transcendence 
			degree 1 clfcdprfmsp1(P,n) coefficient list from 
			common denominator polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1 sclfuprfmsp1(P,n) special coefficient list 
			from univariate polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1 uprfmsp1fcdp(p,P) univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from common denominator 
			polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, derivation, main variable 
			prfmsp1deriv(r,p,P) polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, difference (rekursiv) 
			prfmsp1dif(r,p,P1,P2) polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, extended greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over 
rational                functions over modular single prime, transcendence 
			degree 1, from coefficient list cdprfmsp1fcl(L,p) 
			common denominator polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, from common denominator polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1 uprfmsp1fcdp(p,P) univariate 
			polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, from special coefficient list 
			uprfmsp1fscl(L) univariate polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, from univariate polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1fup(p,P) common denominator 
			polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, hermitian reduction cdmarfmsp1hr(p,M) 
			common denominator matrix of 
rational                functions over modular single prime, transcendence 
			degree 1, identity construction cdmarfmsp1id(n) 
			common denominator matrix of 
rational                functions over modular single prime, transcendence 
			degree 1, inverse cdprfmsp1inv(p,F,A) common 
			denominator polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, list from common denominator matrix of 
			rational functions over modular single prime, 
			transcendence degree 1 cdprfmsp1lfm(M,p) common 
			denominator polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, negation (rekursiv) prfmsp1neg(r,p,P) 
			polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, product (rekursiv) prfmsp1prod(r,p,P1,P2) 
			polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, quotient and remainder (rekursiv) 
			prfmsp1qrem(r,p,P1,P2,pR) polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, rational function over modular single 
			prime, transcendence degree 1, product (rekursiv) 
			prfmsp1rfprd(r,p,P,a) polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, sum (rekursiv) prfmsp1sum(r,p,P1,P2) 
			polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, sum cdprfmsp1sum(p,P1,P2) common 
			denominator polynomial over 
rational                functions over modular single prime, transcendence 
			degree 1, univariate polynomial over modular single 
			prime quotient cdprfmsp1upq(p,F,P) common 
			denominator polynomial over 
rational                functions over modular single primes transcendence 
			degree 1, determinant marfmsp1det(p,M) matrix of 
rational                functions over modular single primes transcendence 
			degree 1, difference marfmsp1dif(p,M,N) (MACRO) 
			matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 ? ismarfmsp1(p,M) (MACRO) is matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 ? isvecrfmsp1(p,V) (MACRO) is vector of 
rational                functions over modular single primes, transcendence 
			degree 1 fgetmarfmsp1(p,V,pf) (MACRO) file get 
			matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 fgetvrfmsp1(p,VL,pf) (MACRO) file get 
			vector of 
rational                functions over modular single primes, transcendence 
			degree 1 fputmarfmsp1(p,M,V,pf) (MACRO) file put 
			matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 fputvrfmsp1(p,V,VL,pf) (MACRO) file put 
			vector of 
rational                functions over modular single primes, transcendence 
			degree 1 getmarfmsp1(p,V) (MACRO) get matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 getvecrfmsp1(p,VL) (MACRO) get vector of 
rational                functions over modular single primes, transcendence 
			degree 1 mpmstmrfmsp1(p,M) matrix of polynomials 
			over modular singles to matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 putmarfmsp1(p,M,V) (MACRO) put matrix of 
rational                functions over modular single primes, transcendence 
			degree 1 putvecrfmsp1(p,V,VL) (MACRO) put vector of 
rational                functions over modular single primes, transcendence 
			degree 1 vpmstvrfmsp1(p,V) vector of polynomials 
			over modular singles to vector of 
rational                functions over modular single primes, transcendence 
			degree 1, construction 1 marfmsp1c1(p,n) (MACRO) 
			matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, difference vecrfmsp1dif(p,U,V) (MACRO) 
			vector of 
rational                functions over modular single primes, transcendence 
			degree 1, exponentiation marfmsp1exp(p,M,n) matrix 
			of 
rational                functions over modular single primes, transcendence 
			degree 1, inverse marfmsp1inv(p,M) matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, linear combination 
			vecrfmsp1lc(p,F1,F2,V1,V2) vector of 
rational                functions over modular single primes, transcendence 
			degree 1, module homomorphism cdprfmsp1mh(p,P,M) 
			common denominator polynomial over 
rational                functions over modular single primes, transcendence 
			degree 1, negation marfmsp1neg(p,M) (MACRO) matrix 
			of 
rational                functions over modular single primes, transcendence 
			degree 1, negation vecrfmsp1neg(p,V) (MACRO) vector 
			of 
rational                functions over modular single primes, transcendence 
			degree 1, null space basis marfmsp1nsb(p,M) matrix 
			of 
rational                functions over modular single primes, transcendence 
			degree 1, product marfmsp1prod(p,M,N) (MACRO) 
			matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, rank marfmsp1rk(p,M) matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, scalar multiplication marfmsp1smul(p,M,F) 
			matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, scalar multiplication vecrfmsp1sm(p,F,V) 
			vector of 
rational                functions over modular single primes, transcendence 
			degree 1, scalar product vecrfmsp1sp(p,V,W) vector 
			of 
rational                functions over modular single primes, transcendence 
			degree 1, solution of a system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, sum marfmsp1sum(p,M,N) (MACRO) matrix of 
rational                functions over modular single primes, transcendence 
			degree 1, sum vecrfmsp1sum(p,U,V) (MACRO) vector of 
rational                functions over modular single primes, transcendence 
			degree 1, vector multiplication marfmsp1vmul(p,A,x) 
			(MACRO) matrix of 
rational                functions over rationals ? ismarfr(r,M) (MACRO) is 
			matrix of 
rational                functions over rationals ? isvecrfr(r,V) (MACRO) is 
			vector of 
rational                functions over rationals characteristic polynomial 
			marfrchpol(r,M) matrix of 
rational                functions over rationals construction 1 
			marfrcons1(r,n) (MACRO) matrix of 
rational                functions over rationals determinant marfrdet(r,M) 
			matrix of 
rational                functions over rationals difference marfrdif(r,M,N) 
			(MACRO) matrix of 
rational                functions over rationals difference 
			vecrfrdif(r,U,V) (MACRO) vector of 
rational                functions over rationals exponentiation 
			marfrexp(r,M,n) matrix of 
rational                functions over rationals fgetmarfr(r,V,pf) (MACRO) 
			file get matrix of 
rational                functions over rationals fgetvecrfr(r,VL,pf) 
			(MACRO) file get vector of 
rational                functions over rationals fputmarfr(r,M,V,pf) 
			(MACRO) file put matrix of 
rational                functions over rationals fputvecrfr(r,V,VL,pf) 
			(MACRO) file put vector of 
rational                functions over rationals getmarfr(r,V) (MACRO) get 
			matrix of 
rational                functions over rationals getvecrfr(r,VL) (MACRO) 
			get vector of 
rational                functions over rationals inverse marfrinv(r,M) 
			matrix of 
rational                functions over rationals linear combination 
			vecrfrlc(r,F1,F2,V1,V2) vector of 
rational                functions over rationals mapitomarfr(r,M) matrix of 
			polynomials over integers to matrix of 
rational                functions over rationals maprtomarfr(r,M) matrix of 
			polynomials over rationals to matrix of 
rational                functions over rationals negation marfrneg(r,M) 
			(MACRO) matrix of 
rational                functions over rationals negation vecrfrneg(r,V) 
			(MACRO) vector of 
rational                functions over rationals product marfrprod(r,M,N) 
			(MACRO) matrix of 
rational                functions over rationals putmarfr(r,M,V) (MACRO) 
			put matrix of 
rational                functions over rationals putvecrfr(r,V,VL) (MACRO) 
			put vector of 
rational                functions over rationals rank marfrrk(r,M) matrix 
			of 
rational                functions over rationals scalar multiplication 
			marfrsmul(r,M,F) matrix of 
rational                functions over rationals scalar multiplication 
			vecrfrsmul(r,F,V) vector of 
rational                functions over rationals scalar product 
			vecrfrsprod(r,V,W) vector of 
rational                functions over rationals solution of a system of 
			linear equations marfrssle(r,A,b,pX,pN) matrix of 
rational                functions over rationals sum marfrsum(r,M,N) 
			(MACRO) matrix of 
rational                functions over rationals sum vecrfrsum(r,U,V) 
			(MACRO) vector of 
rational                functions over rationals vecpitovrfr(r,V) vector of 
			polynomials over integers to vector of 
rational                functions over rationals vecprtovrfr(r,V) vector of 
			polynomials over rationals to vector of 
rational                functions over rationals vector multiplication 
			marfrvecmul(r,A,x) (MACRO) matrix of 
rational                functions over rationals, null space basis 
			marfrnsb(r,M) matrix of 
rational                functions over the rationals Groebner basis 
			augmentation diprfrgba(r1,r2,PL,P) distributive 
			polynomial over 
rational                functions over the rationals Groebner basis 
			diprfrgb(r1,r2,PL) distributive polynomial over 
rational                functions over the rationals Groebner basis 
			recursion diprfrgbr(r1,r2,PL) distributive 
			polynomial over 
rational                functions over the rationals S-polynomial 
			diprfrsp(r1,r2,P1,P2) distributive polynomial over 
rational                functions over the rationals difference 
			diprfrdif(r1,r2,P1,P2) distributive polynomial over 
rational                functions over the rationals in graduated 
			lexicographical order diprfrlotglo(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over 
rational                functions over the rationals in lexicographical 
			order to distributive polynomial over rational 
			functions over the rationals in graduated 
			lexicographical order diprfrlotglo(r1,r2,P) 
			distributive polynomial over 
rational                functions over the rationals in lexicographical 
			order to distributive polynomial over rational 
			functions over the rationals in lexicographical 
			order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive polynomial over 
rational                functions over the rationals in lexicographical 
			order to distributive polynomial over rational 
			functions over the rationals with total degree 
			ordering diprfrlottdo(r1,r2,P) distributive 
			polynomial over 
rational                functions over the rationals in lexicographical 
			order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over 
rational                functions over the rationals list 
			fgetdiprfrl(r1,r2,VL1,VL2,pf) file get distributive 
			polynomial over 
rational                functions over the rationals list 
			fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file put 
			distributive polynomial over 
rational                functions over the rationals list 
			getdiprfrl(r1,r2,VL1,VL2) (MACRO) get distributive 
			polynomial over 
rational                functions over the rationals list 
			putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive polynomial over 
rational                functions over the rationals monic 
			diprfrmonic(r1,r2,P) distributive polynomial over 
rational                functions over the rationals negation 
			diprfrneg(r1,r2,P) distributive polynomial over 
rational                functions over the rationals one ? 
			isdiprfrone(r1,r2,P) is distributive polynomial 
			over 
rational                functions over the rationals product 
			diprfrprod(r1,r2,P1,P2) distributive polynomial 
			over 
rational                functions over the rationals rational function over 
			the rationals product diprfrrfprod(r1,r2,P,A) 
			distributive polynomial over 
rational                functions over the rationals rfrtodiprfr(r1,r2,F) 
			rational function over the rationals to 
			distributive polynomial over 
rational                functions over the rationals sum 
			diprfrsum(r1,r2,P1,P2) distributive polynomial over 
rational                functions over the rationals to rational function 
			over the rationals diprfrtorfr(r1,r2,P) 
			distributive polynomial over 
rational                functions over the rationals transformation 
			marfrtransf(r1,M1,V1,r2,R2,V2,Vn,pV3) matrix of 
rational                functions over the rationals transformation 
			vecrfrtrnsf(r1,W1,V1,r2,R2,V2,Vn,pV3) vector of 
rational                functions over the rationals with total degree 
			ordering diprfrlottdo(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over 
rational                isqnfrat(D,a) (MACRO) is quadratic number field 
			element 
rational                number ? israt(R) is 
rational                number absolute height rabsheight(r) 
rational                number absolute value rabs(R) (MACRO) 
rational                number ceiling rceil(R) 
rational                number comparison rcomp(R,S) 
rational                number construction rcons(A,B) 
rational                number decimal fputrd(R,n,pf) file put 
rational                number decimal putrd(R,n) (MACRO) put 
rational                number denominator rden(R) (MACRO) 
rational                number difference rdif(R,S) (MACRO) 
rational                number exponentiation rexp(R,n) 
rational                number fgetr(pf) file get 
rational                number floor rfloor(R) 
rational                number fltor(f) floating point to 
rational                number fputr(R,pf) file put 
rational                number getr() (MACRO) get 
rational                number inearesttor(r) integer nearest to 
rational                number inverse rinv(R) 
rational                number itor(A) integer to 
rational                number logarithm, base 2 rlog2(R) 
rational                number maximum rmax(R,S) (MACRO) 
rational                number minimum rmin(R,S) (MACRO) 
rational                number negation rneg(R) 
rational                number numerator rnum(R) (MACRO) 
rational                number one ? isrone(A) is 
rational                number power of 2 rp2(n) 
rational                number product (rekursiv) ppfrprod(r,p,P,R) 
			polynomial over p-adic field 
rational                number product (rekursiv) prrprod(r,P,A) polynomial 
			over rationals, 
rational                number product diprrprod(r,P,A) distributive 
			polynomial over rationals, 
rational                number product nfelrprod(F,a,R) number field 
			element 
rational                number product pfelrprod(p,a,R) p-adic field 
			element 
rational                number product rprod(R,S) 
rational                number product udprrprod(P,A) univariate dense 
			polynomial over rationals, 
rational                number putr(R) (MACRO) put 
rational                number quotient rquot(R,S) (MACRO) 
rational                number sgetr(ps) string get 
rational                number signum rsign(R) (MACRO) 
rational                number sputr(R,str) string put 
rational                number square ? isrsqr(R) is 
rational                number sum rsum(R,S) 
rational                number to floating point rtofl(r) 
rational                number to modular integer rtomi(R,M) 
rational                number to number field element rtonf(R) 
rational                number to number field element, sparse 
			representation rtonfs(R) 
rational                number to quadratic number field element 
			rtoqnf(D,A) (MACRO) 
rational                number to rational function over rationals 
			rtorfr(r,R) 
rational                number, difference qnfrdif(D,a,b) (MACRO) quadratic 
			number field element, 
rational                number, product qnfrprod(D,a,b) quadratic number 
			field element, 
rational                number, quadratic number field element, difference 
			rqnfdif(D,a,b) (MACRO) 
rational                number, quadratic number field element, quotient 
			rqnfquot(D,a,b) 
rational                number, quotient qnfrquot(D,a,b) (MACRO) quadratic 
			number field element, 
rational                number, sum qnfrsum(D,a,b) quadratic number field 
			element, 
rational                numbers fgetecr(pf) file get elliptic curve over 
rational                numbers fgetecrp(pf) file get point on elliptic 
			curve over 
rational                numbers fgetlr(pf) file get list of 
rational                numbers getecr() get elliptic curve over 
rational                numbers getlr() (MACRO) get list of 
rational                numbers initialization ecrinit(a1r,a2r,a3r,a4r,a6r) 
			elliptic curve over the 
rational                numbers point getecrp() (MACRO) get elliptic curve 
			over 
rational                numbers putecr(E) (MACRO) put elliptic curve over 
rational                numbers reduction list ecrrl(E) elliptic curve over 
rational                numbers reduction type ecrrt(E,p) elliptic curve 
			over 
rational                numbers, Fourier expansion of the L-series 
			ecrfelser(E,A,z,result) elliptic curve over 
rational                numbers, L-series ecrlser(E) elliptic curve over 
rational                numbers, L-series, first derivative ecrlserfd(E) 
			elliptic curve over 
rational                numbers, L-series, higher derivative ecrlserhd(E,r) 
			elliptic curve over 
rational                numbers, L-series, higher derivative, small 
			conductor ecrlserhdsc(E,A,r,result) elliptic curve 
			over 
rational                numbers, Manin algorithm ecrmaninalg(E) elliptic 
			curve over 
rational                numbers, Tate's values b2, b4, b6, b8 
			ecrtavalb(a1,a2,a3,a4,a6) elliptic curve over 
rational                numbers, Weil height ecracweilhe(E,P) elliptic 
			curve over the 
rational                numbers, actual curve fputecrac(E,pf) file put 
			elliptic curve over 
rational                numbers, actual curve putecrac(E) (MACRO) put 
			elliptic curve over 
rational                numbers, actual curve to global minimal model ( 
			Laska's algorithm ) ecractoecimin(E) elliptic curve 
			over 
rational                numbers, actual curve, Mordell-Weil-group, base 
			ecracmwgbase(E) elliptic curve over the 
rational                numbers, actual curve, a1 ecraca1(E) (MACRO) 
			elliptic curve over 
rational                numbers, actual curve, a2 ecraca2(E) (MACRO) 
			elliptic curve over 
rational                numbers, actual curve, a3 ecraca3(E) (MACRO) 
			elliptic curve over 
rational                numbers, actual curve, a4 ecraca4(E) (MACRO) 
			elliptic curve over 
rational                numbers, actual curve, a6 ecraca6(E) (MACRO) 
			elliptic curve over 
rational                numbers, actual curve, b2 ecracb2(E) elliptic curve 
			over 
rational                numbers, actual curve, b4 ecracb4(E) elliptic curve 
			over 
rational                numbers, actual curve, b6 ecracb6(E) elliptic curve 
			over 
rational                numbers, actual curve, b8 ecracb8(E) elliptic curve 
			over 
rational                numbers, actual curve, birational transformation to 
			short normal form ecracbtsnf(E) elliptic curve over 
rational                numbers, actual curve, c4 ecracc4(E) elliptic curve 
			over 
rational                numbers, actual curve, c6 ecracc6(E) elliptic curve 
			over 
rational                numbers, actual curve, discriminant ecracdisc(E) 
			elliptic curve over 
rational                numbers, actual curve, factorization of 
			discriminant ecracfdisc(E) elliptic curve over 
rational                numbers, actual curve, generators of torsion group 
			ecracgentor(E) elliptic curve over 
rational                numbers, actual curve, multiplication-map 
			ecracmul(E,P,n) elliptic curve over the 
rational                numbers, actual curve, negative point ecracneg(E,P) 
			elliptic curve over the 
rational                numbers, actual curve, sum of points 
			ecracsum(E,P,Q) elliptic curve over the 
rational                numbers, actual curve, torsion group ecractorgr(E) 
			elliptic curve over 
rational                numbers, actual model isponecrac(E,P) is point on 
			elliptic curve over 
rational                numbers, birational transformation of coefficients 
			ecracbtco(E,BT) elliptic curve over 
rational                numbers, birational transformation of coefficients 
			ecrbtco(LC,BT) elliptic curve over 
rational                numbers, birational transformation of list of 
			points ecrbtlistp(LP,BT,modus) elliptic curve over 
rational                numbers, birational transformation of point 
			ecrbtp(P,BT) elliptic curve over 
rational                numbers, birational transformation, concatenation 
			of transformations ecrbtconc(BT1,BT2) elliptic 
			curve over 
rational                numbers, birational transformation, inverse 
			transformation ecrbtinv(BT) elliptic curve over 
rational                numbers, complex period ecrcperiod(E) elliptic 
			curve over the 
rational                numbers, conductor ecrcond(E) elliptic curve over 
rational                numbers, exponent of torsion group ecrexptor(E) 
			elliptic curve over 
rational                numbers, factorization of conductor ecrfcond(E) 
			elliptic curve over 
rational                numbers, invariants fputecrinv(E,pf) file put 
			elliptic curve over the 
rational                numbers, invariants putecrinv(E) (MACRO) put 
			elliptic curve over the 
rational                numbers, j-invariant ecrjinv(E) elliptic curve over 
rational                numbers, list of points fputecrlistp(P,modus,pf) 
			file put elliptic curve over the 
rational                numbers, list of points putecrlistp(P,modus) 
			(MACRO) put elliptic curve over 
rational                numbers, minimal model, double of point 
			ecracdouble(E,P) elliptic curve over the 
rational                numbers, order of Tate- Shafarevic group 
			ecrordtsg(E) elliptic curve over the 
rational                numbers, order of torsion group ecrordtor(E) 
			elliptic curve over 
rational                numbers, point comparison ecrpcomp(P1,P2) elliptic 
			curve over 
rational                numbers, point fputecrp(P,pf) file put elliptic 
			curve over 
rational                numbers, point normalization ecrpnorm(P) elliptic 
			curve over 
rational                numbers, point putecrp(P) (MACRO) put elliptic 
			curve over 
rational                numbers, point to projective representation 
			ecrptoproj(P) elliptic curve over 
rational                numbers, real period ecrrperiod(E) elliptic curve 
			over the 
rational                numbers, regulator ecrregulator(E) elliptic curve 
			over the 
rational                numbers, short normal form, real roots of the right 
			side ecrsnfrroots(a,b) elliptic curve over 
rational                numbers, sign of the functional equation ecrsign(E) 
			elliptic curve over 
rational                numbers, structure of torsion group ecrstrtor(E) 
			elliptic curve over 
rational                quotient prrquot(r,P,A) polynomial over rationals, 
rational                to p-adic field element rtopfel(p,d,R) 
rational                transformation pirtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) 
			polynomial over the integers 
rational                transformation prrtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) 
			polynomial over the rationals 
rationals               (rekursiv) pitopr(r,P) polynomial over integers to 
			polynomial over 
rationals               ? (rekursiv) ispr(r,P) is polynomial over 
rationals               ? isiupr(P) is irreducible univariate polynomial 
			over 
rationals               ? ismadpr(r,M) (MACRO) is matrix of dense 
			polynomials over 
rationals               ? ismapr(r,M) (MACRO) is matrix of polynomials over 
rationals               ? ismar(M) (MACRO) is matrix of 
rationals               ? ismarfr(r,M) (MACRO) is matrix of rational 
			functions over 
rationals               ? isrfr(r,R) is rational function over the 
rationals               ? isvecdpr(r,V) (MACRO) is vector of dense 
			polynomials over 
rationals               ? isvecpr(r,V) (MACRO) is vector of polynomials 
			over 
rationals               ? isvecr(V) (MACRO) is vector of 
rationals               ? isvecrfr(r,V) (MACRO) is vector of rational 
			functions over 
rationals               Euklid- Gauss- step for columns maupregsc(M,A,B) 
			matrix of univariate polynomials over 
rationals               Euklid- Gauss- step for rows maupregsr(M,A,B) 
			matrix of univariate polynomials over 
rationals               Groebner basis augmentation diprfrgba(r1,r2,PL,P) 
			distributive polynomial over rational functions 
			over the 
rationals               Groebner basis augmentation diprgba(r,PL,P) 
			distributive polynomial over 
rationals               Groebner basis diprfrgb(r1,r2,PL) distributive 
			polynomial over rational functions over the 
rationals               Groebner basis diprgb(r,PL) distributive polynomial 
			over 
rationals               Groebner basis recursion diprfrgbr(r1,r2,PL) 
			distributive polynomial over rational functions 
			over the 
rationals               Groebner basis recursion diprgbr(r,PL) distributive 
			polynomial over 
rationals               S-polynomial diprfrsp(r1,r2,P1,P2) distributive 
			polynomial over rational functions over the 
rationals               S-polynomial diprsp(r,P1,P2) distributive 
			polynomial over 
rationals               Tate's values c4, c6 ecrtavalc(a1,a2,a3,a4,a6) 
			elliptic curve over the 
rationals               Z-module homomorphism cdprzmodhom(P,M) common 
			denominator polynomial over the 
rationals               cdprfupr(P) common denominator polynomial over the 
			rationals from univariate polynomial over the 
rationals               cdprlfcdmar(M) common denominator polynomial over 
			the rationals list from common denominator matrix 
			of 
rationals               characteristic polynomial maprchpol(r,M) (MACRO) 
			matrix of polynomials over 
rationals               characteristic polynomial marchpol(M) (MACRO) 
			matrix of 
rationals               characteristic polynomial marfrchpol(r,M) matrix of 
			rational functions over 
rationals               clfcdpr(P,n) coefficient list from common 
			denominator polynomial over the 
rationals               construction 1 maprcons1(r,n) (MACRO) matrix of 
			polynomials over 
rationals               construction 1 marcons1(n) (MACRO) matrix of 
rationals               construction 1 marfrcons1(r,n) (MACRO) matrix of 
			rational functions over 
rationals               construction rfrcons(r,P1,P2) rational function 
			over the 
rationals               derivation, main variable prderiv(r,P) polynomial 
			over 
rationals               derivation, specified variable (rekursiv) 
			prderivsv(r,P,n) polynomial over 
rationals               determinant maprdet(r,M) matrix of polynomials over 
rationals               determinant mardet(M) matrix of 
rationals               determinant marfrdet(r,M) matrix of rational 
			functions over 
rationals               difference (rekursiv) prdif(r,P1,P2) polynomial 
			over 
rationals               difference diprdif(r,P1,P2) distributive polynomial 
			over 
rationals               difference diprfrdif(r1,r2,P1,P2) distributive 
			polynomial over rational functions over the 
rationals               difference maprdif(r,M,N) (MACRO) matrix of 
			polynomials over 
rationals               difference mardif(M,N) (MACRO) matrix of 
rationals               difference marfrdif(r,M,N) (MACRO) matrix of 
			rational functions over 
rationals               difference rfrdif(r,R1,R2) rational function over 
			the 
rationals               difference udprdif(P1,P2) univariate dense 
			polynomial over 
rationals               difference vecprdif(r,U,V) (MACRO) vector of 
			polynomials over 
rationals               difference vecrdif(U,V) (MACRO) vector of 
rationals               difference vecrfrdif(r,U,V) (MACRO) vector of 
			rational functions over 
rationals               diprfrtorfr(r1,r2,P) distributive polynomial over 
			rational functions over the rationals to rational 
			function over the 
rationals               eigenvalues and irreducible factors of the 
			characteristic polynomial marevifcp(M,*pL) matrix 
			of 
rationals               eigenvalues marev(M) (MACRO) matrix of 
rationals               elementary divisor form and cofactors 
			maupredfcf(M,pA,pB) matrix of univariate 
			polynomials over 
rationals               evaluation, main variable preval(r,P,A) polynomial 
			over 
rationals               evaluation, specified variable (rekursiv) 
			prevalsv(r,P,n,A) polynomial over 
rationals               exponentiation maprexp(r,M,n) matrix of polynomials 
			over 
rationals               exponentiation marexp(M,n) matrix of 
rationals               exponentiation marfrexp(r,M,n) matrix of rational 
			functions over 
rationals               exponentiation prexp(r,P,n) polynomial over 
rationals               factorization uprfact(P) univariate polynomial over 
rationals               fgetmapr(r,V,pf) (MACRO) file get matrix of 
			polynomials over 
rationals               fgetmar(pf) (MACRO) file get matrix of 
rationals               fgetmarfr(r,V,pf) (MACRO) file get matrix of 
			rational functions over 
rationals               fgetpr(r,V,pf) file get polynomial over 
rationals               fgetrfr(r,V,pf) file get rational function over 
rationals               fgetvecpr(r,VL,pf) (MACRO) file get vector of 
			polynomials over 
rationals               fgetvecr(pf) (MACRO) file get vector of 
rationals               fgetvecrfr(r,VL,pf) (MACRO) file get vector of 
			rational functions over 
rationals               fputlpr(r,L,V,pf) file put list of polynomials over 
rationals               fputlr(L,pf) file put list of 
rationals               fputmapr(r,M,V,pf) (MACRO) file put matrix of 
			polynomials over 
rationals               fputmar(M,pf) (MACRO) file put matrix of 
rationals               fputmarfr(r,M,V,pf) (MACRO) file put matrix of 
			rational functions over 
rationals               fputpr(r,P,V,pf) file put polynomial over 
rationals               fputrfr(r,R,V,pf) file put rational function over 
rationals               fputvecpr(r,V,VL,pf) (MACRO) file put vector of 
			polynomials over 
rationals               fputvecr(V,pf) (MACRO) file put vector of 
rationals               fputvecrfr(r,V,VL,pf) (MACRO) file put vector of 
			rational functions over 
rationals               from coefficient list cdprfcl(L) common denominator 
			polynomial over the 
rationals               from common denominator polynomial over the 
			rationals uprfcdpr(PC) univariate polynomial over 
			the 
rationals               from univariate polynomial over the rationals 
			cdprfupr(P) common denominator polynomial over the 
rationals               getmapr(r,V) (MACRO) get matrix of polynomials over 
rationals               getmar() (MACRO) get matrix of 
rationals               getmarfr(r,V) (MACRO) get matrix of rational 
			functions over 
rationals               getpr(r,V) (MACRO) get polynomial over 
rationals               getrfr(r,V) (MACRO) get rational function over 
rationals               getvecpr(r,VL) (MACRO) get vector of polynomials 
			over 
rationals               getvecr() (MACRO) get vector of 
rationals               getvecrfr(r,VL) (MACRO) get vector of rational 
			functions over 
rationals               in graduated lexicographical order 
			diprfrlotglo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the 
rationals               in graduated lexicographical order diprlotoglo(r,P) 
			distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over 
rationals               in lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			graduated lexicographical order 
			diprfrlotglo(r1,r2,P) distributive polynomial over 
			rational functions over the 
rationals               in lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			lexicographical order with inverse exponent vector 
			diprfrlotlio(r1,r2,P) distributive polynomial over 
			rational functions over the 
rationals               in lexicographical order to distributive polynomial 
			over rational functions over the rationals with 
			total degree ordering diprfrlottdo(r1,r2,P) 
			distributive polynomial over rational functions 
			over the 
rationals               in lexicographical order to distributive polynomial 
			over rationals in graduated lexicographical order 
			diprlotoglo(r,P) distributive polynomial over 
rationals               in lexicographical order to distributive polynomial 
			over rationals in lexicographical order with 
			inverse exponent vector diprlotolio(r,P) 
			distributive polynomial over 
rationals               in lexicographical order to distributive polynomial 
			over rationals with total degree ordering 
			diprlototdo(r,P) distributive polynomial over 
rationals               in lexicographical order with inverse exponent 
			vector diprfrlotlio(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
rationals               in lexicographical order with inverse exponent 
			vector diprlotolio(r,P) distributive polynomial 
			over rationals in lexicographical order to 
			distributive polynomial over 
rationals               integer quotient cdpriquot(P,I) common denominator 
			polynomial over the 
rationals               integration, main variable printegr(r,P) polynomial 
			over 
rationals               inverse cdprinv(F,A) common denominator polynomial 
			over the 
rationals               inverse maprinv(r,M) matrix of polynomials over 
rationals               inverse marfrinv(r,M) matrix of rational functions 
			over 
rationals               inverse marinv(M) matrix of 
rationals               inverse rfrinv(r,R) rational function over the 
rationals               linear combination vecprlc(r,P1,P2,V1,V2) vector of 
			polynomials over 
rationals               linear combination vecrfrlc(r,F1,F2,V1,V2) vector 
			of rational functions over 
rationals               linear combination vecrlc(s1,s2,V1,V2) vector of 
rationals               list fgetdiprfrl(r1,r2,VL1,VL2,pf) file get 
			distributive polynomial over rational functions 
			over the 
rationals               list fgetdiprl(r,VL,pf) file get distributive 
			polynomial over 
rationals               list fputdiprfrl(r1,r2,PL,VL1,VL2,pf) file put 
			distributive polynomial over rational functions 
			over the 
rationals               list fputdiprl(r,PL,VL,pf) file put distributive 
			polynomial over 
rationals               list from common denominator matrix of rationals 
			cdprlfcdmar(M) common denominator polynomial over 
			the 
rationals               list getdiprfrl(r1,r2,VL1,VL2) (MACRO) get 
			distributive polynomial over rational functions 
			over the 
rationals               list getdiprl(r,VL) (MACRO) get distributive 
			polynomial over 
rationals               list putdiprfrl(r1,r2,PL,VL1,VL2) (MACRO) put 
			distributive polynomial over rational functions 
			over the 
rationals               list putdiprl(r,PL,VL) (MACRO) put distributive 
			polynomial over 
rationals               maitomar(M) matrix of integers to matrix of 
rationals               manftomudpr(F,M) matrix of number field elements to 
			matrix of univariate dense polynomials over 
rationals               mapitomapr(r,M) matrix of integers to matrix of 
rationals               mapitomarfr(r,M) matrix of polynomials over 
			integers to matrix of rational functions over 
rationals               mapnftomapr(r,M) matrix of polynomials over number 
			field to matrix of polynomials over 
rationals               maprtomarfr(r,M) matrix of polynomials over 
			rationals to matrix of rational functions over 
rationals               maprtompmpr(r,M,P) matrix of polynomials over 
			rationals to matrix of polynomials modulo 
			polynomial over 
rationals               martomapr(r,M) matrix of rationals to matrix of 
			polynomials over 
rationals               monic diprfrmonic(r1,r2,P) distributive polynomial 
			over rational functions over the 
rationals               monic diprmonic(r,P) distributive polynomial over 
rationals               mudpitmudpr(M) matrix of univariate dense 
			polynomials over integers to matrix of univariate 
			dense polynomials over 
rationals               negation (rekursiv) prneg(r,P) polynomial over 
rationals               negation diprfrneg(r1,r2,P) distributive polynomial 
			over rational functions over the 
rationals               negation diprneg(r,P) distributive polynomial over 
rationals               negation maprneg(r,M) (MACRO) matrix of polynomials 
			over 
rationals               negation marfrneg(r,M) (MACRO) matrix of rational 
			functions over 
rationals               negation marneg(M) (MACRO) matrix of 
rationals               negation rfrneg(r,R) rational function over the 
rationals               negation udprneg(P) univariate dense polynomial 
			over 
rationals               negation vecprneg(r,V) (MACRO) vector of 
			polynomials over 
rationals               negation vecrfrneg(r,V) (MACRO) vector of rational 
			functions over 
rationals               negation vecrneg(V) (MACRO) vector of 
rationals               nfeltoudpr(a) number field element to univariate 
			dense polynomial over 
rationals               null space basis marnsb(M) matrix of 
rationals               number field element evaluation first variable 
			special version maprnfevlfvs(r,F,M) matrix of 
			polynomials over 
rationals               number field element evaluation first variable 
			special version prnfevalfvs(r,F,P) polynomial over 
rationals               number field element evaluation first variable 
			special version vprnfevalfvs(r,F,V) vector of 
			polynomials over 
rationals               number field element evaluation uprnfeval(P,F,a) 
			univariate polynomial over 
rationals               number field element, sparse representation, 
			evaluation uprnfseval(P,F,a) univariate polynomial 
			over 
rationals               numerator and denominator prnumden(r,P,pA) 
			polynomial over the 
rationals               one ? isdiprfrone(r1,r2,P) is distributive 
			polynomial over rational functions over the 
rationals               one ? isdiprone(r,P) is distributive polynomial 
			over 
rationals               one isrfrone(r,A) is rational function over 
rationals               pitorfr(r,P) polynomial over integers to rational 
			function over the 
rationals               pnftopr(r,P) polynomial over number field to 
			polynomial over 
rationals               point at infinity ? ispecrpai(P) (MACRO) is point 
			of an elliptic curve over the 
rationals               product (rekursiv) prprod(r,P1,P2) polynomial over 
rationals               product diprfrprod(r1,r2,P1,P2) distributive 
			polynomial over rational functions over the 
rationals               product diprfrrfprod(r1,r2,P,A) distributive 
			polynomial over rational functions over the 
			rationals rational function over the 
rationals               product diprprod(r,P1,P2) distributive polynomial 
			over 
rationals               product maprprod(r,M,N) (MACRO) matrix of 
			polynomials over 
rationals               product marfrprod(r,M,N) (MACRO) matrix of rational 
			functions over 
rationals               product marprod(M,N) (MACRO) matrix of 
rationals               product rfrprod(r,R1,R2) rational function over the 
rationals               product udprprod(P1,P2) univariate dense polynomial 
			over 
rationals               prtorfr(r,P) polynomial over the rationals to 
			rational function over the 
rationals               putmapr(r,M,V) (MACRO) put matrix of polynomials 
			over 
rationals               putmar(M) (MACRO) put matrix of 
rationals               putmarfr(r,M,V) (MACRO) put matrix of rational 
			functions over 
rationals               putpr(r,P,V) (MACRO) put polynomial over 
rationals               putrfr(r,R,V) (MACRO) put rational function over 
rationals               putvecpr(r,V,VL) (MACRO) put vector of polynomials 
			over 
rationals               putvecr(V) (MACRO) put vector of 
rationals               putvecrfr(r,V,VL) (MACRO) put vector of rational 
			functions over 
rationals               quotient and remainder (rekursiv) 
			prqrem(r,P1,P2,pR) polynomial over 
rationals               quotient and remainder udprqrem(P1,P2,pP3) 
			univariate dense polynomial over 
rationals               quotient prquot(r,P1,P2) (MACRO) polynomial over 
rationals               quotient rfrquot(r,R1,R2) rational function over 
			the 
rationals               rank marfrrk(r,M) matrix of rational functions over 
rationals               rank marrk(M) matrix of 
rationals               rational function over the rationals product 
			diprfrrfprod(r1,r2,P,A) distributive polynomial 
			over rational functions over the 
rationals               rational transformation 
			prrtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) polynomial over 
			the 
rationals               remainder prrem(r,P1,P2) (MACRO) polynomial over 
rationals               rfrtodiprfr(r1,r2,F) rational function over the 
			rationals to distributive polynomial over rational 
			functions over the 
rationals               rtorfr(r,R) rational number to rational function 
			over 
rationals               scalar multiplication maprsmul(r,M,P) matrix of 
			polynomials over 
rationals               scalar multiplication marfrsmul(r,M,F) matrix of 
			rational functions over 
rationals               scalar multiplication marsmul(M,el) matrix of 
rationals               scalar multiplication vecprsmul(r,P,V) vector of 
			polynomials over 
rationals               scalar multiplication vecrfrsmul(r,F,V) vector of 
			rational functions over 
rationals               scalar multiplication vecrsmul(s,V) vector of 
rationals               scalar product vecprsprod(r,V,W) vector of 
			polynomials over 
rationals               scalar product vecrfrsprod(r,V,W) vector of 
			rational functions over 
rationals               scalar product vecrsprod(V,W) vector of 
rationals               solution of a system of linear equations 
			marfrssle(r,A,b,pX,pN) matrix of rational functions 
			over 
rationals               solution of a system of linear equations 
			marssle(A,b,pX,pN) matrix of 
rationals               substitution, main variable prsubst(r,P1,P2) 
			polynomial over 
rationals               substitution, specified variable (rekursiv) 
			prsubstsv(r,P1,n,P2) polynomial over 
rationals               sum (rekursiv) prsum(r,P1,P2) polynomial over 
rationals               sum cdprsum(P1,P2) common denominator polynomial 
			over the 
rationals               sum diprfrsum(r1,r2,P1,P2) distributive polynomial 
			over rational functions over the 
rationals               sum diprsum(r,P1,P2) distributive polynomial over 
rationals               sum maprsum(r,M,N) (MACRO) matrix of polynomials 
			over 
rationals               sum marfrsum(r,M,N) (MACRO) matrix of rational 
			functions over 
rationals               sum marsum(M,N) (MACRO) matrix of 
rationals               sum rfrsum(r,R1,R2) rational function over the 
rationals               sum udprsum(P1,P2) univariate dense polynomial over 
rationals               sum vecprsum(r,U,V) (MACRO) vector of polynomials 
			over 
rationals               sum vecrfrsum(r,U,V) (MACRO) vector of rational 
			functions over 
rationals               sum vecrsum(U,V) (MACRO) vector of 
rationals               to distributive polynomial over rational functions 
			over the rationals rfrtodiprfr(r1,r2,F) rational 
			function over the 
rationals               to matrix of modular integers martomami(m,M) matrix 
			of 
rationals               to matrix of number field elements martomanf(M) 
			matrix of 
rationals               to matrix of number field elements maudprtomnf(M) 
			matrix of univariate dense polynomials over 
rationals               to matrix of number field elements, sparse 
			representation martomanfs(M) matrix of 
rationals               to matrix of polynomials modulo polynomial over 
			rationals maprtompmpr(r,M,P) matrix of polynomials 
			over 
rationals               to matrix of polynomials over modular integers 
			maprtomapmi(r,M,m) matrix of polynomials over 
rationals               to matrix of polynomials over number field 
			maprtomapnf(r,M) matrix of polynomials over 
rationals               to matrix of polynomials over rationals 
			martomapr(r,M) matrix of 
rationals               to matrix of rational functions over rationals 
			maprtomarfr(r,M) matrix of polynomials over 
rationals               to number field element udprtonfel(P) univariate 
			dense polynomial over 
rationals               to number field element uprtonfel(F,P) univariate 
			polynomial over 
rationals               to polynomial over modular integers (rekursiv) 
			prtopmi(r,P,M) polynomial over 
rationals               to polynomial over number field (rekursiv) 
			prtopnf(r,P) polynomial over 
rationals               to polynomial over p-adic field prtoppf(r,P,p,d) 
			polynomial over 
rationals               to rational function over the rationals 
			diprfrtorfr(r1,r2,P) distributive polynomial over 
			rational functions over the 
rationals               to rational function over the rationals 
			prtorfr(r,P) polynomial over the 
rationals               to univariate dense polynomial over p-adic field 
			udprtoudppf(P,p,d) univariate dense polynomial over 
rationals               to vector of modular integers vecrtovecmi(m,V) 
			vector of 
rationals               to vector of number field elements vecrtovecnf(V) 
			vector of 
rationals               to vector of number field elements vudprtovnf(V) 
			vector of univariate dense polynomials over 
rationals               to vector of number field elements, sparse 
			representation vecrtovnfs(V) vector of 
rationals               to vector of polynomials modulo polynomial over 
			rationals vecprtvpmpr(r,V,P) vector of polynomials 
			over 
rationals               to vector of polynomials over modular integers 
			vecprtovpmi(r,V,m) vector of polynomials over 
rationals               to vector of polynomials over number field 
			vecprtovpnf(r,V) vector of polynomials over 
rationals               to vector of polynomials over rationals 
			vecrtovecpr(r,V) vector of 
rationals               to vector of rational functions over rationals 
			vecprtovrfr(r,V) vector of polynomials over 
rationals               transformation maprtransf(r1,M1,V1,r2,P2,V2,Vn,pV3) 
			matrix of polynomials over the 
rationals               transformation 
			marfrtransf(r1,M1,V1,r2,R2,V2,Vn,pV3) matrix of 
			rational functions over the 
rationals               transformation prtransf(r1,P1,V1,r2,P2,V2,Vn,pV3) 
			polynomial over the 
rationals               transformation rfrtransf(r1,R1,V1,r2,R2,V2,Vn,pV3) 
			rational function over the 
rationals               transformation 
			vecprtransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over the 
rationals               transformation 
			vecrfrtrnsf(r1,W1,V1,r2,R2,V2,Vn,pV3) vector of 
			rational functions over the 
rationals               translation, all variables (rekursiv) 
			prtransav(r,P,LR) polynomial over 
rationals               translation, main variable prtrans(r,P,A) 
			polynomial over 
rationals               udpitoudpr(P) univariate polynomial over integers 
			to univariate polynomial over 
rationals               uprfcdpr(PC) univariate polynomial over the 
			rationals from common denominator polynomial over 
			the 
rationals               vecitovecr(V) vector of integers to vector of 
rationals               vecpitovpr(V) vector of polynomials over integers 
			to vector of polynomials over 
rationals               vecpitovrfr(r,V) vector of polynomials over 
			integers to vector of rational functions over 
rationals               vecpnftovpr(r,V) vector of polynomials over number 
			field to vector of polynomials over 
rationals               vecprtovrfr(r,V) vector of polynomials over 
			rationals to vector of rational functions over 
rationals               vecprtvpmpr(r,V,P) vector of polynomials over 
			rationals to vector of polynomials modulo 
			polynomial over 
rationals               vecrtovecpr(r,V) vector of rationals to vector of 
			polynomials over 
rationals               vector multiplication maprvecmul(r,A,x) (MACRO) 
			matrix of polynomials over 
rationals               vector multiplication marfrvecmul(r,A,x) (MACRO) 
			matrix of rational functions over 
rationals               vector multiplication marvecmul(A,x) (MACRO) matrix 
			of 
rationals               vnftovudpr(F,V) vector of number field elements to 
			vector of univariate dense polynomials over 
rationals               vudpitvudpr(V) vector of univariate dense 
			polynomials over integers to vector of univariate 
			dense polynomials over 
rationals               with total degree ordering diprfrlottdo(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order to 
			distributive polynomial over rational functions 
			over the 
rationals               with total degree ordering diprlototdo(r,P) 
			distributive polynomial over rationals in 
			lexicographical order to distributive polynomial 
			over 
rationals,              L-series, 'rank'-th derivative ecrlserrkd(E) 
			elliptic curve over the 
rationals,              L-series, first derivative, special version 
			ecrlserfds(E,A,result) elliptic curve over the 
rationals,              L-series, higher derivative, large conductor 
			ecrlserhdlc(E,A,s,result) elliptic curve over the 
rationals,              L-series, special version ecrlsers(E,A,result) 
			elliptic curve over the 
rationals,              LLL reduction marlllred(bas) matrix of 
rationals,              actual curve, birational transformation to minimal 
			model ecracbtmin(E) elliptic curve over the 
rationals,              coefficients of L- series ecrclser(E,A,n) elliptic 
			curve over the 
rationals,              factorization of the denominator of the j-invariant 
			ecrfdenjinv(E) elliptic curve over the 
rationals,              hermitian reduction cdmarhermred(M) common 
			denominator matrix of 
rationals,              identity construction cdmarid(n) common denominator 
			matrix of 
rationals,              null space basis marfrnsb(r,M) matrix of rational 
			functions over 
rationals,              product over all c_p- values ecrprodcp(E) elliptic 
			curve over the 
rationals,              rank ecrrank(E) elliptic curve over the 
rationals,              rational number product (rekursiv) prrprod(r,P,A) 
			polynomial over 
rationals,              rational number product diprrprod(r,P,A) 
			distributive polynomial over 
rationals,              rational number product udprrprod(P,A) univariate 
			dense polynomial over 
rationals,              rational quotient prrquot(r,P,A) polynomial over 
rationals,              sign of the functional equation, special version 
			ecrsigns(E,A,C) elliptic curve over the 
rationals?              (rekursiv) isdpr(r,P) is dense polynomial over 
raval(m,R)              rational additive m-adic value 
ravalint(M,R)           rational additive value with respect to integer 
rceil(R)                rational number ceiling 
rcomp(R,S)              rational number comparison 
rcons(A,B)              rational number construction 
rden(R)                 (MACRO) rational number denominator 
rdif(R,S)               (MACRO) rational number difference 
rdiscupifact(rd,c,pL)   reduced discriminant and discriminant of an 
			univariate polynomial over the integers 
			factorization 
real                    ? isupid4real(P) is univariate polynomial over 
			integers of degree 4 
real                    and imaginary part ccri(re,im) (MACRO) complex 
			construction from 
real                    case qffmsicggir(m,D,d,H,L,pIT) quadratic function 
			field over modular singles ideal class group 
			generators and isomorphy type, 
real                    case qffmsicgrr(m,D,d) quadratic function field 
			over modular singles ideal class group system of 
			representatives, 
real                    case qffmsicgstr(m,D,d,LG,pHid) quadratic function 
			field over modular singles ideal class group 
			structure, 
real                    case qffmsordsicr(m,D,d,LE,ID,OS) quadratic 
			function field over modular singles order of one 
			single ideal class, 
real                    case qffmszcgitr(m,D,d,H,LG,R,IT) quadratic 
			function field over modular singles zero class 
			group isomorphy type, 
real                    case, qffmspidgenr(m,D,Q,P,G,pB) quadratic function 
			field over modular singles, principal ideal 
			generating element, 
real                    case, reduction of a primitive ideal 
			qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, 
real                    case, sparse representation, reduction of a 
			primitive ideal qffmsrspidrd(m,D,d,Q,P,pQr,pPr) 
			quadratic function field over modular singles, 
real                    part creal(z) (MACRO) complex 
real                    period ecrrperiod(E) elliptic curve over the 
			rational numbers, 
real                    quadratic irrational qffmsrqired(m,D,d,Q,P,pPr) 
			quadratic function field over modular singles 
			reduction of a 
real                    quadratic irrational qffmssrqired(m,D,d,Q,P,pPr) 
			quadratic function field over modular singles, 
			sparse representation, reduction of a 
real                    quadratic number field fundamental unit 
			rqnffu(D,pl) 
real                    roots of the right side ecrsnfrroots(a,b) elliptic 
			curve over rational numbers, short normal form, 
recursion               dipgfsgbr(r,p,AL,PL) distributive polynomial over 
			Galois-field with single characteristic Groebner 
			basis 
recursion               dipigbr(r,PL) distributive polynomial over integers 
			Groebner basis 
recursion               dipmipgbr(r,p,PL) distributive polynomial over 
			modular integer primes Groebner basis 
recursion               dipmspgbr(r,p,PL) distributive polynomial over 
			modular single primes Groebner basis 
recursion               dipnfgbr(r,F,PL) distributive polynomial over 
			number field Groebner basis 
recursion               dippigbr(r1,r2,PL) distributive polynomial over 
			polynomials over integers Groebner basis 
recursion               diprfrgbr(r1,r2,PL) distributive polynomial over 
			rational functions over the rationals Groebner 
			basis 
recursion               diprgbr(r,PL) distributive polynomial over 
			rationals Groebner basis 
recursive               part (rekursiv) lsizerec(l,n) list size 
reduced                 ? isbasilllred(bas) is basis over the integers LLL 
			- 
reduced                 comprehensive Groebner basis 
			dippircgb(r1,r2,VL1,VL2,PL,CONDS,OPL,pGS,pi,pf) 
			distributive polynomial over polynomials over 
			integers 
reduced                 discriminant and content of resultant equation 
			upireddiscc(P,pc) univariate polynomial over the 
			integers 
reduced                 discriminant and discriminant of an univariate 
			polynomial over the integers factorization 
			rdiscupifact(rd,c,pL) 
reduced                 discriminant upprmsp1redd(p,F) univariate 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, 
reduced                 positive definite binary quadratic forms 
			iprpdbqf(D,h1,h2) integer primitive 
reductants              next lrednext(L) list of 
reduction               ) by Pollard divisor search rhofrpds(N,b,z) rho- 
			method ( fast 
reduction               cdmarfmsp1hr(p,M) common denominator matrix of 
			rational functions over modular single prime, 
			transcendence degree 1, hermitian 
reduction               cdmarhermred(M) common denominator matrix of 
			rationals, hermitian 
reduction               list ecrrl(E) elliptic curve over rational numbers 
reduction               marlllred(bas) matrix of rationals, LLL 
reduction               modilllred(bas) module over the integers, LLL 
reduction               of a primitive ideal qffmsispidrd(m,D,Q,P,pQr,pPr) 
			quadratic function field over modular singles, 
			imaginary case, sparse representation, 
reduction               of a primitive ideal 
			qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real case, 
reduction               of a primitive ideal 
			qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real case, sparse 
			representation, 
reduction               of a real quadratic irrational 
			qffmsrqired(m,D,d,Q,P,pPr) quadratic function field 
			over modular singles 
reduction               of a real quadratic irrational 
			qffmssrqired(m,D,d,Q,P,pPr) quadratic function 
			field over modular singles, sparse representation, 
reduction               of polynomial variables pvred(r,P,V,pV) 
reduction               qffmsipidred(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular singles, imaginary case, 
			primitive ideal 
reduction               type eciminredtype(E) elliptic curve with integer 
			coefficients, minimal model, 
reduction               type ecrrt(E,p) elliptic curve over rational 
			numbers 
reduction               type modulo prime eciminbrtmp(E,p,n) elliptic curve 
			with integer coefficients, minimal model, bad 
reduction               type modulo prime eciminmrtmp(E,p) elliptic curve 
			with integer coefficients, minimal model, 
			multiplicative 
reduction,              special maihermspec(M,r,pD) matrix of integers 
			hermitian 
reduction,              special maupmshermsp(p,M,r,pD) matrix of univariate 
			polynomials over modular single primes hermitian 
reductum                dpred(r,P) dense polynomial 
reductum                lred(L) (MACRO) list 
reductum                lsred(L1,L2) (MACRO) list set 
reductum                pred(r,P) (MACRO) polynomial 
reductum,               2 objects lred2(L) (MACRO) list 
reductum,               3 objects lred3(L) (MACRO) list 
reductum,               4 objects lred4(L) (MACRO) list 
reductum,               5 objects lred5(L) (MACRO) list 
reductum,               6 objects lred6(L) list 
reductum,               general lreduct(L,k) list 
reference               to SIMATH divs(A,B) (MACRO) division with 
reference               to SIMATH mods(A,B) (MACRO) modulo with 
regulation              afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) algebraic 
			function over modular single primes, transcendence 
			degree 1, 
regulation              with respect to integer primes 
			ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field element 
regulation,             version1 ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) 
			integral p-primary number field element 
regulation,             version2 ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) 
			integral p-primary number field element 
regulator               eciminreg(E,LP,n,modus) elliptic curve with integer 
			coefficients, minimal model, 
regulator               ecrregulator(E) elliptic curve over the rational 
			numbers, 
regulator               qffmsreg(m,P) quadratic function field over modular 
			singles 
regulator,              baby step - giant step version qffmsregbg(m,D) 
			quadratic function field over modular singles 
regulator,              baby step - giant step version, first case 
			qffmsregbg1(m,D,s) quadratic function field over 
			modular singles 
regulator,              baby step - giant step version, fourth case 
			qffmsregbg4(m,D,s) quadratic function field over 
			modular singles 
regulator,              baby step - giant step version, second case 
			qffmsregbg2(m,D,s) quadratic function field over 
			modular singles 
regulator,              baby step - giant step version, third case 
			qffmsregbg3(m,D,s) quadratic function field over 
			modular singles 
regulator,              baby step version qffmsregbs(m,D) quadratic 
			function field over modular singles 
regulator,              original baby step - giant step version 
			qffmsregobg(m,D) quadratic function field over 
			modular singles 
regulator,              original baby step version qffmsregobs(m,D) 
			quadratic function field over modular singles 
reinitialization        gcreinit(bls,blnrm) garbage collector 
relative                class number abnfrelcl(q,g) abelian number field 
relative                class number modulo prime abnfrelclmp(m,q,g) 
			abelian number field 
relative                prime factorization upgfsrelpfac(p,AL,P,Fak,pA2) 
			univariate polynomial over Galois-field with single 
			characteristic 
relative                prime factorization upmirelpfact(P,F,Fak,pA2) 
			univariate polynomial over modular integers 
relative                prime factorization upmsrelpfact(p,P,Fak,pA2) 
			univariate polynomial over modular singles 
remainder               (rekursiv) pgf2qrem(r,G,P1,P2,pR) polynomial over 
			Galois-field with characteristic 2 quotient and 
remainder               (rekursiv) pgfsqrem(r,p,AL,P1,P2,pR) polynomial 
			over Galois-field with single characteristic 
			quotient and 
remainder               (rekursiv) piqrem(r,P1,P2,pR) polynomial over 
			integers quotient and 
remainder               (rekursiv) pmiqrem(r,M,P1,P2,pR) polynomial over 
			modular integers quotient and 
remainder               (rekursiv) pmsqrem(r,m,P1,P2,pR) polynomial over 
			modular singles quotient and 
remainder               (rekursiv) pnfqrem(r,F,P1,P2,pR) polynomial over 
			number field quotient and 
remainder               (rekursiv) prfmsp1qrem(r,p,P1,P2,pR) polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, quotient and 
remainder               (rekursiv) prqrem(r,P1,P2,pR) polynomial over 
			rationals quotient and 
remainder               algorithm (rekursiv) picra(r,P1,P2,M,m,a) 
			polynomial over integers chinese 
remainder               algorithm micra(M1,M2,N1,A1,A2) modular integer 
			chinese 
remainder               algorithm milcra(m1,m2,L1,L2) modular integer list 
			chinese 
remainder               algorithm miscra(M,m,m1,A,a) modular integer single 
			chinese 
remainder               algorithm mscra(m1,m2,n1,a1,a2) modular single 
			chinese 
remainder               algorithm mslcra(m1,m2,L1,L2) modular single list 
			chinese 
remainder               algorithm, n arguments (rekursiv) micran(n,LM,LA) 
			modular integer chinese 
remainder               algorithm, n arguments (rekursiv) mscran(n,Lm,La) 
			modular single chinese 
remainder               flqrem(A,B,pQ,pR) floating quotient and 
remainder               iqrem(A,B,pQ,pR) integer quotient and 
remainder               irem(A,B) (MACRO) integer 
remainder               isqrem(A,b,pQ,pr) integer single-precision quotient 
			and 
remainder               isrem(A,b) (MACRO) integer single-precision 
remainder               pgf2expprem(r,G,F,E,M) polynomial over Galois-field 
			with characteristic 2, exponentiation, polynomial 
remainder               pgf2rem(r,G,P1,P2) (MACRO) polynomial over 
			Galois-field with characteristic 2 
remainder               pgfsexpprem(r,p,AL,F,E,M) polynomial over 
			Galois-field with single characteristic, 
			exponentiation, polynomial 
remainder               pgfsrem(r,p,AL,P1,P2) (MACRO) polynomial over 
			Galois-field with single characteristic 
remainder               pipsrem(r,P1,P2) polynomial over integers pseudo 
remainder               pirem(r,P1,P2) (MACRO) polynomial over integers 
remainder               pmimidqrem(r,M,S,P1,P2,pR) polynomial over modular 
			integers monic, modular ideal quotient and 
remainder               pmipsrem(r,m,P1,P2) polynomial over modular 
			integers pseudo 
remainder               pmirem(r,M,P1,P2) (MACRO) polynomial over modular 
			integers 
remainder               pmspsrem(r,m,P1,P2) polynomial over modular singles 
			pseudo 
remainder               pmsrem(r,m,P1,P2) (MACRO) polynomial over modular 
			singles 
remainder               pnfrem(r,F,P1,P2) (MACRO) polynomial over number 
			field 
remainder               prrem(r,P1,P2) (MACRO) polynomial over rationals 
remainder               special version 3 iqrem_3(A,B,pQ,pR) integer 
			quotient and 
remainder               sqrem(a,b,d,pq,pr) single-precision quotient and 
remainder               system (rekursiv) pmitos(r,M,P) polynomial over 
			modular integers to symmetric 
remainder               system mihoms(M,A) modular integer homomorphism, 
			symmetric 
remainder               system mitos(M,A) modular integer to symmetric 
remainder               system mshoms(m,A) (MACRO) modular single-precision 
			homomorphism, symmetric 
remainder               udpipsrem(P1,P2) univariate dense polynomial over 
			integers pseudo 
remainder               udpmiqrem(m,P1,P2,pP3) univariate dense polynomial 
			over modular integers quotient and 
remainder               udpmirem(ip,P,P2) univariate dense polynomial over 
			modular integers 
remainder               udpmsqrem(m,P1,P2,pP3) univariate dense polynomial 
			over modular singles quotient and 
remainder               udpmsrem(m,P1,P2) univariate dense polynomial over 
			modular singles 
remainder               udprqrem(P1,P2,pP3) univariate dense polynomial 
			over rationals quotient and 
remainder               upgf22pvprem(G,m,P) univariate polynomial over 
			Galois-field with characteristic 2, 2^m-th power of 
			variable, polynomial, 
remainder               upgf2mprem(G,a,T,P) univariate polynomial over 
			Galois-field with characteristic 2, monomial, 
			polynomial, 
remainder               upgfsmieprem(p,AL,a,t,P) univariate polynomial over 
			Galois-field, monomial, integer exponentiation, 
			polynomial, 
remainder               upgfsmprem(p,AL,a,T,P) univariate polynomial over 
			Galois-field, monomial, polynomial, 
remainder               upmimprem(ip,K,E,P) univariate polynomial over 
			modular integers, monomial, polynomial, 
remainder               upmirem(M,P1,P2) univariate polynomial over modular 
			integers 
remainder               upmsmprem(m,k,T,P) univariate polynomial over 
			modular singles, monomial, polynomial, 
remainder               upmsrem(m,P1,P2) univariate polynomial over modular 
			singles 
remainder,              lists only iqrem_lo(A,B,pQ,pR) integer quotient and 
remainder,              old version iqrem_2(A,B,pQ,pR) integer quotient and 
remainder,              special version udpgf2remsp(G,P1,P2,ilc) univariate 
			dense polynomial over Galois-field with 
			characteristic 2 
representation          ? ismanfs(F,M) (MACRO) is matrix of number field 
			elements, sparse 
representation          ? isnfels(F,a) is number field element, sparse 
representation          ? isvecnfs(F,V) (MACRO) is vector of number field 
			elements, sparse 
representation          as a norm in an imaginary quadratic field 
			iprniqf(p,D) integer prime 
representation          ecrptoproj(P) elliptic curve over rational numbers, 
			point to projective 
representation          fgetmanfs(F,VL,pf) (MACRO) file get matrix of 
			number field elements, sparse 
representation          fgetnfels(F,V,pf) file get number field element, 
			sparse 
representation          fgetvecnfs(F,VL,pf) (MACRO) file get vector of 
			number field elements, sparse 
representation          fputmanfs(F,M,VL,pf) (MACRO) file put matrix of 
			number field elements, sparse 
representation          fputnfels(F,a,V,pf) file put number field element, 
			sparse 
representation          fputvecnfs(F,V,VL,pf) (MACRO) file put vector of 
			number field elements, sparse 
representation          getmanfs(F,VL) (MACRO) get matrix of number field 
			elements, sparse 
representation          getnfels(F,V) (MACRO) get number field element, 
			sparse 
representation          getvecnfs(F,VL) (MACRO) get vector of number field 
			elements, sparse 
representation          itonfs(A) integer to number field element, sparse 
representation          maitomanfs(M) matrix of integers to matrix of 
			number field elements, sparse 
representation          martomanfs(M) matrix of rationals to matrix of 
			number field elements, sparse 
representation          nfelnormal(L) number field element normalized 
representation          of projective point ecgf2srpp(G,P) elliptic curve 
			over Galois-field with characteristic 2, standard 
representation          of projective point ecmpsrpp(p,P) elliptic curve 
			over modular primes, standard 
representation          of projective point ecnfsrpp(F,P) elliptic curve 
			over number field standard 
representation          putmanfs(F,M,VL) (MACRO) put matrix of number field 
			elements, sparse 
representation          putnfels(F,a,V) (MACRO) put number field element, 
			sparse 
representation          putvecnfs(F,V,VL) (MACRO) put vector of number 
			field elements, sparse 
representation          qnfminrep(D,a) quadratic number field element 
			minimal 
representation          rtonfs(R) rational number to number field element, 
			sparse 
representation          vecitovnfs(V) vector of integers to vector of 
			number field elements, sparse 
representation          vecrtovnfs(V) vector of rationals to vector of 
			number field elements, sparse 
representation,         construction 1 manfscons1(F,n) (MACRO) matrix of 
			number field elements, sparse 
representation,         determinant manfsdet(F,M) matrix of number field 
			elements, sparse 
representation,         difference manfsdif(F,M,N) (MACRO) matrix of number 
			field elements, sparse 
representation,         difference nfsdif(F,a,b) (MACRO) number field, 
			sparse 
representation,         difference vecnfsdif(F,U,V) (MACRO) vector of 
			number field elements, sparse 
representation,         evaluation upinfseval(P,F,a) univariate polynomial 
			over integers number field element, sparse 
representation,         evaluation uprnfseval(P,F,a) univariate polynomial 
			over rationals number field element, sparse 
representation,         exponentiation manfsexp(F,M,n) matrix of number 
			field elements, sparse 
representation,         inverse manfsinv(F,M) matrix of number field 
			elements, sparse 
representation,         inverse nfsinv(F,a) number field, sparse 
representation,         linear combination vecnfslc(F,s1,s2,L1,L2) vector 
			of number field elements, sparse 
representation,         negation as function nfsnegf(F,a) number field, 
			sparse 
representation,         negation manfsneg(F,M) (MACRO) matrix of number 
			field elements, sparse 
representation,         negation nfsneg(F,a) (MACRO) number field, sparse 
representation,         negation vecnfsneg(F,V) (MACRO) vector of number 
			field elements, sparse 
representation,         null space basis manfsnsb(F,M) matrix of number 
			field elements, sparse 
representation,         primitive ideal product 
			qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
representation,         primitive ideal product, special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
representation,         primitive ideal square 
			qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, sparse 
representation,         primitive ideal square, special version 
			qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, sparse 
representation,         product manfsprod(F,M,N) (MACRO) matrix of number 
			field elements, sparse 
representation,         product nfsprod(F,a,b) number field, sparse 
representation,         quotient nfsquot(F,a,b) number field, sparse 
representation,         rank manfsrk(F,M) matrix of number field elements, 
			sparse 
representation,         reduction of a primitive ideal 
			qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular singles, imaginary case, sparse 
representation,         reduction of a primitive ideal 
			qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real case, sparse 
representation,         reduction of a real quadratic irrational 
			qffmssrqired(m,D,d,Q,P,pPr) quadratic function 
			field over modular singles, sparse 
representation,         scalar multiplication manfssmul(F,M,el) matrix of 
			number field elements, sparse 
representation,         scalar multiplication vecnfssmul(F,V,el) vector of 
			number field elements, sparse 
representation,         scalar product vecnfssprod(F,V,W) vector of number 
			field elements, sparse 
representation,         solution of a system of linear equations 
			manfsssle(F,A,b,pX,pN) matrix of number field 
			elements, sparse 
representation,         sum as function nfssumf(F,a,b) number field, sparse 
representation,         sum manfssum(F,M,N) (MACRO) matrix of number field 
			elements, sparse 
representation,         sum nfssum(F,a,b) (MACRO) number field, sparse 
representation,         sum vecnfssum(F,U,V) (MACRO) vector of number field 
			elements, sparse 
representation,         vector multiplication manfsvecmul(F,A,x) (MACRO) 
			matrix of number field elements, sparse 
representatives         modulo a prime ideal qnfsysrmodpi(D,P,pi,z,k) 
			quadratic number field system of 
representatives         qffmsicgrep(m,D,pHid) quadratic function field over 
			modular singles ideal class group system of 
representatives,        imaginary case qffmsicgri(m,D,pHid) quadratic 
			function field over modular singles ideal class 
			group system of 
representatives,        real case qffmsicgrr(m,D,d) quadratic function 
			field over modular singles ideal class group system 
			of 
residue                 ? ismifr(M,A,B) is modular integer Fermat 
residue                 class fields qnfdegrescf(D,p) quadratic number 
			field degrees of the 
residue                 list ifrl(N,pm) integer Fermat 
residue                 list msfrl(m,a) modular single Fermat 
resolvent               upid4cubres(P) univariate polynomial over integers 
			of degree 4 cubic 
respect                 to a cubic equation bpmisubcubeq(p,P,R) bivariate 
			polynomial over modular integers substitution with 
respect                 to an integer intppint(P,A) integer P-part with 
respect                 to integer iavalint(M,I) integer additive value 
			with 
respect                 to integer prime upihlfaip(p,P,L,k) univariate 
			polynomial over integers, Hensel lemma 
			factorization approximation with 
respect                 to integer prime upihliip(P,F,L) univariate 
			polynomial over integers, Hensel lemma 
			initialization with 
respect                 to integer prime upihlqsip(P,p_k,p_l,F,L1,L2,A) 
			univariate polynomial over integers, Hensel lemma 
			quadratic step with 
respect                 to integer primes infempmppip(F,a,p,e,Q) integral 
			number field element minimal polynomial modulo 
			p-power with 
respect                 to integer primes infepptfip(F,p,Q,ppot,a0,z) 
			integral number field element p-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial with 
respect                 to integer primes infepstarvip(P,A) integral number 
			field element p-star valuation with 
respect                 to integer primes ippnfecalip(F,P,Q,mp) integral 
			P-primary number field element, core algorithm with 
respect                 to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
			denominator of the p-star value with 
respect                 to integer primes 
			ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field element regulation with 
respect                 to integer primes ouspibaslmoi(F,P,Q,pk) order of 
			an univariate separable polynomial over the 
			integers basis of a local maximal over-order with 
respect                 to integer ravalint(M,R) rational additive value 
			with 
resultant               and cofactor of resultant equation 
			upiresulc(P1,P2,pB) univariate polynomial over the 
			integers 
resultant               and cofactor of resultant equation 
			upmiresulc(m,P1,P2,pC) univariate polynomial over 
			modular integers 
resultant               and cofactor of resultant equation 
			upmsresulc(m,P1,P2,pC) univariate polynomial over 
			modular singles 
resultant               equation upireddiscc(P,pc) univariate polynomial 
			over the integers reduced discriminant and content 
			of 
resultant               equation upiresulc(P1,P2,pB) univariate polynomial 
			over the integers resultant and cofactor of 
resultant               equation upmiresulc(m,P1,P2,pC) univariate 
			polynomial over modular integers resultant and 
			cofactor of 
resultant               equation upmsresulc(m,P1,P2,pC) univariate 
			polynomial over modular singles resultant and 
			cofactor of 
resultant               pgfsres(r,p,AL,P1,P2) polynomial over Galois-field 
			with single characteristic 
resultant               pmires(r,m,P1,P2,n) polynomial over modular 
			integers 
resultant               pmsres(r,m,P1,P2,n) polynomial over modular singles 
resultant               upmires(m,P1,P2) univariate polynomial over modular 
			integers 
resultant               upmsres(m,P1,P2) univariate polynomial over modular 
			singles 
resultant,              Bezout algorithm piresbez(r,P1,P2) polynomial over 
			integers 
resultant,              Collins algorithm (rekursiv) pmirescoll(r,m,P1,P2) 
			polynomial over modular integers 
resultant,              Collins algorithm (rekursiv) pmsrescoll(r,m,P1,P2) 
			polynomial over modular singles 
resultant,              Collins algorithm pirescoll(r,P1,P2,n) polynomial 
			over integers 
resultant,              Collins algorithm special pirescspec(r,P1,P2,n) 
			polynomial over the integers 
resultant,              Sylvester algorithm piressylv(r,P1,P2) polynomial 
			over integers 
resultant,              Sylvester algorithm pprmsp1ress(r,p,P1,P2) 
			polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, 
resultant,              Sylvester algorithm upprmsp1ress(p,P1,P2) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
rexp(R,n)               rational number exponentiation 
rfloor(R)               rational number floor 
rfmsp1cons(p,P1,P2)     rational function over modular single prime 
			construction, transcendence degree 1 
rfmsp1dif(p,R1,R2)      rational function over modular single prime 
			difference, transcendence degree 1 
rfmsp1inv(p,R)          rational function over modular single primes, 
			transcendence degree 1, inverse 
rfmsp1neg(p,R)          rational function over modular single prime 
			negation, transcendence degree 1 
rfmsp1prod(p,R1,R2)     rational function over modular single prime 
			product, transcendence degree 1 
rfmsp1quot(p,R1,R2)     rational function over modular single prime 
			quotient, transcendence degree 1 
rfmsp1sum(p,R1,R2)      rational function over modular single prime sum, 
			transcendence degree 1 
rfrcons(r,P1,P2)        rational function over the rationals construction 
rfrdif(r,R1,R2)         rational function over the rationals difference 
rfrinv(r,R)             rational function over the rationals inverse 
rfrneg(r,R)             rational function over the rationals negation 
rfrprod(r,R1,R2)        rational function over the rationals product 
rfrquot(r,R1,R2)        rational function over the rationals quotient 
rfrsum(r,R1,R2)         rational function over the rationals sum 
rfrtodiprfr(r1,r2,F)    rational function over the rationals to 
			distributive polynomial over rational functions 
			over the rationals 
rfrtransf(r1,R1,V1,r2,R2,V2,Vn,pV3) rational function over the rationals 
			transformation 
rho-                    method ( fast reduction ) by Pollard divisor search 
			rhofrpds(N,b,z) 
rho-                    method by Pollard divisor search ( lists only ) 
			rhopds_lo(N,b,z) 
rho-                    method by Pollard divisor search rhopds(N,b,z) 
rhofrpds(N,b,z)         rho- method ( fast reduction ) by Pollard divisor 
			search 
rhopds(N,b,z)           rho- method by Pollard divisor search 
rhopds_lo(N,b,z)        rho- method by Pollard divisor search ( lists only 
			) 
right                   shift irshift(A) integer 
right                   side ecrsnfrroots(a,b) elliptic curve over rational 
			numbers, short normal form, real roots of the 
ring                    of an univariate separable polynomial over the 
			integers normelpruspi(P,a) norm of an element of 
			the polynomial 
ring                    of an univariate separable polynomial over the 
			integers vepvelpruspi(F,a,p,k,v) values of the 
			extensions of the p-adic valuation of an element of 
			the polynomial 
ring                    over modular single prime, transcendence degree 1 
			nepousppmsp1(p,F,a) norm of an element of the 
			polynomial order of an univariate separable 
			polynomial over the polynomial 
ring                    over modular single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the extensions 
			of the P-adic valuation of an element of the 
			polynomial order of a univariate separable 
			polynomial over the polynomial 
ring                    over modular single prime, transcendence degree 1, 
			Dedekind maximality test ouspprmsp1dm(p,P,F) order 
			of an univariate separable polynomial over 
			polynomial 
ring                    over modular single prime, transcendence degree 1, 
			Hensel factorization approximation 
			upprmsp1hfa(p,F,P,L,k) univariate polynomial over 
			polynomial 
ring                    over modular single prime, transcendence degree 1, 
			Hensel lemma initialization upprmsp1hli(p,F,P,L) 
			univariate polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			Hensel quadratic step upprmsp1hqs(p,F,T,L1,L2,A) 
			univariate polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			algebraic function over modular single prime, 
			transcendence degree 1, evaluation special 
			upprmsp1afes(p,F,P,a) univariate polynomial over 
			polynomial 
ring                    over modular single prime, transcendence degree 1, 
			approximation of P-adic factorization 
			uspprmsp1apf(p,P,F,k) univariate separable 
			polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			basis from generators oprmsp1basfg(p,F,L) order 
			over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			basis of a local maximal over-order 
			ouspprmsp1bl(p,F,P,Q,pk) order of an univariate 
			separable polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			decomposition law ouspprmsp1dl(p,F,P,k) order of a 
			univariate separable polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			discriminant upprmsp1disc(p,F) univariate 
			polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			integral basis ouspprmsp1ib(p,F,pL) order of an 
			univariate separable polynomial over the polynomial 
ring                    over modular single prime, transcendence degree 1, 
			reduced discriminant upprmsp1redd(p,F) univariate 
			polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			resultant, Sylvester algorithm 
			pprmsp1ress(r,p,P1,P2) polynomial over polynomial 
ring                    over modular single prime, transcendence degree 1, 
			resultant, Sylvester algorithm 
			upprmsp1ress(p,P1,P2) univariate polynomial over 
			polynomial 
ring                    over modular single primes, transcendence degree 1, 
			element test modprmsp1elt(B,p,a) module over 
			polynomial 
rinv(R)                 rational number inverse 
rlog2(R)                rational number logarithm, base 2 
rmax(R,S)               (MACRO) rational number maximum 
rmin(R,S)               (MACRO) rational number minimum 
rneg(R)                 rational number negation 
rnum(R)                 (MACRO) rational number numerator 
root                    ( lists only ) isqrt_lo(A) integer square 
root                    all solutions misqrtas(N,r) modular integer square 
root                    csqrt(z) complex square 
root                    finding (rekursiv) upgfsrf(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic 
root                    finding (rekursiv) upmirf(ip,P) univariate 
			polynomial over modular integers, 
root                    finding (rekursiv) upmsrf(m,P) univariate 
			polynomial over modular singles, 
root                    finding, special (rekursiv) upmirfspec(ip,P) 
			univariate polynomial over modular integers, 
root                    flsqrt(f) floating point square 
root                    iroot(A,n,ps) integer 
root                    isqrt(A) integer square 
root                    miproot(Q) modular integer primitive 
root                    mipsqrt(p,r) modular integer prime square 
root                    misqrt(m,a) modular integer square 
root                    mppsqrt(p,n,r,xk,k) modular prime power square 
root                    mpsqrt(p,a) modular primes square 
root                    nf3sqrt(F,el) number field of degree 3 square 
root                    power series upmssrpser(m,P,i) univariate 
			polynomial over modular singles square 
root                    principal part upmssrpp(m,P) univariate polynomial 
			over modular singles square 
root                    search misqrtsrch(m,a) modular integer square 
root                    ssqrt(n) single-precision square 
roots                   of the right side ecrsnfrroots(a,b) elliptic curve 
			over rational numbers, short normal form, real 
rotation                lerot(L,k,l) list element 
round                   flround(f) floating point 
row                     and 1 column madel1rc(pM,i,j) matrix delete 1 
rows                    and columns madelsrc(pM,I,J) (MACRO) matrix delete 
			several 
rows                    madelsr(pM,I) matrix delete several 
rows                    maiegsr(M,A,B) matrix of integers Euklid- Gauss- 
			step for 
rows                    manrrow(M) (MACRO) matrix number of 
rows                    maupmipegsr(p,M,A,B) matrix of univariate 
			polynomials over modular integer primes Euklid- 
			Gauss- step for 
rows                    maupmspegsr(p,M,A,B) matrix of univariate 
			polynomials over modular single primes Euklid- 
			Gauss- step for 
rows                    maupregsr(M,A,B) matrix of univariate polynomials 
			over rationals Euklid- Gauss- step for 
rp2(n)                  rational number power of 2 
rprod(R,S)              rational number product 
rqnfdif(D,a,b)          (MACRO) rational number, quadratic number field 
			element, difference 
rqnffu(D,pl)            real quadratic number field fundamental unit 
rqnfquot(D,a,b)         rational number, quadratic number field element, 
			quotient 
rquot(R,S)              (MACRO) rational number quotient 
rsign(R)                (MACRO) rational number signum 
rsum(R,S)               rational number sum 
rtofl(r)                rational number to floating point 
rtomi(R,M)              rational number to modular integer 
rtonf(R)                rational number to number field element 
rtonfs(R)               rational number to number field element, sparse 
			representation 
rtopfel(p,d,R)          rational to p-adic field element 
rtoqnf(D,A)             (MACRO) rational number to quadratic number field 
			element 
rtorfr(r,R)             rational number to rational function over rationals 
sabs(a)                 (MACRO) single-precision absolute value 
sbtoudpm2(a)            (MACRO) special bit-representation to univariate 
			dense polynomial over modular 2 
scalar                  multiplication magfssmul(p,AL,M,el) matrix of 
			Galois-field with single characteristic elements 
scalar                  multiplication maismul(M,el) matrix of integers 
scalar                  multiplication mamismul(m,M,el) matrix of modular 
			integers 
scalar                  multiplication mamssmul(m,M,el) matrix of modular 
			singles 
scalar                  multiplication manfsmul(F,M,el) matrix of number 
			field elements 
scalar                  multiplication manfssmul(F,M,el) matrix of number 
			field elements, sparse representation, 
scalar                  multiplication mapgfssmul(r,p,AL,M,el) matrix of 
			polynomials over Galois-field with single 
			characteristic 
scalar                  multiplication mapismul(r,M,P) matrix of 
			polynomials over integers 
scalar                  multiplication mapmismul(r,m,M,P) matrix of 
			polynomials over modular integers 
scalar                  multiplication mapmssmul(r,m,M,P) matrix of 
			polynomials over modular singles 
scalar                  multiplication mapnfsmul(r,F,M,el) matrix of 
			polynomials over number field 
scalar                  multiplication maprsmul(r,M,P) matrix of 
			polynomials over rationals 
scalar                  multiplication marfmsp1smul(p,M,F) matrix of 
			rational functions over modular single primes, 
			transcendence degree 1, 
scalar                  multiplication marfrsmul(r,M,F) matrix of rational 
			functions over rationals 
scalar                  multiplication marsmul(M,el) matrix of rationals 
scalar                  multiplication vecgfssmul(p,AL,V,el) vector of 
			Galois-field with single characteristic elements 
scalar                  multiplication vecismul(s,V) vector of integers 
scalar                  multiplication vecmismul(m,s,V) vector of modular 
			integers 
scalar                  multiplication vecmssmul(m,s,V) vector of modular 
			singles 
scalar                  multiplication vecnfsmul(F,V,el) vector of number 
			field elements 
scalar                  multiplication vecnfssmul(F,V,el) vector of number 
			field elements, sparse representation, 
scalar                  multiplication vecpgfssmul(r,p,AL,V,el) vector of 
			polynomials over Galois-field with single 
			characteristic 
scalar                  multiplication vecpismul(r,P,V) vector of 
			polynomials over integers 
scalar                  multiplication vecpmismul(r,m,P,V) vector of 
			polynomials over modular integers 
scalar                  multiplication vecpmssmul(r,m,P,V) vector of 
			polynomials over modular singles 
scalar                  multiplication vecpnfsmul(r,F,U,el) vector of 
			polynomials over number field 
scalar                  multiplication vecprsmul(r,P,V) vector of 
			polynomials over rationals 
scalar                  multiplication vecrfmsp1sm(p,F,V) vector of 
			rational functions over modular single primes, 
			transcendence degree 1, 
scalar                  multiplication vecrfrsmul(r,F,V) vector of rational 
			functions over rationals 
scalar                  multiplication vecrsmul(s,V) vector of rationals 
scalar                  product vecgf2sprod(G,V,W) vector of Galois-field 
			with characteristic 2 elements 
scalar                  product vecgfssprod(p,AL,V,W) vector of 
			Galois-field with single characteristic elements 
scalar                  product vecisprod(V,W) vector of integers 
scalar                  product vecmisprod(M,V,W) vector of modular 
			integers 
scalar                  product vecmssprod(m,V,W) vector of modular singles 
scalar                  product vecnfsprod(F,V,W) vector of number field 
			elements 
scalar                  product vecnfssprod(F,V,W) vector of number field 
			elements, sparse representation, 
scalar                  product vecpisprod(r,V,W) vector of polynomials 
			over integers 
scalar                  product vecpmisprod(r,m,V,W) vector of polynomials 
			over modular integers 
scalar                  product vecpmssprod(r,m,V,W) vector of polynomials 
			over modular singles 
scalar                  product vecprsprod(r,V,W) vector of polynomials 
			over rationals 
scalar                  product vecrfmsp1sp(p,V,W) vector of rational 
			functions over modular single primes, transcendence 
			degree 1, 
scalar                  product vecrfrsprod(r,V,W) vector of rational 
			functions over rationals 
scalar                  product vecrsprod(V,W) vector of rationals 
scalar                  product vpgfssprod(r,p,AL,V,W) vector of 
			polynomials over Galois-field with single 
			characteristic 
scalar                  product vpnfsprod(r,F,V,W) vector of polynomials 
			over number field 
sclfupi(P,n)            special coefficient list from univariate polynomial 
			over the integers 
sclfuprfmsp1(P,n)       special coefficient list from univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1 
sdiff(L1,L2)            set difference 
sdisccleq(D,L)          single discriminant class equation 
search                  ( lists only ) rhopds_lo(N,b,z) rho- method by 
			Pollard divisor 
search                  (rekursiv) irds(n,G,p) integer random divisor 
search                  dpipds(a,N) double precision integer prime divisor 
search                  elcfds(N,b,e) elliptic curve fast divisor 
search                  elcpds(N,a,z) elliptic curve pure divisor 
search                  ilpds(N,A,B,pP,pN1) integer large prime divisor 
search                  impds(N,A,B,pP,pQ) integer medium prime divisor 
search                  imspds(N,a,b) integer medium single prime divisor 
search                  ispd(N,pM) integer small prime divisors 
search                  lsrch(a,L) list 
search                  misqrtsrch(m,a) modular integer square root 
search                  rhofrpds(N,b,z) rho- method ( fast reduction ) by 
			Pollard divisor 
search                  rhopds(N,b,z) rho- method by Pollard divisor 
search                  sum elcpdssum(N,x1,y1,x2,y2,px3,py3,a) elliptic 
			curve prime divisor 
second                  case qffmsregbg2(m,D,s) quadratic function field 
			over modular singles regulator, baby step - giant 
			step version, 
second                  lsecond(L) (MACRO) list 
segcd(a,b,pu,pv)        single-precision extended greatest common divisor 
select                  element maselel(M,m,n) (MACRO) matrix 
selected                variable ppfderivsv(r,p,P,n) polynomial over p-adic 
			field derivation, 
selected                variable ppfevalsv(r,p,P,n,A) polynomial over 
			p-adic field evaluation, 
selected                variable ppfsubstsv(r,p,P1,n,P2) polynomial over 
			p-adic field substitution, 
separable               polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Dedekind maximality 
			test ouspprmsp1dm(p,P,F) order of an univariate 
separable               polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, approximation of 
			P-adic factorization uspprmsp1apf(p,P,F,k) 
			univariate 
separable               polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, basis of a local 
			maximal over-order ouspprmsp1bl(p,F,P,Q,pk) order 
			of an univariate 
separable               polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, decomposition law 
			ouspprmsp1dl(p,F,P,k) order of a univariate 
separable               polynomial over the integers approximation of 
			p-adic factorization of the defining polynomial, 
			generators of p-maximal orders of the p-adic 
			divisors of the defining polynomial and p-minimal 
			polynomials of the generators ouspiapfgmic(p,P,k) 
			order of an univariate 
separable               polynomial over the integers basis of a local 
			maximal over-order ouspibaslmo(F,p,Q,pk) order of 
			an univariate 
separable               polynomial over the integers basis of a local 
			maximal over-order with respect to integer primes 
			ouspibaslmoi(F,P,Q,pk) order of an univariate 
separable               polynomial over the integers basis of the integral 
			closure ( ORDMAX, Ordmax, ordmax, integral basis ) 
			ouspibasisic(F,pL) order of an univariate 
separable               polynomial over the integers normelpruspi(P,a) norm 
			of an element of the polynomial ring of an 
			univariate 
separable               polynomial over the integers 
			vepvelpruspi(F,a,p,k,v) values of the extensions of 
			the p-adic valuation of an element of the 
			polynomial ring of an univariate 
separable               polynomial over the integers, approximation of 
			p-adic factorization uspiapf(p,P,k) univariate 
separable               polynomial over the polynomial ring over modular 
			single prime, transcendence degree 1 
			nepousppmsp1(p,F,a) norm of an element of the 
			polynomial order of an univariate 
separable               polynomial over the polynomial ring over modular 
			single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the extensions 
			of the P-adic valuation of an element of the 
			polynomial order of a univariate 
separable               polynomial over the polynomial ring over modular 
			single prime, transcendence degree 1, integral 
			basis ouspprmsp1ib(p,F,pL) order of an univariate 
separate                factor of equal degree upgf2sfed(G,H,d) univariate 
			polynomial over Galois-field with characteristic 2, 
separate                factor of equal degree upmisfed(ip,G,d) univariate 
			polynomial over modular integers 
separate                factors of equal degree upgfssfed(p,AL,G,d) 
			univariate polynomial over Galois-field with single 
			characteristic, 
series                  ecrclser(E,A,n) elliptic curve over the rationals, 
			coefficients of L- 
series                  upmssrpser(m,P,i) univariate polynomial over 
			modular singles square root power 
set                     NTH_EPS eciminntheps(E,d) elliptic curve with 
			integer coefficients, minimal model, 
set                     SPACE setspace(anz) 
set                     STACK setstack(anz) 
set                     difference sdiff(L1,L2) 
set                     difference usdiff(L1,L2) unordered 
set                     element masetel(M,m,n,el) (MACRO) matrix 
set                     first lsfirst(L,a) (MACRO) list 
set                     from partition csetpart(L) characteristic 
set                     intersection csetinter(S,T) characteristic 
set                     intersection sinter(L1,L2) 
set                     intersection usinter(L1,L2) unordered 
set                     leset(L,k,a) list element 
set                     output-counter setocnt(pf,n) 
set                     precision flsetprec(k,N) floating point 
set                     reductum lsred(L1,L2) (MACRO) list 
set                     symmetrical difference ussdiff(L1,L2) unordered 
set                     time settime() 
set                     union csetunion(S,T) characteristic 
set                     union sunion(L1,L2) 
set                     union usunion(L1,L2) (MACRO) unordered 
setocnt(pf,n)           set output-counter 
setspace(anz)           set SPACE 
setstack(anz)           set STACK 
settime()               set time 
seven(a)                (MACRO) single-precision even 
several                 columns madelsc(pM,I) matrix delete 
several                 rows and columns madelsrc(pM,I,J) (MACRO) matrix 
			delete 
several                 rows madelsr(pM,I) matrix delete 
sexp(a,n)               (MACRO) single-precision exponentiation 
sfact(n)                single factorization 
sfactors(n)             single factors 
sfel(n)                 single factor exponent list 
sgcd(a,b)               single-precision greatest common divisor 
sgeta(ps)               string get atom 
sgetc(ps)               string get character 
sgetcb(pf)              string get character, skipping blanks 
sgetcs(ps)              string get character, skipping space 
sgetfl(ps)              string get floating point 
sgetflsp(ps)            string get floating point special version 
sgeti(ps)               string get integer 
sgetl(ps)               string get list (rekursiv) 
sgetr(ps)               string get rational number 
sgetsi(ps)              string get single 
shift                   irshift(A) integer right 
shiftings               PAFshift() Papanikolaou floating point package: 
short                   normal form ? iselecmpsnf(p,a,b,P) is element of an 
			elliptic curve over modular primes, 
short                   normal form ? iselecnfsnf(F,a,b,P) is element of an 
			elliptic curve over number field, 
short                   normal form eciminbtsnf(E) elliptic curve with 
			integer coefficients, minimal model, birational 
			transformation to 
short                   normal form ecimintosnf(E) elliptic curve with 
			integer coefficients, minimal model to 
short                   normal form ecmptosnf(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular primes to 
short                   normal form ecnftosnf(F,a1,a2,a3,a4,a6) elliptic 
			curve over number field to 
short                   normal form ecracbtsnf(E) elliptic curve over 
			rational numbers, actual curve, birational 
			transformation to 
short                   normal form fputecisnf(E,*pf) file put elliptic 
			curve with integer coefficients, 
short                   normal form isponecisnf(E,P) is point on elliptic 
			curve with integer coefficients, model in 
short                   normal form line through points 
			ecnfsnflp(F,a,b,P1,P2) elliptic curve over number 
			field 
short                   normal form multiplication-map 
			ecnfsnfmul(F,a,b,n,P1) elliptic curve over number 
			field 
short                   normal form negative point ecnfsnfneg(F,a,b,P) 
			elliptic curve over number field 
short                   normal form number of points special version 
			ecmipsnfnpsv(p,a4,a6) elliptic curve over modular 
			integer primes 
short                   normal form putecisnf(E) (MACRO) put elliptic curve 
			with integer coefficients, 
short                   normal form sum of points ecnfsnfsum(F,a,b,P1,P2) 
			elliptic curve over number field 
short                   normal form, Mordell-Weil-group, base 
			ecisnfmwgbase(E) elliptic curve with integer 
			coefficients, 
short                   normal form, Shanks' algorithm ecmspsnfsha(p,a4,a6) 
			(MACRO) elliptic curve over modular single primes, 
short                   normal form, a4 ecisnfa4(E) elliptic curve with 
			integer coefficients, 
short                   normal form, a6 ecisnfa6(E) elliptic curve with 
			integer coefficients, 
short                   normal form, b2 ecisnfb2(E) elliptic curve with 
			integer coefficients, 
short                   normal form, b4 ecisnfb4(E) elliptic curve with 
			integer coefficients, 
short                   normal form, b6 ecisnfb6(E) elliptic curve with 
			integer coefficients, 
short                   normal form, b8 ecisnfb8(E) elliptic curve with 
			integer coefficients, 
short                   normal form, birational transformation of 
			coefficients ecisnfbtco(E,BT) elliptic curve with 
			integer coefficients, 
short                   normal form, birational transformation to actual ( 
			rational ) model ecisnfbtac(E) elliptic curve with 
			integer coefficients, 
short                   normal form, birational transformation to minimal 
			model ecisnfbtmin(E) elliptic curve with integer 
			coefficients, 
short                   normal form, c4 ecisnfc4(E) elliptic curve with 
			integer coefficients, 
short                   normal form, c6 ecisnfc6(E) elliptic curve with 
			integer coefficients, 
short                   normal form, combined Schoof- Shanks- algorithm 
			ecmpsnfcssa(p,a4,a6,s,pl,ts) elliptic curve over 
			modular primes, 
short                   normal form, construction of division polynomials 
			ecmpsnfcdivp(P,a4,a6,n) elliptic curve over modular 
			primes, 
short                   normal form, difference between Weil height and 
			Neron-Tate height ecisnfdwhnth(E) elliptic curve 
			with integer coefficients, 
short                   normal form, discriminant ecisnfdisc(E) elliptic 
			curve with integer coefficients, 
short                   normal form, discriminant ecmpsnfdisc(p,a4,a6) 
			elliptic curve over modular primes, 
short                   normal form, discriminant ecnfsnfdisc(F,a,b) 
			elliptic curve over number field, 
short                   normal form, double of point ecisnfdouble(E,P) 
			elliptic curve with integer coefficients, 
short                   normal form, elliptic logarithm of point 
			ecisnfelogp(E,P,n) elliptic curve with integer 
			coefficients, 
short                   normal form, factorization of discriminant 
			ecisnffdisc(E) elliptic curve with integer 
			coefficients, 
short                   normal form, find point ecmpsnffp(p,a4,a6) elliptic 
			curve over modular primes, 
short                   normal form, finding a multiple of the order of a 
			point with the Pollard Lambda method 
			ecmpsnffmopl(p,a4,a6,P,L,N) elliptic curve over 
			modular primes, 
short                   normal form, finding a multiple of the order of a 
			point with the Pollard Rho method 
			ecmpsnffmopr(p,a4,a6,P,k) elliptic curve over 
			modular primes, 
short                   normal form, generators of the torsion group 
			ecisnfgentor(E) elliptic curve with integer 
			coefficients, 
short                   normal form, j-invariant ecmpsnfjinv(p,a4,a6) 
			elliptic curve over modular primes, 
short                   normal form, j-invariant ecnfsnfjinv(F,a,b) 
			elliptic curve over number field, 
short                   normal form, line through points 
			ecmpsnflp(p,a4,a6,P1,P2) elliptic curve over 
			modular primes, 
short                   normal form, modified Shanks' algorithm, first part 
			ecmpsnfmsha1(p,a4,a6,P,a,m,pl,ts) elliptic curve 
			over modular primes, 
short                   normal form, multiple of the order of a point to 
			exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular primes, 
short                   normal form, multiplication-map ecisnfmul(E,P,n) 
			elliptic curve with integer coefficients, 
short                   normal form, multiplication-map 
			ecmpsnfmul(p,a4,a6,n,P1) elliptic curve over 
			modular primes, 
short                   normal form, multiplication-map, special version 
			ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve over 
			modular primes, 
short                   normal form, negative of point ecisnfneg(E,P) 
			elliptic curve with integer coefficients, 
short                   normal form, negative point ecmpsnfneg(p,a4,a6,P) 
			elliptic curve over modular primes, 
short                   normal form, number of points ecmspsnfnp(p,a4,a6) 
			elliptic curve over modular single primes, 
short                   normal form, number of points modulo 2 
			ecmpsnfnpm2(P,a4,a6) elliptic curve over modular 
			primes, 
short                   normal form, number of points modulo a single prime 
			determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
			modular primes, 
short                   normal form, number of points modulo an integer 
			determined with the Schoof algorithm 
			ecmpsnfnpmi(P,a4,a6,S,pM) elliptic curve over 
			modular primes, 
short                   normal form, points of bounded Weil height 
			ecisnfpbwh(E,PL,lb,ub,modus,hmin,BL) elliptic curve 
			with integer coefficients, 
short                   normal form, real roots of the right side 
			ecrsnfrroots(a,b) elliptic curve over rational 
			numbers, 
short                   normal form, sum of points ecisnfsum(E,P,Q) 
			elliptic curve with integer coefficients, 
short                   normal form, sum of points 
			ecmpsnfsum(p,a4,a6,P1,P2) elliptic curve over 
			modular primes, 
short                   normal form, sum of points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve 
			over modular primes, 
short                   normal form, torsion group ecisnftorgr(E) elliptic 
			curve with integer coefficients, 
side                    ecrsnfrroots(a,b) elliptic curve over rational 
			numbers, short normal form, real roots of the right 
sign                    and upper bound itoEsb(A,e,grenze) ( SIMATH ) 
			integer to Essen integer, 
sign                    flsign(f) (MACRO) floating point 
sign                    isign(A) integer 
sign                    of the functional equation ecrsign(E) elliptic 
			curve over rational numbers, 
sign                    of the functional equation, special version 
			ecrsigns(E,A,C) elliptic curve over the rationals, 
sign,                   base variable pisign(r,P) polynomial over integers 
signum                  dipevsign(r,EV) distributive polynomial exponent 
			vector 
signum                  rsign(R) (MACRO) rational number 
signum                  ssign(a) (MACRO) single-precision 
single                  ? isms(m,a) is modular 
single                  ? issingle(a) (MACRO) is 
single                  Fermat residue list msfrl(m,a) modular 
single                  XOR product special sxprods(a,b) 
single                  XOR product sxprod(a,b,pc,pd) 
single                  XOR square sxsqu(a,pc,pd) 
single                  characteristic (rekursiv) pgf2topgfs(r,G,P) 
			polynomial over Galois-field with characteristic 2 
			to polynomial over Galois-field with 
single                  characteristic (rekursiv) pmstopgfs(r,p,P) 
			polynomial over modular singles to polynomial over 
			Galois-field with 
single                  characteristic ? (rekursiv) ispgfs(r,p,AL,P) is 
			polynomial over Galois-field with 
single                  characteristic ? ismapgfs(r,p,AL,M) (MACRO) is 
			matrix of polynomials over Galois-field with 
single                  characteristic ? isvecpgfs(r,p,AL,V) (MACRO) is 
			vector of polynomials over Galois-field with 
single                  characteristic Berlekamp Q polynomials construction 
			upgfsbqp(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic Berlekamp factorization 
			upgfsbfact(p,AL,P,d) univariate polynomial over 
			Galois-field with 
single                  characteristic Berlekamp factorization, Zassenhaus 
			method upgfsbfzm(p,AL,s,P,G) univariate polynomial 
			over Galois-field with 
single                  characteristic Berlekamp factorization, last step 
			upgfsbfls(p,AL,P,B,d) univariate polynomial over 
			Galois-field with 
single                  characteristic Groebner basis augmentation 
			dipgfsgba(r,p,AL,PL,P) distributive polynomial over 
			Galois-field with 
single                  characteristic Groebner basis dipgfsgb(r,p,AL,PL) 
			distributive polynomial over Galois-field with 
single                  characteristic Groebner basis recursion 
			dipgfsgbr(r,p,AL,PL) distributive polynomial over 
			Galois-field with 
single                  characteristic S-polynomial dipgfssp(r,p,AL,P1,P2) 
			distributive polynomial over Galois-field with 
single                  characteristic arithmetic list ? isgfsal(p,AL) is 
			Galois-field with 
single                  characteristic arithmetic list generator 
			gfsalgen(p,n,G) Galois-field with 
single                  characteristic arithmetic list generator isomorphic 
			embedding of subfield gfsalgenies(p,m,n,ALn) 
			Galois-field with 
single                  characteristic characteristic polynomial 
			mapgfschpol(r,p,AL,M) (MACRO) matrix of polynomials 
			over Galois-field with 
single                  characteristic complete factorization special 
			upgfscfacts(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic complete factorization 
			upgfscfact(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic construction 1 mapgfscons1(r,p,AL,n) 
			(MACRO) matrix of polynomials over Galois-field 
			with 
single                  characteristic derivation, main variable 
			pgfsderiv(r,p,AL,P) polynomial over Galois-field 
			with 
single                  characteristic derivation, specified variable 
			(rekursiv) pgfsderivsv(r,p,AL,P,i) polynomial over 
			Galois-field with 
single                  characteristic determinant mapgfsdet(r,p,AL,M) 
			matrix of polynomials over Galois-field with 
single                  characteristic difference (rekursiv) 
			pgfsdif(r,p,AL,P1,P2) polynomial over Galois-field 
			with 
single                  characteristic difference dipgfsdif(r,p,AL,P1,P2) 
			distributive polynomial over Galois-field with 
single                  characteristic difference gfsdif(p,AL,a,b) (MACRO) 
			Galois-field with 
single                  characteristic difference mapgfsdif(r,p,AL,M,N) 
			(MACRO) matrix of polynomials over Galois-field 
			with 
single                  characteristic difference vecpgfsdif(r,p,AL,U,V) 
			(MACRO) vector of polynomials over Galois-field 
			with 
single                  characteristic distinct degree factorization 
			upgfsddfact(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic eigenvalues and irreducible factors 
			of the characteristic polynomial 
			magfsevifcp(p,AL,M,pL) matrix over Galois-field 
			with 
single                  characteristic element ? isgfsel(p,AL,a) is 
			Galois-field with 
single                  characteristic element evaluation first variable 
			special version (rekursiv) pigfsevalfvs(r,p,AL,P) 
			polynomial over integers Galois-field with 
single                  characteristic element evaluation first variable 
			special version mapigfsevfvs(r,p,AL,M) matrix over 
			polynomials over integers Galois-field with 
single                  characteristic element evaluation first variable 
			special version vecpigfsefvs(r,p,AL,V) vector over 
			polynomials over integers Galois-field with 
single                  characteristic element fgetgfsel(p,AL,V,pf) file 
			get Galois-field with 
single                  characteristic element fputgfsel(p,AL,a,V,pf) file 
			put Galois-field with 
single                  characteristic element getgfsel(p,AL,V) (MACRO) get 
			Galois-field with 
single                  characteristic element gf2eltogfsel(G,a) (MACRO) 
			Galois-field with characteristic 2 element to 
			Galois-field with 
single                  characteristic element one ? isgfsone(p,AL,a) is 
			Galois-field with 
single                  characteristic element product (rekursiv) 
			pgfsgfsprod(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic, 
			Galois-field with 
single                  characteristic element product 
			dipgfsgfprod(r,p,AL,P,a) distributive polynomial 
			over Galois-field with single characteristic, 
			Galois-field with 
single                  characteristic element putgfsel(p,AL,a,V) (MACRO) 
			put Galois-field with 
single                  characteristic element quotient (rekursiv) 
			pgfsgfsquot(r,p,AL,P,a) polynomial over 
			Galois-field with single characteristic, 
			Galois-field with 
single                  characteristic element to Galois-field with 
			characteristic 2 element gfseltogf2el(G,a) 
			Galois-field with 
single                  characteristic elements ? islistgfs(p,AL,L) is list 
			of Galois-field with 
single                  characteristic elements ? ismagfs(p,AL,M) (MACRO) 
			is matrix of Galois-field with 
single                  characteristic elements ? isvecgfs(p,AL,A) (MACRO) 
			is vector of Galois-field with 
single                  characteristic elements characteristic polynomial 
			magfschpol(p,AL,M) (MACRO) matrix of Galois-field 
			with 
single                  characteristic elements construction 1 
			magfscons1(p,AL,n) (MACRO) matrix of Galois-field 
			with 
single                  characteristic elements determinant 
			magfsdet(p,AL,M) matrix of Galois-field with 
single                  characteristic elements difference 
			magfsdif(p,AL,M,N) (MACRO) matrix of Galois-field 
			with 
single                  characteristic elements difference 
			vecgfsdif(p,AL,U,V) (MACRO) vector of Galois-field 
			with 
single                  characteristic elements exponentiation 
			magfsexp(p,AL,M,n) matrix of Galois-field with 
single                  characteristic elements fgetmagfs(p,AL,V,pf) 
			(MACRO) file get matrix of Galois-field with 
single                  characteristic elements fgetvecgfs(p,AL,VL,pf) 
			(MACRO) file get vector of Galois-field with 
single                  characteristic elements fputmagfs(p,AL,M,V,pf) 
			(MACRO) file put matrix of Galois-field with 
single                  characteristic elements fputvecgfs(p,AL,V,VL,pf) 
			(MACRO) file put vector of Galois-field with 
single                  characteristic elements getmagfs(p,AL,V) (MACRO) 
			get matrix of Galois-field with 
single                  characteristic elements getvecgfs(p,AL,VL) (MACRO) 
			get vector of Galois-field with 
single                  characteristic elements inverse magfsinv(p,AL,M) 
			matrix of Galois-field with 
single                  characteristic elements linear combination 
			vecgfslc(p,AL,s1,s2,L1,L2) vector of Galois-field 
			with 
single                  characteristic elements negation magfsneg(p,AL,M) 
			(MACRO) matrix of Galois-field with 
single                  characteristic elements negation vecgfsneg(p,AL,V) 
			(MACRO) vector of Galois-field with 
single                  characteristic elements product magfsprod(p,AL,M,N) 
			(MACRO) matrix of Galois-field with 
single                  characteristic elements putmagfs(p,AL,M,V) (MACRO) 
			put matrix of Galois-field with 
single                  characteristic elements putvecgfs(p,AL,V,VL) 
			(MACRO) put vector of Galois-field with 
single                  characteristic elements rank magfsrk(p,AL,M) matrix 
			of Galois-field with 
single                  characteristic elements scalar multiplication 
			magfssmul(p,AL,M,el) matrix of Galois-field with 
single                  characteristic elements scalar multiplication 
			vecgfssmul(p,AL,V,el) vector of Galois-field with 
single                  characteristic elements scalar product 
			vecgfssprod(p,AL,V,W) vector of Galois-field with 
single                  characteristic elements solution of a system of 
			linear equations magfsssle(p,AL,A,b,pX,pN) matrix 
			of Galois-field with 
single                  characteristic elements sum magfssum(p,AL,M,N) 
			(MACRO) matrix of Galois-field with 
single                  characteristic elements sum vecgfssum(p,AL,U,V) 
			(MACRO) vector of Galois-field with 
single                  characteristic elements vector multiplication 
			magfsvecmul(p,AL,A,x) (MACRO) matrix of 
			Galois-field with 
single                  characteristic elements, null space basis 
			magfsnsb(p,AL,M) matrix of Galois-field with 
single                  characteristic embedding in field extension 
			(rekursiv) pgfsefe(r,p,ALm,P,g) polynomial over 
			Galois-field with 
single                  characteristic embedding in field extension 
			gfsefe(p,ALm,a,g) Galois-field with 
single                  characteristic embedding in field extension 
			magfsefe(p,ALm,M,g) matrix over Galois-field with 
single                  characteristic embedding in field extension 
			mapgfsefe(r,p,ALm,M,g) matrix over polynomials over 
			Galois-field with 
single                  characteristic embedding in field extension 
			vecgfsefe(p,ALm,V,g) vector over Galois-field with 
single                  characteristic embedding in field extension 
			vecpgfsefe(r,p,ALm,V,g) vector over polynomials 
			over Galois-field with 
single                  characteristic evaluation, main variable 
			pgfseval(r,p,AL,P,a) polynomial over Galois-field 
			with 
single                  characteristic evaluation, specified variable 
			(rekursiv) pgfsevalsv(r,p,AL,P,d,a) polynomial over 
			Galois-field with 
single                  characteristic exponentiation gfsexp(p,AL,a,m) 
			Galois-field with 
single                  characteristic exponentiation mapgfsexp(r,p,AL,M,n) 
			matrix of polynomials over Galois-field with 
single                  characteristic exponentiation pgfsexp(r,p,AL,P,m) 
			polynomial over Galois-field with 
single                  characteristic extended greatest common divisor 
			upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate polynomial 
			over Galois-field with 
single                  characteristic fgetmapgfs(r,p,AL,V,Vgfs,pf) (MACRO) 
			file get matrix of polynomials over Galois-field 
			with 
single                  characteristic fgetpgfs(r,p,AL,V,Vgfs,pf) file get 
			polynomial over Galois-field with 
single                  characteristic fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) 
			file get vector of polynomials over Galois-field 
			with 
single                  characteristic fputmapgfs(r,p,AL,M,V,Vgfs,pf) 
			(MACRO) file put matrix of polynomials over 
			Galois-field with 
single                  characteristic fputvpgfs(r,p,AL,W,V,Vgfs,pf) 
			(MACRO) file put vector of polynomials over 
			Galois-field with 
single                  characteristic getmapgfs(r,p,AL,V,Vgfs) (MACRO) get 
			matrix of polynomials over Galois-field with 
single                  characteristic getpgfs(r,p,AL,V,Vgfs) (MACRO) get 
			polynomial over Galois-field with 
single                  characteristic getvpgfs(r,p,AL,V,Vgfs) (MACRO) get 
			vector of polynomials over Galois-field with 
single                  characteristic greatest common divisor 
			upgfsgcd(p,AL,P1,P2) univariate polynomial over 
			Galois-field with 
single                  characteristic greatest squarefree divisor 
			(rekursiv) upgfsgsd(p,AL,P) univariate polynomial 
			over Galois-field with 
single                  characteristic half extended greatest common 
			divisor upgfshegcd(p,AL,P1,P2,pP3) univariate 
			polynomial over Galois-field with 
single                  characteristic in graduated lexicographical order 
			dipgfslotglo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with 
single                  characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in graduated lexicographical 
			order dipgfslotglo(r,p,AL,P) distributive 
			polynomial over Galois-field with 
single                  characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
single                  characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) distributive polynomial over 
			Galois-field with 
single                  characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
single                  characteristic inverse gfsinv(p,AL,a) Galois-field 
			with 
single                  characteristic inverse mapgfsinv(r,p,AL,M) matrix 
			of polynomials over Galois-field with 
single                  characteristic linear combination 
			vecpgfslc(r,p,AL,s1,s2,L1,L2) vector of polynomials 
			over Galois-field with 
single                  characteristic list fgetdipgfsl(r,p,AL,VL,Vgfs,pf) 
			file get distributive polynomial over Galois-field 
			with 
single                  characteristic list 
			fputdipgfsl(r,p,AL,PL,VL,Vgfs,pf) file put 
			distributive polynomial over Galois-field with 
single                  characteristic list getdipgfsl(r,p,AL,VL,Vgfs) 
			(MACRO) get distributive polynomial over 
			Galois-field with 
single                  characteristic list putdipgfsl(r,p,AL,PL,VL,Vgfs) 
			(MACRO) put distributive polynomial over 
			Galois-field with 
single                  characteristic maitomagfs(p,M) matrix over integers 
			to matrix over Galois-field with 
single                  characteristic monic dipgfsmonic(r,p,AL,P) 
			distributive polynomial over Galois-field with 
single                  characteristic monic pgfsmonic(r,p,AL,P) polynomial 
			over Galois-field with 
single                  characteristic mpgfstompmp(r,p,AL,P,M) matrix of 
			polynomials over Galois-field with single 
			characteristic to matrix of polynomials modulo 
			polynomial over Galois-field with 
single                  characteristic mpmstompgfs(r,p,M) matrix of 
			polynomials over modular singles to matrix of 
			polynomials over Galois-field with 
single                  characteristic negation (rekursiv) 
			pgfsneg(r,p,AL,P) polynomial over Galois-field with 
single                  characteristic negation as function gfsnegf(p,AL,a) 
			Galois-field with 
single                  characteristic negation dipgfsneg(r,p,AL,P) 
			distributive polynomial over Galois-field with 
single                  characteristic negation gfsneg(p,AL,a) (MACRO) 
			Galois-field with 
single                  characteristic negation mapgfsneg(r,p,AL,M) (MACRO) 
			matrix of polynomials over Galois-field with 
single                  characteristic negation vecpgfsneg(r,p,AL,V) 
			(MACRO) vector of polynomials over Galois-field 
			with 
single                  characteristic number of irreducible factors 
			upgfsnif(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic product (rekursiv) 
			pgfsprod(r,p,AL,P1,P2) polynomial over Galois-field 
			with 
single                  characteristic product dipgfsprod(r,p,AL,P1,P2) 
			distributive polynomial over Galois-field with 
single                  characteristic product gfsprod(p,AL,a,b) 
			Galois-field with 
single                  characteristic product mapgfsprod(r,p,AL,M,N) 
			(MACRO) matrix of polynomials over Galois-field 
			with 
single                  characteristic putmapgfs(r,p,AL,M,V,Vgfs) (MACRO) 
			put matrix of polynomials over Galois-field with 
single                  characteristic putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) 
			put vector of polynomials over Galois-field with 
single                  characteristic quotient and remainder (rekursiv) 
			pgfsqrem(r,p,AL,P1,P2,pR) polynomial over 
			Galois-field with 
single                  characteristic quotient gfsquot(p,AL,a,b) 
			Galois-field with 
single                  characteristic quotient pgfsquot(r,p,AL,P1,P2) 
			(MACRO) polynomial over Galois-field with 
single                  characteristic randomize upgfsrand(p,AL,m) 
			univariate polynomial over Galois-field with 
single                  characteristic randomize, positive degree 
			upgfsrandpd(p,AL,m) univariate polynomial over 
			Galois-field with 
single                  characteristic relative prime factorization 
			upgfsrelpfac(p,AL,P,Fak,pA2) univariate polynomial 
			over Galois-field with 
single                  characteristic remainder pgfsrem(r,p,AL,P1,P2) 
			(MACRO) polynomial over Galois-field with 
single                  characteristic resultant pgfsres(r,p,AL,P1,P2) 
			polynomial over Galois-field with 
single                  characteristic root finding (rekursiv) 
			upgfsrf(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic scalar multiplication 
			mapgfssmul(r,p,AL,M,el) matrix of polynomials over 
			Galois-field with 
single                  characteristic scalar multiplication 
			vecpgfssmul(r,p,AL,V,el) vector of polynomials over 
			Galois-field with 
single                  characteristic scalar product 
			vpgfssprod(r,p,AL,V,W) vector of polynomials over 
			Galois-field with 
single                  characteristic squarefree factorization (rekursiv) 
			upgfssfact(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic squarefree part upgfssfp(p,AL,P) 
			univariate polynomial over Galois-field with 
single                  characteristic sum (rekursiv) pgfssum(r,p,AL,P1,P2) 
			polynomial over Galois-field with 
single                  characteristic sum as function gfssumf(p,AL,a,b) 
			Galois-field with 
single                  characteristic sum dipgfssum(r,p,AL,P1,P2) 
			distributive polynomial over Galois-field with 
single                  characteristic sum gfssum(p,AL,a,b) (MACRO) 
			Galois-field with 
single                  characteristic sum mapgfssum(r,p,AL,M,N) (MACRO) 
			matrix of polynomials over Galois-field with 
single                  characteristic sum vecpgfssum(r,p,AL,U,V) (MACRO) 
			vector of polynomials over Galois-field with 
single                  characteristic to matrix of polynomials modulo 
			polynomial over Galois-field with single 
			characteristic mpgfstompmp(r,p,AL,P,M) matrix of 
			polynomials over Galois-field with 
single                  characteristic to polynomial over Galois-field with 
			characteristic 2 (rekursiv) pgfstopgf2(r,G,P) 
			polynomial over Galois-field with 
single                  characteristic to vector of polynomials modulo 
			polynomial over Galois-field with single 
			characteristic vpgfstovpmp(r,p,AL,P,V) vector of 
			polynomials over Galois-field with 
single                  characteristic transformation 
			mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) matrix 
			of polynomials over Galois-field with 
single                  characteristic transformation 
			pgfstransf(r1,p,AL,P1,V1,r2,P2,V2,Vn,pV3) 
			polynomial over Galois-field with 
single                  characteristic transformation 
			vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) vector 
			of polynomials over Galois-field with 
single                  characteristic vecitovecgfs(p,V) vector over 
			integers to vector over Galois-field with 
single                  characteristic vector multiplication 
			mapgfsvmul(r,p,AL,A,x) (MACRO) matrix of 
			polynomials over Galois-field with 
single                  characteristic vpgfstovpmp(r,p,AL,P,V) vector of 
			polynomials over Galois-field with single 
			characteristic to vector of polynomials modulo 
			polynomial over Galois-field with 
single                  characteristic vpmstovpgfs(r,p,V) vector of 
			polynomials over modular singles to vector of 
			polynomials over Galois-field with 
single                  characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with 
single                  characteristic, Ben-Or factorization 
			upgfsbofact(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic, Ben-Or factorization, special 
			upgfsbofacts(p,AL,P) univariate polynomial over 
			Galois-field with 
single                  characteristic, Galois-field with single 
			characteristic element product (rekursiv) 
			pgfsgfsprod(r,p,AL,P,a) polynomial over 
			Galois-field with 
single                  characteristic, Galois-field with single 
			characteristic element product 
			dipgfsgfprod(r,p,AL,P,a) distributive polynomial 
			over Galois-field with 
single                  characteristic, Galois-field with single 
			characteristic element quotient (rekursiv) 
			pgfsgfsquot(r,p,AL,P,a) polynomial over 
			Galois-field with 
single                  characteristic, element randomize gfselrand(p,AL) 
			Galois-field with 
single                  characteristic, exponentiation, polynomial 
			remainder pgfsexpprem(r,p,AL,F,E,M) polynomial over 
			Galois-field with 
single                  characteristic, separate factors of equal degree 
			upgfssfed(p,AL,G,d) univariate polynomial over 
			Galois-field with 
single                  characteristic, trace function upgfstf(p,AL,G,d,M) 
			univariate polynomial over Galois-field with 
single                  chinese remainder algorithm miscra(M,m,m1,A,a) 
			modular integer 
single                  chinese remainder algorithm mscra(m1,m2,n1,a1,a2) 
			modular 
single                  chinese remainder algorithm, n arguments (rekursiv) 
			mscran(n,Lm,La) modular 
single                  difference msdif(m,a,b) (MACRO) modular 
single                  discriminant class equation sdisccleq(D,L) 
single                  exponentiation csexp(v,n) complex 
single                  exponentiation flsexp(f,n) floating point 
single                  exponentiation msexp(m,a,n) modular 
single                  factor exponent list sfel(n) 
single                  factorization sfact(n) 
single                  factors sfactors(n) 
single                  fgetms(m,pf) file get modular 
single                  fgetsi(pf) file get 
single                  fputms(m,a,pf) file put modular 
single                  getms(m) (MACRO) get modular 
single                  homomorphism mshom(m,A) modular 
single                  ideal class, imaginary case 
			qffmsordsici(m,D,Q,P,OS) quadratic function field 
			over modular singles order of one 
single                  ideal class, real case qffmsordsicr(m,D,d,LE,ID,OS) 
			quadratic function field over modular singles order 
			of one 
single                  inverse msinv(m,a) modular 
single                  list chinese remainder algorithm 
			mslcra(m1,m2,L1,L2) modular 
single                  negation as function msnegf(m,a) modular 
single                  negation msneg(m,a) (MACRO) modular 
single                  power of a prime ? isspprime(a,pc) is 
single                  precision bubble sort lsbsort(L) list of 
single                  precision fputsi(n,pf) file put 
single                  precision getsi() (MACRO) get 
single                  precision putsi(n) (MACRO) put 
single                  precisions bubble merge sort lsbmsort(L) list of 
single                  precisions insert lsins(n,L) list of 
single                  precisions merge lsmerge(L1,L2) list of 
single                  prime ? issprime(a,pc) is 
single                  prime construction, transcendence degree 1 
			rfmsp1cons(p,P1,P2) rational function over modular 
single                  prime decomposition law nfspdeclaw(F,p) number 
			field, 
single                  prime determined with the Schoof algorithm 
			ecmpsnfnpmsp(P,a4,a6,p,L) elliptic curve over 
			modular primes, short normal form, number of points 
			modulo a 
single                  prime determined with the Schoof algorithm, version 
			1 ecgf2npmspv1(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a 
single                  prime determined with the Schoof algorithm, version 
			2 ecgf2npmspv2(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a 
single                  prime difference, transcendence degree 1 
			rfmsp1dif(p,R1,R2) rational function over modular 
single                  prime divisor search imspds(N,a,b) integer medium 
single                  prime generator spgen(a,b) 
single                  prime negation, transcendence degree 1 
			rfmsp1neg(p,R) rational function over modular 
single                  prime product, transcendence degree 1 
			rfmsp1prod(p,R1,R2) rational function over modular 
single                  prime quotient cdprfmsp1upq(p,F,P) common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1, 
			univariate polynomial over modular 
single                  prime quotient, transcendence degree 1 
			rfmsp1quot(p,R1,R2) rational function over modular 
single                  prime sum, transcendence degree 1 
			rfmsp1sum(p,R1,R2) rational function over modular 
single                  prime unimodular transformation 
			vecupmsunimt(p,V,W,i,pV1,pW1) vector of univariate 
			polynomials over modular 
single                  prime, complete factorization special 
			upmscfacts(p,A) univariate polynomial over modular 
single                  prime, number of points ecmspnp(p,a1,a2,a3,a4,a6) 
			elliptic curve over modular 
single                  prime, transcendence degree 1 ? isrfmsp1(p,R) is 
			rational function over modular 
single                  prime, transcendence degree 1 cdprfmsp1fup(p,P) 
			common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, from univariate polynomial over rational 
			functions over modular 
single                  prime, transcendence degree 1 cdprfmsp1lfm(M,p) 
			common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, list from common denominator matrix of 
			rational functions over modular 
single                  prime, transcendence degree 1 clfcdprfmsp1(P,n) 
			coefficient list from common denominator polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1 fputrfmsp1(p,R,V,pf) 
			(MACRO) file put rational function over modular 
single                  prime, transcendence degree 1 nepousppmsp1(p,F,a) 
			norm of an element of the polynomial order of an 
			univariate separable polynomial over the polynomial 
			ring over modular 
single                  prime, transcendence degree 1 pmstorfmsp1(p,P) 
			(MACRO) polynomial over modular singles to rational 
			function over modular 
single                  prime, transcendence degree 1 putrfmsp1(p,R,V) 
			(MACRO) put rational function over modular 
single                  prime, transcendence degree 1 sclfuprfmsp1(P,n) 
			special coefficient list from univariate polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1 uprfmsp1fcdp(p,P) 
			univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			common denominator polynomial over rational 
			functions over modular 
single                  prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the extensions 
			of the P-adic valuation of an element of the 
			polynomial order of a univariate separable 
			polynomial over the polynomial ring over modular 
single                  prime, transcendence degree 1, Dedekind maximality 
			test ouspprmsp1dm(p,P,F) order of an univariate 
			separable polynomial over polynomial ring over 
			modular 
single                  prime, transcendence degree 1, Hensel factorization 
			approximation upprmsp1hfa(p,F,P,L,k) univariate 
			polynomial over polynomial ring over modular 
single                  prime, transcendence degree 1, Hensel lemma 
			initialization upprmsp1hli(p,F,P,L) univariate 
			polynomial over polynomial ring over modular 
single                  prime, transcendence degree 1, Hensel quadratic 
			step upprmsp1hqs(p,F,T,L1,L2,A) univariate 
			polynomial over polynomial ring over modular 
single                  prime, transcendence degree 1, P-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial afmsp1pptf(p,F,P,Q,Pp,a0,z) 
			algebraic function over modular 
single                  prime, transcendence degree 1, P-star valuation 
			iafmsp1psval(p,P,A) integral algebraic function 
			over modular 
single                  prime, transcendence degree 1, algebraic function 
			over modular single prime, transcendence degree 1, 
			evaluation special upprmsp1afes(p,F,P,a) univariate 
			polynomial over polynomial ring over modular 
single                  prime, transcendence degree 1, approximation of 
			P-adic factorization uspprmsp1apf(p,P,F,k) 
			univariate separable polynomial over polynomial 
			ring over modular 
single                  prime, transcendence degree 1, basis from 
			generators oprmsp1basfg(p,F,L) order over 
			polynomial ring over modular 
single                  prime, transcendence degree 1, basis of a local 
			maximal over-order ouspprmsp1bl(p,F,P,Q,pk) order 
			of an univariate separable polynomial over 
			polynomial ring over modular 
single                  prime, transcendence degree 1, decomposition law 
			affmsp1decl(p,F,P) algebraic function field over 
			modular 
single                  prime, transcendence degree 1, decomposition law 
			ouspprmsp1dl(p,F,P,k) order of a univariate 
			separable polynomial over polynomial ring over 
			modular 
single                  prime, transcendence degree 1, derivation, main 
			variable prfmsp1deriv(r,p,P) polynomial over 
			rational functions over modular 
single                  prime, transcendence degree 1, difference 
			(rekursiv) prfmsp1dif(r,p,P1,P2) polynomial over 
			rational functions over modular 
single                  prime, transcendence degree 1, discriminant 
			upprmsp1disc(p,F) univariate polynomial over 
			polynomial ring over modular 
single                  prime, transcendence degree 1, evaluation special 
			upprmsp1afes(p,F,P,a) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, algebraic function over 
			modular 
single                  prime, transcendence degree 1, exponentiation 
			special afmsp1expsp(p,F,a,e,M) algebraic function 
			over modular 
single                  prime, transcendence degree 1, extended greatest 
			common divisor uprfmsp1egcd(p,P1,P2,pF1,pF2) 
			univariate polynomial over rational functions over 
			modular 
single                  prime, transcendence degree 1, from coefficient 
			list cdprfmsp1fcl(L,p) common denominator 
			polynomial over rational functions over modular 
single                  prime, transcendence degree 1, from common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) univariate polynomial over 
			rational functions over modular 
single                  prime, transcendence degree 1, from special 
			coefficient list uprfmsp1fscl(L) univariate 
			polynomial over rational functions over modular 
single                  prime, transcendence degree 1, from univariate 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common denominator polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1, hermitian reduction 
			cdmarfmsp1hr(p,M) common denominator matrix of 
			rational functions over modular 
single                  prime, transcendence degree 1, identity 
			construction cdmarfmsp1id(n) common denominator 
			matrix of rational functions over modular 
single                  prime, transcendence degree 1, integral basis 
			ouspprmsp1ib(p,F,pL) order of an univariate 
			separable polynomial over the polynomial ring over 
			modular 
single                  prime, transcendence degree 1, inverse 
			cdprfmsp1inv(p,F,A) common denominator polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1, list from common 
			denominator matrix of rational functions over 
			modular single prime, transcendence degree 1 
			cdprfmsp1lfm(M,p) common denominator polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1, negation (rekursiv) 
			prfmsp1neg(r,p,P) polynomial over rational 
			functions over modular 
single                  prime, transcendence degree 1, product (rekursiv) 
			prfmsp1prod(r,p,P1,P2) polynomial over rational 
			functions over modular 
single                  prime, transcendence degree 1, product (rekursiv) 
			prfmsp1rfprd(r,p,P,a) polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, rational function over modular 
single                  prime, transcendence degree 1, product special 
			afmsp1prodsp(p,F,a,b,M) algebraic function over 
			modular 
single                  prime, transcendence degree 1, quotient and 
			remainder (rekursiv) prfmsp1qrem(r,p,P1,P2,pR) 
			polynomial over rational functions over modular 
single                  prime, transcendence degree 1, rational function 
			over modular single prime, transcendence degree 1, 
			product (rekursiv) prfmsp1rfprd(r,p,P,a) polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1, reduced discriminant 
			upprmsp1redd(p,F) univariate polynomial over 
			polynomial ring over modular 
single                  prime, transcendence degree 1, resultant, Sylvester 
			algorithm pprmsp1ress(r,p,P1,P2) polynomial over 
			polynomial ring over modular 
single                  prime, transcendence degree 1, resultant, Sylvester 
			algorithm upprmsp1ress(p,P1,P2) univariate 
			polynomial over polynomial ring over modular 
single                  prime, transcendence degree 1, sum (rekursiv) 
			prfmsp1sum(r,p,P1,P2) polynomial over rational 
			functions over modular 
single                  prime, transcendence degree 1, sum 
			cdprfmsp1sum(p,P1,P2) common denominator polynomial 
			over rational functions over modular 
single                  prime, transcendence degree 1, univariate 
			polynomial over modular single prime quotient 
			cdprfmsp1upq(p,F,P) common denominator polynomial 
			over rational functions over modular 
single                  primes Euklid- Gauss- step for columns 
			maupmspegsc(p,M,A,B) matrix of univariate 
			polynomials over modular 
single                  primes Euklid- Gauss- step for rows 
			maupmspegsr(p,M,A,B) matrix of univariate 
			polynomials over modular 
single                  primes Groebner basis augmentation 
			dipmspgba(r,p,PL,P) distributive polynomial over 
			modular 
single                  primes Groebner basis dipmspgb(r,p,PL) distributive 
			polynomial over modular 
single                  primes Groebner basis recursion dipmspgbr(r,p,PL) 
			distributive polynomial over modular 
single                  primes S-polynomial dipmspsp(r,p,P1,P2) 
			distributive polynomial over modular 
single                  primes difference dipmspdif(r,p,P1,P2) distributive 
			polynomial over modular 
single                  primes elementary divisor form and cofactors 
			maupmspedfcf(p,M,pA,pB) matrix of univariate 
			polynomials over modular 
single                  primes hermitian reduction, special 
			maupmshermsp(p,M,r,pD) matrix of univariate 
			polynomials over modular 
single                  primes iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, minimal polynomial modulo power of an 
			univariate prime polynomial over modular 
single                  primes in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular 
single                  primes in lexicographical order to distributive 
			polynomial over modular single primes in graduated 
			lexicographical order dipmsplotglo(r,p,P) 
			distributive polynomial over modular 
single                  primes in lexicographical order to distributive 
			polynomial over modular single primes in 
			lexicographical order with inverse exponent vector 
			dipmsplotlio(r,p,P) distributive polynomial over 
			modular 
single                  primes in lexicographical order to distributive 
			polynomial over modular single primes with total 
			degree ordering dipmsplottdo(r,p,P) distributive 
			polynomial over modular 
single                  primes in lexicographical order with inverse 
			exponent vector dipmsplotlio(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular 
single                  primes list fgetdipmspl(r,p,VL,pf) file get 
			distributive polynomial over modular 
single                  primes list fputdipmspl(r,p,PL,VL,pf) file put 
			distributive polynomial over modular 
single                  primes list getdipmspl(r,p,VL) (MACRO) get 
			distributive polynomial over modular 
single                  primes list putdipmspl(r,p,PL,VL) (MACRO) put 
			distributive polynomial over modular 
single                  primes monic dipmspmonic(r,p,P) distributive 
			polynomial over modular 
single                  primes negation dipmspneg(r,p,P) distributive 
			polynomial over modular 
single                  primes product dipmspmsprod(r,p,P,a) distributive 
			polynomial over modular single primes, modular 
single                  primes product dipmspprod(r,p,P1,P2) distributive 
			polynomial over modular 
single                  primes sum dipmspsum(r,p,P1,P2) distributive 
			polynomial over modular 
single                  primes transcendence degree 1, determinant 
			marfmsp1det(p,M) matrix of rational functions over 
			modular 
single                  primes transcendence degree 1, difference 
			marfmsp1dif(p,M,N) (MACRO) matrix of rational 
			functions over modular 
single                  primes with total degree ordering 
			dipmsplottdo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular 
single                  primes, modular single primes product 
			dipmspmsprod(r,p,P,a) distributive polynomial over 
			modular 
single                  primes, short normal form, Shanks' algorithm 
			ecmspsnfsha(p,a4,a6) (MACRO) elliptic curve over 
			modular 
single                  primes, short normal form, number of points 
			ecmspsnfnp(p,a4,a6) elliptic curve over modular 
single                  primes, transcendence degree 1 ? ismarfmsp1(p,M) 
			(MACRO) is matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1 ? isvecrfmsp1(p,V) 
			(MACRO) is vector of rational functions over 
			modular 
single                  primes, transcendence degree 1 fgetmarfmsp1(p,V,pf) 
			(MACRO) file get matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1 fgetrfmsp1(p,V,pf) 
			file get rational function over modular 
single                  primes, transcendence degree 1 fgetvrfmsp1(p,VL,pf) 
			(MACRO) file get vector of rational functions over 
			modular 
single                  primes, transcendence degree 1 
			fputmarfmsp1(p,M,V,pf) (MACRO) file put matrix of 
			rational functions over modular 
single                  primes, transcendence degree 1 
			fputvrfmsp1(p,V,VL,pf) (MACRO) file put vector of 
			rational functions over modular 
single                  primes, transcendence degree 1 getmarfmsp1(p,V) 
			(MACRO) get matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1 getrfmsp1(p,V) 
			(MACRO) get rational function over modular 
single                  primes, transcendence degree 1 getvecrfmsp1(p,VL) 
			(MACRO) get vector of rational functions over 
			modular 
single                  primes, transcendence degree 1 mpmstmrfmsp1(p,M) 
			matrix of polynomials over modular singles to 
			matrix of rational functions over modular 
single                  primes, transcendence degree 1 putmarfmsp1(p,M,V) 
			(MACRO) put matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1 putvecrfmsp1(p,V,VL) 
			(MACRO) put vector of rational functions over 
			modular 
single                  primes, transcendence degree 1 vpmstvrfmsp1(p,V) 
			vector of polynomials over modular singles to 
			vector of rational functions over modular 
single                  primes, transcendence degree 1, construction 1 
			marfmsp1c1(p,n) (MACRO) matrix of rational 
			functions over modular 
single                  primes, transcendence degree 1, core algorithm 
			afmsp1coreal(p,F,P,Q,mp) algebraic function over 
			modular 
single                  primes, transcendence degree 1, difference 
			vecrfmsp1dif(p,U,V) (MACRO) vector of rational 
			functions over modular 
single                  primes, transcendence degree 1, element test 
			modprmsp1elt(B,p,a) module over polynomial ring 
			over modular 
single                  primes, transcendence degree 1, exponentiation 
			marfmsp1exp(p,M,n) matrix of rational functions 
			over modular 
single                  primes, transcendence degree 1, increasing the 
			denominator of the P-star value 
			afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over modular 
single                  primes, transcendence degree 1, inverse 
			marfmsp1inv(p,M) matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1, inverse 
			rfmsp1inv(p,R) rational function over modular 
single                  primes, transcendence degree 1, linear combination 
			vecrfmsp1lc(p,F1,F2,V1,V2) vector of rational 
			functions over modular 
single                  primes, transcendence degree 1, minimal polynomial 
			afmsp1minpol(p,F,a) algebraic function over modular 
single                  primes, transcendence degree 1, minimal polynomial 
			iafmsp1mpol(p,F,a,Q) integral algebraic function 
			over modular 
single                  primes, transcendence degree 1, minimal polynomial 
			modulo power of an univariate prime polynomial over 
			modular single primes iafmsp1mpmpp(p,F,a,P,e,Q) 
			integral algebraic function over modular 
single                  primes, transcendence degree 1, module homomorphism 
			cdprfmsp1mh(p,P,M) common denominator polynomial 
			over rational functions over modular 
single                  primes, transcendence degree 1, negation 
			marfmsp1neg(p,M) (MACRO) matrix of rational 
			functions over modular 
single                  primes, transcendence degree 1, negation 
			vecrfmsp1neg(p,V) (MACRO) vector of rational 
			functions over modular 
single                  primes, transcendence degree 1, null space basis 
			marfmsp1nsb(p,M) matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1, product 
			marfmsp1prod(p,M,N) (MACRO) matrix of rational 
			functions over modular 
single                  primes, transcendence degree 1, rank 
			marfmsp1rk(p,M) matrix of rational functions over 
			modular 
single                  primes, transcendence degree 1, regulation 
			afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) algebraic 
			function over modular 
single                  primes, transcendence degree 1, scalar 
			multiplication marfmsp1smul(p,M,F) matrix of 
			rational functions over modular 
single                  primes, transcendence degree 1, scalar 
			multiplication vecrfmsp1sm(p,F,V) vector of 
			rational functions over modular 
single                  primes, transcendence degree 1, scalar product 
			vecrfmsp1sp(p,V,W) vector of rational functions 
			over modular 
single                  primes, transcendence degree 1, solution of a 
			system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
			functions over modular 
single                  primes, transcendence degree 1, sum 
			marfmsp1sum(p,M,N) (MACRO) matrix of rational 
			functions over modular 
single                  primes, transcendence degree 1, sum 
			vecrfmsp1sum(p,U,V) (MACRO) vector of rational 
			functions over modular 
single                  primes, transcendence degree 1, vector 
			multiplication marfmsp1vmul(p,A,x) (MACRO) matrix 
			of rational functions over modular 
single                  product (rekursiv) pmsmsprod(r,m,P,a) polynomial 
			over modular singles, modular 
single                  product msprod(m,a,b) modular 
single                  product udpmsmsprod(m,P,a) univariate dense 
			polynomial over modular singles, modular 
single                  putms(m,a) (MACRO) put modular 
single                  quotient (rekursiv) pmsmsquot(r,m,P,a) polynomial 
			over modular singles, modular 
single                  quotient flsquot(f,n) floating point 
single                  quotient msquot(m,a,b) (MACRO) modular 
single                  sgetsi(ps) string get 
single                  sum as function mssumf(m,a,b) modular 
single                  sum mssum(m,a,b) (MACRO) modular 
single                  trailing base coefficient udpmstbc(m,P) univariate 
			dense polynomial over modular 
single                  units msunits(m) modular 
single                  variable pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) 
			polynomial over modular integers, modular ideal, 
			Hensel lemma quadratic step on a 
single-precision        absolute value sabs(a) (MACRO) 
single-precision        even seven(a) (MACRO) 
single-precision        exponentiation sexp(a,n) (MACRO) 
single-precision        extended greatest common divisor segcd(a,b,pu,pv) 
single-precision        greatest common divisor sgcd(a,b) 
single-precision        homomorphism, symmetric remainder system 
			mshoms(m,A) (MACRO) modular 
single-precision        logarithm, base 2 slog2(a) 
single-precision        maximum smax(a,b) (MACRO) 
single-precision        minimum smin(a,b) (MACRO) 
single-precision        odd sodd(a) (MACRO) 
single-precision        product isprod(A,b) integer 
single-precision        product sprod(a,b,pc,pd) 
single-precision        quotient and remainder isqrem(A,b,pQ,pr) integer 
single-precision        quotient and remainder sqrem(a,b,d,pq,pr) 
single-precision        quotient isquot(A,b) (MACRO) integer 
single-precision        remainder isrem(A,b) (MACRO) integer 
single-precision        signum ssign(a) (MACRO) 
single-precision        square root ssqrt(n) 
singles                 (rekursiv) pitopms(r,P,m) polynomial over integers 
			to polynomial over modular 
singles                 ? (rekursiv) isdpms(r,m,P) is dense polynomial over 
			modular 
singles                 ? (rekursiv) ispms(r,m,P) is polynomial over 
			modular 
singles                 ? isimupms(p,A) is irreducible, monic, univariate 
			polynomial over modular 
singles                 ? islistms(m,A) is list of modular 
singles                 ? islistnns(A) is list of non negative 
singles                 ? islists(A) is list of 
singles                 ? ismadpms(r,m,M) (MACRO) is matrix of dense 
			polynomials over modular 
singles                 ? ismams(m,M) (MACRO) is matrix of modular 
singles                 ? ismapms(r,m,M) (MACRO) is matrix of polynomials 
			over modular 
singles                 ? ismas(M) is matrix of 
singles                 ? issortls(A) is sorted list of 
singles                 ? isvecdpms(r,m,V) (MACRO) is vector of dense 
			polynomials over modular 
singles                 ? isvecms(m,A) (MACRO) is vector of modular 
singles                 ? isvecpms(r,m,V) (MACRO) is vector of polynomials 
			over modular 
singles                 Berlekamp factorization, last step 
			upmsbfls(m,P,B,d) univariate polynomial over 
			modular 
singles                 Bezout-matrix pmsbezout(r,m,P1,P2) polynomial over 
			modular 
singles                 Jacobi-symbol udpmsjacsym(m,P1,P2) univariate dense 
			polynomial over modular 
singles                 Jacobi-symbol upmsjacsym(m,P1,P2) univariate 
			polynomial over modular 
singles                 additive valuation upmsaddval(p,P1,P) univariate 
			polynomial over modular 
singles                 characteristic polynomial mamschpol(m,M) (MACRO) 
			matrix of modular 
singles                 characteristic polynomial mapmschpol(r,m,M) (MACRO) 
			matrix of polynomials over modular 
singles                 comparison special version lscomps(L1,L2) list of 
singles                 comparison, lexicographical order lscomp(L1,L2) 
			list of 
singles                 complete factorization upmscfact(p,A) univariate 
			polynomial over modular 
singles                 construction 1 mamscons1(m,n) (MACRO) matrix of 
			modular 
singles                 construction 1 mapmscons1(r,m,n) (MACRO) matrix of 
			polynomials over modular 
singles                 derivation udpmsderiv(m,P) univariate dense 
			polynomial over modular 
singles                 derivation, main variable pmsderiv(r,m,P) 
			polynomial over modular 
singles                 derivation, specified variable (rekursiv) 
			pmsderivsv(r,m,P,n) polynomial over modular 
singles                 determinant mamsdet(m,M) matrix of modular 
singles                 determinant mapmsdet(r,m,M) matrix of polynomials 
			over modular 
singles                 difference (rekursiv) dpmsdif(r,m,P1,P2) dense 
			polynomial over modular 
singles                 difference (rekursiv) pmsdif(r,m,P1,P2) polynomial 
			over modular 
singles                 difference mamsdif(m,M,N) (MACRO) matrix of modular 
singles                 difference mapmsdif(r,m,M,N) (MACRO) matrix of 
			polynomials over modular 
singles                 difference udpmsdif(m,P1,P2) univariate dense 
			polynomial over modular 
singles                 difference vecmsdif(m,U,V) (MACRO) vector of 
			modular 
singles                 difference vecpmsdif(r,m,U,V) (MACRO) vector of 
			polynomials over modular 
singles                 discriminant pmsdiscr(r,m,P,n) polynomial over 
			modular 
singles                 divisor class number qffmsdcn(m,P) quadratic 
			function field over modular 
singles                 divisor class number subroutine 1 qffmsdcns1(m,P) 
			quadratic function field over modular 
singles                 divisor class number subroutine 2 qffmsdcns2(m,P) 
			quadratic function field over modular 
singles                 divisor class number subroutine 3 qffmsdcns3(m,P) 
			quadratic function field over modular 
singles                 eigenvalues and irreducible factors of the 
			characteristic polynomial mamsevifcp(p,M,pL) matrix 
			of modular 
singles                 eigenvalues mamsev(p,M) (MACRO) matrix of modular 
singles                 evaluation, main variable pmseval(r,m,P,a) 
			polynomial over modular 
singles                 evaluation, specified variable (rekursiv) 
			pmsevalsv(r,m,P,n,a) polynomial over modular 
singles                 exponentiation mamsexp(m,M,n) matrix of modular 
singles                 exponentiation mapmsexp(r,m,M,n) matrix of 
			polynomials over modular 
singles                 exponentiation pmsexp(r,m,P,n) polynomial over 
			modular 
singles                 extended greatest common divisor 
			udpmsegcd(m,P1,P2,pPX,pPY) univariate dense 
			polynomial over modular 
singles                 extended greatest common divisor 
			upmsegcd(m,P1,P2,pP3,pP4) univariate polynomial 
			over modular 
singles                 factorization, Berlekamp algorithm upmsbfact(p,A,d) 
			univariate polynomial over modular 
singles                 fgetmams(m,pf) (MACRO) file get matrix of modular 
singles                 fgetmapms(r,m,V,pf) (MACRO) file get matrix of 
			polynomials over modular 
singles                 fgetpms(r,m,V,pf) file get polynomial over modular 
singles                 fgetvecms(m,pf) (MACRO) file get vector of modular 
singles                 fgetvecpms(r,m,VL,pf) (MACRO) file get vector of 
			polynomials over modular 
singles                 fputmams(m,M,pf) (MACRO) file put matrix of modular 
singles                 fputmapms(r,m,M,V,pf) (MACRO) file put matrix of 
			polynomials over modular 
singles                 fputmas(M) file put matrix of 
singles                 fputpms(r,m,P,V,pf) file put polynomial over 
			modular 
singles                 fputvecms(m,V,pf) (MACRO) file put vector of 
			modular 
singles                 fputvecpms(r,m,V,VL,pf) (MACRO) file put vector of 
			polynomials over modular 
singles                 fundamental unit, baby step version qffmsfubs(m,D) 
			quadratic function field over modular 
singles                 fundamental unit, original version qffmsfuobs(m,D) 
			quadratic function field over modular 
singles                 getmams(m) (MACRO) get matrix of modular 
singles                 getmapms(r,m,V) (MACRO) get matrix of polynomials 
			over modular 
singles                 getpms(r,m,V) (MACRO) get polynomial over modular 
singles                 getvecms(m) (MACRO) get vector of modular 
singles                 getvecpms(r,m,VL) (MACRO) get vector of polynomials 
			over modular 
singles                 greatest common divisor and cofactors (rekursiv) 
			pmsgcdcf(r,m,P1,P2,pQ1,pQ2) polynomial over modular 
singles                 greatest common divisor udpmsgcd(m,P1,P2) 
			univariate dense polynomial over modular 
singles                 greatest common divisor upmsgcd(m,P1,P2) univariate 
			polynomial over modular 
singles                 greatest squarefree divisor (rekursiv) upmsgsd(m,P) 
			univariate polynomial over modular 
singles                 half extended greatest common divisor 
			udpmshegcd(m,P1,P2,pP3) univariate dense polynomial 
			over modular 
singles                 half extended greatest common divisor 
			upmshegcd(m,P1,P2,pP3) univariate polynomial over 
			modular 
singles                 ideal class group generators and isomorphy type, 
			imaginary case qffmsicggii(m,D,H,L,pIT) quadratic 
			function field over modular 
singles                 ideal class group generators and isomorphy type, 
			real case qffmsicggir(m,D,d,H,L,pIT) quadratic 
			function field over modular 
singles                 ideal class group structure, imaginary case 
			qffmsicgsti(m,D,L) quadratic function field over 
			modular 
singles                 ideal class group structure, real case 
			qffmsicgstr(m,D,d,LG,pHid) quadratic function field 
			over modular 
singles                 ideal class group system of representatives 
			qffmsicgrep(m,D,pHid) quadratic function field over 
			modular 
singles                 ideal class group system of representatives, 
			imaginary case qffmsicgri(m,D,pHid) quadratic 
			function field over modular 
singles                 ideal class group system of representatives, real 
			case qffmsicgrr(m,D,d) quadratic function field 
			over modular 
singles                 ideal class number qffmsicn(m,P) quadratic function 
			field over modular 
singles                 interpolation (rekursiv) pmsinter(r,m,P1,P2,P3,a,b) 
			polynomial over modular 
singles                 inverse mamsinv(m,M) matrix of modular 
singles                 inverse mapmsinv(r,m,M) matrix of polynomials over 
			modular 
singles                 is element of an ideal class qffmsiselic(m,D,L,Q,P) 
			quadratic function field over modular 
singles                 is equal ideal special 
			qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic function 
			field over modular 
singles                 linear combination vecmslc(m,s1,s2,L1,L2) vector of 
			modular 
singles                 linear combination vecpmslc(r,m,P1,P2,V1,V2) vector 
			of polynomials over modular 
singles                 maitomams(m,M) matrix of integers to matrix of 
			modular 
singles                 mapitomapms(r,M,m) matrix of polynomials over 
			integers to matrix of polynomials over modular 
singles                 mapmstomapmp(r,m,P,M) matrix of polynomials over 
			modular singles to matrix of polynomials modulo 
			polynomial over modular 
singles                 maximum special version lsmaxs(L1,L2) list of 
singles                 minimum special version lsmins(L1,L2) list of 
singles                 monic pmsmonic(r,m,P) polynomial over modular 
singles                 monic udpmsmonic(m,P) univariate dense polynomial 
			over modular 
singles                 negation (rekursiv) dpmsneg(r,m,P) dense polynomial 
			over modular 
singles                 negation (rekursiv) pmsneg(r,m,P) polynomial over 
			modular 
singles                 negation mamsneg(m,M) (MACRO) matrix of modular 
singles                 negation mapmsneg(r,m,M) (MACRO) matrix of 
			polynomials over modular 
singles                 negation udpmsneg(m,P) univariate dense polynomial 
			over modular 
singles                 negation vecmsneg(m,V) (MACRO) vector of modular 
singles                 negation vecpmsneg(r,m,V) (MACRO) vector of 
			polynomials over modular 
singles                 null space basis mamsnsb(p,A) (MACRO) matrix of 
			modular 
singles                 order of one single ideal class, imaginary case 
			qffmsordsici(m,D,Q,P,OS) quadratic function field 
			over modular 
singles                 order of one single ideal class, real case 
			qffmsordsicr(m,D,d,LE,ID,OS) quadratic function 
			field over modular 
singles                 primitive ideal product 
			qffmspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular 
singles                 primitive ideal product, special version 
			qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular 
singles                 primitive ideal square qffmspidsqu(m,D,Q1,P1,pQ,pP) 
			quadratic function field over modular 
singles                 primitive ideal square, special version 
			qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular 
singles                 product (rekursiv) dpmsprod(r,m,P1,P2) dense 
			polynomial over modular 
singles                 product (rekursiv) pmsprod(r,m,P1,P2) polynomial 
			over modular 
singles                 product (rekursiv) pmsupmsprod(r,m,P1,P2) 
			polynomial over modular singles, univariate 
			polynomial over modular 
singles                 product mamsprod(m,M,N) (MACRO) matrix of modular 
singles                 product mapmsprod(r,m,M,N) (MACRO) matrix of 
			polynomials over modular 
singles                 product udpmsprod(m,P1,P2) univariate dense 
			polynomial over modular 
singles                 pseudo remainder pmspsrem(r,m,P1,P2) polynomial 
			over modular 
singles                 putmams(m,M) (MACRO) put matrix of modular 
singles                 putmapms(r,m,M,V) (MACRO) put matrix of polynomials 
			over modular 
singles                 putpms(r,m,P,V) (MACRO) put polynomial over modular 
singles                 putvecms(m,V) (MACRO) put vector of modular 
singles                 putvecpms(r,m,V,VL) (MACRO) put vector of 
			polynomials over modular 
singles                 quotient (rekursiv) pmsupmsquot(r,m,P1,P2) 
			polynomial over modular singles, univariate 
			polynomial over modular 
singles                 quotient and remainder (rekursiv) 
			pmsqrem(r,m,P1,P2,pR) polynomial over modular 
singles                 quotient and remainder udpmsqrem(m,P1,P2,pP3) 
			univariate dense polynomial over modular 
singles                 quotient pmsquot(r,m,P1,P2) (MACRO) polynomial over 
			modular 
singles                 quotient udpmsquot(m,P1,P2) (MACRO) univariate 
			dense polynomial over modular 
singles                 random permutation lsrandperm(n) list of 
singles                 randomize masrand(m,n,grenze) matrix of 
singles                 reduction of a real quadratic irrational 
			qffmsrqired(m,D,d,Q,P,pPr) quadratic function field 
			over modular 
singles                 regulator qffmsreg(m,P) quadratic function field 
			over modular 
singles                 regulator, baby step - giant step version 
			qffmsregbg(m,D) quadratic function field over 
			modular 
singles                 regulator, baby step - giant step version, first 
			case qffmsregbg1(m,D,s) quadratic function field 
			over modular 
singles                 regulator, baby step - giant step version, fourth 
			case qffmsregbg4(m,D,s) quadratic function field 
			over modular 
singles                 regulator, baby step - giant step version, second 
			case qffmsregbg2(m,D,s) quadratic function field 
			over modular 
singles                 regulator, baby step - giant step version, third 
			case qffmsregbg3(m,D,s) quadratic function field 
			over modular 
singles                 regulator, baby step version qffmsregbs(m,D) 
			quadratic function field over modular 
singles                 regulator, original baby step - giant step version 
			qffmsregobg(m,D) quadratic function field over 
			modular 
singles                 regulator, original baby step version 
			qffmsregobs(m,D) quadratic function field over 
			modular 
singles                 relative prime factorization 
			upmsrelpfact(p,P,Fak,pA2) univariate polynomial 
			over modular 
singles                 remainder pmsrem(r,m,P1,P2) (MACRO) polynomial over 
			modular 
singles                 remainder udpmsrem(m,P1,P2) univariate dense 
			polynomial over modular 
singles                 remainder upmsrem(m,P1,P2) univariate polynomial 
			over modular 
singles                 resultant and cofactor of resultant equation 
			upmsresulc(m,P1,P2,pC) univariate polynomial over 
			modular 
singles                 resultant pmsres(r,m,P1,P2,n) polynomial over 
			modular 
singles                 resultant upmsres(m,P1,P2) univariate polynomial 
			over modular 
singles                 resultant, Collins algorithm (rekursiv) 
			pmsrescoll(r,m,P1,P2) polynomial over modular 
singles                 scalar multiplication mamssmul(m,M,el) matrix of 
			modular 
singles                 scalar multiplication mapmssmul(r,m,M,P) matrix of 
			polynomials over modular 
singles                 scalar multiplication vecmssmul(m,s,V) vector of 
			modular 
singles                 scalar multiplication vecpmssmul(r,m,P,V) vector of 
			polynomials over modular 
singles                 scalar product vecmssprod(m,V,W) vector of modular 
singles                 scalar product vecpmssprod(r,m,V,W) vector of 
			polynomials over modular 
singles                 solution of a system of linear equations 
			mamsssle(p,A,b,pX,pN) matrix of modular 
singles                 square root power series upmssrpser(m,P,i) 
			univariate polynomial over modular 
singles                 square root principal part upmssrpp(m,P) univariate 
			polynomial over modular 
singles                 squarefree factorization (rekursiv) upmssfact(m,P) 
			univariate polynomial over modular 
singles                 squarefree part upmssfp(m,P) univariate polynomial 
			over modular 
singles                 substitution, main variable pmssubst(r,m,P1,P2) 
			polynomial over modular 
singles                 substitution, specified variable (rekursiv) 
			pmssubstsv(r,m,P1,n,P2) polynomial over modular 
singles                 sum (rekursiv) dpmssum(r,m,P1,P2) dense polynomial 
			over modular 
singles                 sum (rekursiv) pmssum(r,m,P1,P2) polynomial over 
			modular 
singles                 sum mamssum(m,M,N) (MACRO) matrix of modular 
singles                 sum mapmssum(r,m,M,N) (MACRO) matrix of polynomials 
			over modular 
singles                 sum udpmssum(m,P1,P2) univariate dense polynomial 
			over modular 
singles                 sum vecmssum(m,U,V) (MACRO) vector of modular 
singles                 sum vecpmssum(r,m,U,V) (MACRO) vector of 
			polynomials over modular 
singles                 to matrix of polynomials modulo polynomial over 
			modular singles mapmstomapmp(r,m,P,M) matrix of 
			polynomials over modular 
singles                 to matrix of polynomials over Galois-field with 
			single characteristic mpmstompgfs(r,p,M) matrix of 
			polynomials over modular 
singles                 to matrix of rational functions over modular single 
			primes, transcendence degree 1 mpmstmrfmsp1(p,M) 
			matrix of polynomials over modular 
singles                 to polynomial over Galois-field with single 
			characteristic (rekursiv) pmstopgfs(r,p,P) 
			polynomial over modular 
singles                 to rational function over modular single prime, 
			transcendence degree 1 pmstorfmsp1(p,P) (MACRO) 
			polynomial over modular 
singles                 to vector of polynomials modulo polynomial over 
			modular singles vecpmstovpmp(r,m,P,V) vector of 
			polynomials over modular 
singles                 to vector of polynomials over Galois-field with 
			single characteristic vpmstovpgfs(r,p,V) vector of 
			polynomials over modular 
singles                 to vector of rational functions over modular single 
			primes, transcendence degree 1 vpmstvrfmsp1(p,V) 
			vector of polynomials over modular 
singles                 transformation 
			mapmstransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over modular 
singles                 transformation 
			pmstransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over modular 
singles                 transformation upmstransf(m,P,r,P1) univariate 
			polynomial over modular 
singles                 transformation 
			vpmstransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over modular 
singles                 translation, all variables (rekursiv) 
			pmstransav(r,m,P,Lms) polynomial over modular 
singles                 translation, main variable pmstrans(r,m,P,a) 
			polynomial over modular 
singles                 unit? ispmsunit(r,m,P) is polynomial over modular 
singles                 univariate content (rekursiv) pmsucont(r,m,P) 
			polynomial over modular 
singles                 vecitovecms(m,V) vector of integers to vector of 
			modular 
singles                 vecpitovpms(r,V,m) vector of polynomials over 
			integers to vector of polynomials over modular 
singles                 vecpmstovpmp(r,m,P,V) vector of polynomials over 
			modular singles to vector of polynomials modulo 
			polynomial over modular 
singles                 vector multiplication mamsvecmul(m,A,x) (MACRO) 
			matrix of modular 
singles                 vector multiplication mapmsvecmul(r,m,A,x) (MACRO) 
			matrix of polynomials over modular 
singles                 zero class group isomorphy type, imaginary case 
			qffmszcgiti(m,D,LG,IT) quadratic function field 
			over modular 
singles                 zero class group isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function 
			field over modular 
singles,                Berlekamp Q polynomials construction upmsbqp(p,A) 
			univariate polynomial over modular 
singles,                Berlekamp factorization, Zassenhaus method 
			upmsbfzm(m,s,P,G) univariate polynomial over 
			modular 
singles,                imaginary case, primitive ideal reduction 
			qffmsipidred(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular 
singles,                imaginary case, sparse representation, reduction of 
			a primitive ideal qffmsispidrd(m,D,Q,P,pQr,pPr) 
			quadratic function field over modular 
singles,                irreducible and monic trinomial, generator 
			upmsimtgen(p,n) univariate polynomial over modular 
singles,                irreducible and monic, generator upmsimgen(p,n) 
			univariate polynomial over modular 
singles,                modular single product (rekursiv) 
			pmsmsprod(r,m,P,a) polynomial over modular 
singles,                modular single product udpmsmsprod(m,P,a) 
			univariate dense polynomial over modular 
singles,                modular single quotient (rekursiv) 
			pmsmsquot(r,m,P,a) polynomial over modular 
singles,                monomial, polynomial, remainder upmsmprem(m,k,T,P) 
			univariate polynomial over modular 
singles,                number of irreducible factors upmsnif(m,P) 
			univariate polynomial over modular 
singles,                principal ideal generating element, real case, 
			qffmspidgenr(m,D,Q,P,G,pB) quadratic function field 
			over modular 
singles,                real case, reduction of a primitive ideal 
			qffmsrpidred(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular 
singles,                real case, sparse representation, reduction of a 
			primitive ideal qffmsrspidrd(m,D,d,Q,P,pQr,pPr) 
			quadratic function field over modular 
singles,                root finding (rekursiv) upmsrf(m,P) univariate 
			polynomial over modular 
singles,                sparse representation, primitive ideal product 
			qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular 
singles,                sparse representation, primitive ideal product, 
			special version 
			qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular 
singles,                sparse representation, primitive ideal square 
			qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
			field over modular 
singles,                sparse representation, primitive ideal square, 
			special version qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) 
			quadratic function field over modular 
singles,                sparse representation, reduction of a real 
			quadratic irrational qffmssrqired(m,D,d,Q,P,pPr) 
			quadratic function field over modular 
singles,                summation over Jacobi-symbols udpmssumjs(m,P,n) 
			univariate dense polynomial over modular 
singles,                univariate polynomial over modular singles product 
			(rekursiv) pmsupmsprod(r,m,P1,P2) polynomial over 
			modular 
singles,                univariate polynomial over modular singles quotient 
			(rekursiv) pmsupmsquot(r,m,P1,P2) polynomial over 
			modular 
sinter(L1,L2)           set intersection 
sinus                   flsin(a) floating point 
sinus                   special version flsin_sp(f) floating point 
sixth                   lsixth(L) list 
size                    lsize(l) (MACRO) list 
size                    recursive part (rekursiv) lsizerec(l,n) list 
skipping                blanks fgetcb(pf) file get character, 
skipping                blanks getcb() (MACRO) get character, 
skipping                blanks sgetcb(pf) string get character, 
skipping                space fgetcs(pf) file get character, 
skipping                space getcs() (MACRO) get character, 
skipping                space sgetcs(ps) string get character, 
slog2(a)                single-precision logarithm, base 2 
small                   conductor ecrlserhdsc(E,A,r,result) elliptic curve 
			over rational numbers, L-series, higher derivative, 
small                   prime divisors ( lists only ) ispd_lo(N,pM) integer 
small                   prime divisors search ispd(N,pM) integer 
smax(a,b)               (MACRO) single-precision maximum 
smin(a,b)               (MACRO) single-precision minimum 
sodd(a)                 (MACRO) single-precision odd 
solution                of a system of linear equations 
			magfsssle(p,AL,A,b,pX,pN) matrix of Galois-field 
			with single characteristic elements 
solution                of a system of linear equations 
			mamsssle(p,A,b,pX,pN) matrix of modular singles 
solution                of a system of linear equations 
			manfssle(F,A,b,pX,pN) matrix of number field 
			elements 
solution                of a system of linear equations 
			manfsssle(F,A,b,pX,pN) matrix of number field 
			elements, sparse representation, 
solution                of a system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, 
solution                of a system of linear equations 
			marfrssle(r,A,b,pX,pN) matrix of rational functions 
			over rationals 
solution                of a system of linear equations marssle(A,b,pX,pN) 
			matrix of rationals 
solution                of equation pmimidse(r,M,S,P1,P2,F1,F2,H,pV) 
			polynomial over modular integers modular ideal 
solution                of the diophantine equation x^2+q*y^2=m using the 
			algorithm of cornaccia cornaccia(m,q,x0,pX,pY) 
			determine a 
solutions               misqrtas(N,r) modular integer square root all 
sort                    dipbsort(r,P) distributive polynomial bubble 
sort                    libsort(L) list of integers bubble 
sort                    lsbmsort(L) list of single precisions bubble merge 
sort                    lsbsort(L) list of single precision bubble 
sort                    vlsort(V,pPI) variable list 
sort,                   special lpbsorts(r,L) list of polynomials bubble 
sorted                  list of singles ? issortls(A) is 
space                   basis magfsnsb(p,AL,M) matrix of Galois-field with 
			single characteristic elements, null 
space                   basis maminsb(P,M) matrix of modular integers, null 
space                   basis mamsnsb(p,A) (MACRO) matrix of modular 
			singles null 
space                   basis manfnsb(F,M) matrix of number field elements 
			null 
space                   basis manfsnsb(F,M) matrix of number field 
			elements, sparse representation, null 
space                   basis marfmsp1nsb(p,M) matrix of rational functions 
			over modular single primes, transcendence degree 1, 
			null 
space                   basis marfrnsb(r,M) matrix of rational functions 
			over rationals, null 
space                   basis marnsb(M) matrix of rationals null 
space                   fgetcs(pf) file get character, skipping 
space                   getcs() (MACRO) get character, skipping 
space                   sgetcs(ps) string get character, skipping 
sparse                  representation ? ismanfs(F,M) (MACRO) is matrix of 
			number field elements, 
sparse                  representation ? isnfels(F,a) is number field 
			element, 
sparse                  representation ? isvecnfs(F,V) (MACRO) is vector of 
			number field elements, 
sparse                  representation fgetmanfs(F,VL,pf) (MACRO) file get 
			matrix of number field elements, 
sparse                  representation fgetnfels(F,V,pf) file get number 
			field element, 
sparse                  representation fgetvecnfs(F,VL,pf) (MACRO) file get 
			vector of number field elements, 
sparse                  representation fputmanfs(F,M,VL,pf) (MACRO) file 
			put matrix of number field elements, 
sparse                  representation fputnfels(F,a,V,pf) file put number 
			field element, 
sparse                  representation fputvecnfs(F,V,VL,pf) (MACRO) file 
			put vector of number field elements, 
sparse                  representation getmanfs(F,VL) (MACRO) get matrix of 
			number field elements, 
sparse                  representation getnfels(F,V) (MACRO) get number 
			field element, 
sparse                  representation getvecnfs(F,VL) (MACRO) get vector 
			of number field elements, 
sparse                  representation itonfs(A) integer to number field 
			element, 
sparse                  representation maitomanfs(M) matrix of integers to 
			matrix of number field elements, 
sparse                  representation martomanfs(M) matrix of rationals to 
			matrix of number field elements, 
sparse                  representation putmanfs(F,M,VL) (MACRO) put matrix 
			of number field elements, 
sparse                  representation putnfels(F,a,V) (MACRO) put number 
			field element, 
sparse                  representation putvecnfs(F,V,VL) (MACRO) put vector 
			of number field elements, 
sparse                  representation rtonfs(R) rational number to number 
			field element, 
sparse                  representation vecitovnfs(V) vector of integers to 
			vector of number field elements, 
sparse                  representation vecrtovnfs(V) vector of rationals to 
			vector of number field elements, 
sparse                  representation, construction 1 manfscons1(F,n) 
			(MACRO) matrix of number field elements, 
sparse                  representation, determinant manfsdet(F,M) matrix of 
			number field elements, 
sparse                  representation, difference manfsdif(F,M,N) (MACRO) 
			matrix of number field elements, 
sparse                  representation, difference nfsdif(F,a,b) (MACRO) 
			number field, 
sparse                  representation, difference vecnfsdif(F,U,V) (MACRO) 
			vector of number field elements, 
sparse                  representation, evaluation upinfseval(P,F,a) 
			univariate polynomial over integers number field 
			element, 
sparse                  representation, evaluation uprnfseval(P,F,a) 
			univariate polynomial over rationals number field 
			element, 
sparse                  representation, exponentiation manfsexp(F,M,n) 
			matrix of number field elements, 
sparse                  representation, inverse manfsinv(F,M) matrix of 
			number field elements, 
sparse                  representation, inverse nfsinv(F,a) number field, 
sparse                  representation, linear combination 
			vecnfslc(F,s1,s2,L1,L2) vector of number field 
			elements, 
sparse                  representation, negation as function nfsnegf(F,a) 
			number field, 
sparse                  representation, negation manfsneg(F,M) (MACRO) 
			matrix of number field elements, 
sparse                  representation, negation nfsneg(F,a) (MACRO) number 
			field, 
sparse                  representation, negation vecnfsneg(F,V) (MACRO) 
			vector of number field elements, 
sparse                  representation, null space basis manfsnsb(F,M) 
			matrix of number field elements, 
sparse                  representation, primitive ideal product 
			qffmsspidpr(m,D,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, 
sparse                  representation, primitive ideal product, special 
			version qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over modular singles, 
sparse                  representation, primitive ideal square 
			qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, 
sparse                  representation, primitive ideal square, special 
			version qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic 
			function field over modular singles, 
sparse                  representation, product manfsprod(F,M,N) (MACRO) 
			matrix of number field elements, 
sparse                  representation, product nfsprod(F,a,b) number 
			field, 
sparse                  representation, quotient nfsquot(F,a,b) number 
			field, 
sparse                  representation, rank manfsrk(F,M) matrix of number 
			field elements, 
sparse                  representation, reduction of a primitive ideal 
			qffmsispidrd(m,D,Q,P,pQr,pPr) quadratic function 
			field over modular singles, imaginary case, 
sparse                  representation, reduction of a primitive ideal 
			qffmsrspidrd(m,D,d,Q,P,pQr,pPr) quadratic function 
			field over modular singles, real case, 
sparse                  representation, reduction of a real quadratic 
			irrational qffmssrqired(m,D,d,Q,P,pPr) quadratic 
			function field over modular singles, 
sparse                  representation, scalar multiplication 
			manfssmul(F,M,el) matrix of number field elements, 
sparse                  representation, scalar multiplication 
			vecnfssmul(F,V,el) vector of number field elements, 
sparse                  representation, scalar product vecnfssprod(F,V,W) 
			vector of number field elements, 
sparse                  representation, solution of a system of linear 
			equations manfsssle(F,A,b,pX,pN) matrix of number 
			field elements, 
sparse                  representation, sum as function nfssumf(F,a,b) 
			number field, 
sparse                  representation, sum manfssum(F,M,N) (MACRO) matrix 
			of number field elements, 
sparse                  representation, sum nfssum(F,a,b) (MACRO) number 
			field, 
sparse                  representation, sum vecnfssum(F,U,V) (MACRO) vector 
			of number field elements, 
sparse                  representation, vector multiplication 
			manfsvecmul(F,A,x) (MACRO) matrix of number field 
			elements, 
special                 (rekursiv) upmirfspec(ip,P) univariate polynomial 
			over modular integers, root finding, 
special                 ? ismaspec_(M,is,anzahlargs,arg1,...,arg5) is 
			matrix of ____, 
special                 ? isvecspec_(V,is,anzahlargs,arg1,...,arg5) is 
			vector of ____, 
special                 afmsp1expsp(p,F,a,e,M) algebraic function over 
			modular single prime, transcendence degree 1, 
			exponentiation 
special                 afmsp1prodsp(p,F,a,b,M) algebraic function over 
			modular single prime, transcendence degree 1, 
			product 
special                 bit-representation ? isgf2impsb(G) is Galois-field 
			with characteristic 2 irreducible and monic 
			polynomial in 
special                 bit-representation ? isudpm2sb(A) is univariate 
			dense polynomial over modular 2 in 
special                 bit-representation generator gf2impsbgen(n,H) 
			Galois-field with characteristic 2 irreducible and 
			monic polynomial in 
special                 bit-representation to univariate dense polynomial 
			over modular 2 sbtoudpm2(a) (MACRO) 
special                 bit-representation udpm2tosb(P) univariate dense 
			polynomial over modular 2 to 
special                 cdedeetas(q,ln_q) complex Dedekind eta function 
special                 coefficient list from univariate polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1 sclfuprfmsp1(P,n) 
special                 coefficient list from univariate polynomial over 
			the integers sclfupi(P,n) 
special                 coefficient list upifscl(L) univariate polynomial 
			over the integers from 
special                 coefficient list uprfmsp1fscl(L) univariate 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, from 
special                 fgetmaspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
			file get matrix 
special                 fgetvecspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
			file get vector 
special                 form, multiplication-map, special version 
			ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve over 
			Galois-field with characteristic 2, 
special                 form, sum of points, special version 
			ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic curve over 
			Galois-field with characteristic 2, 
special                 fputmaspec(M,pf,fputfkt,anzahlargs,arg1,...,arg8) 
			file put matrix 
special                 fputvecspec(V,pf,fputfkt,anzahlargs,arg1,...,arg8) 
			file put vector 
special                 lpbsorts(r,L) list of polynomials bubble sort, 
special                 
			machpolspec(M,det,minusEins,anzahlargs,arg1,...,arg5) 
			matrix characteristic polynomial 
special                 maihermspec(M,r,pD) matrix of integers hermitian 
			reduction, 
special                 manegspec(M,neg,anzahlargs,arg1,...,arg5) matrix 
			negation 
special                 maprodspec(M,N,prod,sum,anzahlargs,arg1,...,arg5) 
			matrix product 
special                 masumspec(M,N,sum,anzahlargs,arg1,...,arg5) matrix 
			sum 
special                 maupmshermsp(p,M,r,pD) matrix of univariate 
			polynomials over modular single primes hermitian 
			reduction, 
special                 mavmulspec(A,x,prod,sum,anzahlargs,arg1,...,arg5) 
			matrix vector multiplication 
special                 minimal polynomial, Collins algorithm, version1 
			nfespecmpc1(F,a) number field element 
special                 minimal polynomial, Collins algorithm, version2 
			nfespecmpc2(F,a) number field element 
special                 nfeexpspec(F,a,e,M) number field element 
			exponentiation 
special                 nfeprodspec(F,a,b,M) number field element product 
special                 p-adic field element fgetspfel(p,pf) file get 
special                 p-adic field element fputspfel(p,a,pf) file put 
special                 p-adic field element getspfel(p) (MACRO) get 
special                 p-adic field element putspfel(p,a) (MACRO) put 
special                 pirescspec(r,P1,P2,n) polynomial over the integers 
			resultant, Collins algorithm 
special                 qffmsiseqids(m,D,Q1,P1,Q2,P2) quadratic function 
			field over modular singles is equal ideal 
special                 sxprods(a,b) single XOR product 
special                 upgf2bofacts(G,P) univariate polynomial over 
			Galois-field with characteristic 2 Ben-Or 
			factorization, 
special                 upgf2tf(G,F,d,M) polynomial over Galois-field with 
			characteristic 2, trace function, 
special                 upgfsbofacts(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic, Ben-Or 
			factorization, 
special                 upgfscfacts(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic complete 
			factorization 
special                 upinfeevals(F,P,a) univariate polynomial over the 
			integers number field element evaluation 
special                 upmibofacts(ip,P) univariate polynomial over 
			modular integers Ben-Or factorization, 
special                 upmicfacts(P,F) univariate polynomial over modular 
			integers, complete factorization 
special                 upmitfsp(ip,G,d,M) univariate polynomial over 
			modular integers, trace function, 
special                 upmscfacts(p,A) univariate polynomial over modular 
			single prime, complete factorization 
special                 upprmsp1afes(p,F,P,a) univariate polynomial over 
			polynomial ring over modular single prime, 
			transcendence degree 1, algebraic function over 
			modular single prime, transcendence degree 1, 
			evaluation 
special                 vecnegspec(V,neg,anzahlargs,arg1,...,arg5) vector 
			negation 
special                 vecsumspec(U,V,sum,anzahlargs,arg1,...,arg5) vector 
			sum 
special                 version (rekursiv) pigf2evalfvs(r,G,P) polynomial 
			over integers Galois-field with characteristic 2 
			element evaluation first variable 
special                 version (rekursiv) pigfsevalfvs(r,p,AL,P) 
			polynomial over integers Galois-field with single 
			characteristic element evaluation first variable 
special                 version 3 iqrem_3(A,B,pQ,pR) integer quotient and 
			remainder 
special                 version cexpsv(z,n) complex exponential function 
special                 version ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve 
			over Galois-field with characteristic 2, special 
			form, multiplication-map, 
special                 version ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic 
			curve over Galois-field with characteristic 2, 
			special form, sum of points, 
special                 version ecimindivs(E,P,h,ug,PL,n) elliptic curve 
			with integer coefficients, minimal model, division 
			of a point by an integer, 
special                 version ecmipsnfnpsv(p,a4,a6) elliptic curve over 
			modular integer primes short normal form number of 
			points 
special                 version ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve 
			over modular primes, short normal form, 
			multiplication-map, 
special                 version ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic 
			curve over modular primes, short normal form, sum 
			of points, 
special                 version ecrlserfds(E,A,result) elliptic curve over 
			the rationals, L-series, first derivative, 
special                 version ecrlsers(E,A,result) elliptic curve over 
			the rationals, L-series, 
special                 version ecrsigns(E,A,C) elliptic curve over the 
			rationals, sign of the functional equation, 
special                 version flath_sp(f) floating point area tangens 
			hyperbolicus 
special                 version flatn_sp(f) floating point arcus tangens 
special                 version flcos_sp(f) floating point cosinus 
special                 version flsin_sp(f) floating point sinus 
special                 version iecjtoeqsv(p,j,pi) integer elliptic curve 
			j-invariant to equation 
special                 version itoI_sp(A,lA,h) ( SIMATH ) integer to ( 
			Heidelberg ) Integer 
special                 version lscomps(L1,L2) list of singles comparison 
special                 version lsmaxs(L1,L2) list of singles maximum 
special                 version lsmins(L1,L2) list of singles minimum 
special                 version mapigfsevfvs(r,p,AL,M) matrix over 
			polynomials over integers Galois-field with single 
			characteristic element evaluation first variable 
special                 version mapinfevlfvs(r,F,M) matrix of polynomials 
			over integers number field element evaluation first 
			variable 
special                 version maprnfevlfvs(r,F,M) matrix of polynomials 
			over rationals number field element evaluation 
			first variable 
special                 version pinfevalfvs(r,F,P) polynomial over integers 
			number field element evaluation first variable 
special                 version prnfevalfvs(r,F,P) polynomial over 
			rationals number field element evaluation first 
			variable 
special                 version qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over modular singles 
			primitive ideal product, 
special                 version qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic 
			function field over modular singles primitive ideal 
			square, 
special                 version qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) 
			quadratic function field over modular singles, 
			sparse representation, primitive ideal product, 
special                 version qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, primitive ideal square, 
special                 version qnfielpifacts(D,a,L) quadratic number field 
			integral element prime ideal factorization, 
special                 version sgetflsp(ps) string get floating point 
special                 version sputflsp(prec,f,str) string put floating 
			point 
special                 version udpgf2remsp(G,P1,P2,ilc) univariate dense 
			polynomial over Galois-field with characteristic 2 
			remainder, 
special                 version upgf2modexps(G,F,m,P,pM) univariate 
			polynomial over Galois-field with characteristic 2, 
			modular exponentiation, 
special                 version vecpigfsefvs(r,p,AL,V) vector over 
			polynomials over integers Galois-field with single 
			characteristic element evaluation first variable 
special                 version vpinfevalfvs(r,F,V) vector of polynomials 
			over integers number field element evaluation first 
			variable 
special                 version vprnfevalfvs(r,F,V) vector of polynomials 
			over rationals number field element evaluation 
			first variable 
specified               variable (rekursiv) pdegreesv(r,P,n) polynomial 
			degree, 
specified               variable (rekursiv) pgf2derivsv(r,G,P,i) polynomial 
			over Galois-field with characteristic 2 derivation, 
specified               variable (rekursiv) pgfsderivsv(r,p,AL,P,i) 
			polynomial over Galois-field with single 
			characteristic derivation, 
specified               variable (rekursiv) pgfsevalsv(r,p,AL,P,d,a) 
			polynomial over Galois-field with single 
			characteristic evaluation, 
specified               variable (rekursiv) piderivsv(r,P,n) polynomial 
			over integers derivation, 
specified               variable (rekursiv) pievalsv(r,P,n,A) polynomial 
			over integers evaluation, 
specified               variable (rekursiv) pisubstsv(r,P1,n,P2) polynomial 
			over integers substitution, 
specified               variable (rekursiv) pmiderivsv(r,m,P,n) polynomial 
			over modular integers derivation, 
specified               variable (rekursiv) pmievalsv(r,m,P,n,a) polynomial 
			over modular integers evaluation, 
specified               variable (rekursiv) pmisubstsv(r,m,P1,n,P2) 
			polynomial over modular integers substitution, 
specified               variable (rekursiv) pmsderivsv(r,m,P,n) polynomial 
			over modular singles derivation, 
specified               variable (rekursiv) pmsevalsv(r,m,P,n,a) polynomial 
			over modular singles evaluation, 
specified               variable (rekursiv) pmssubstsv(r,m,P1,n,P2) 
			polynomial over modular singles substitution, 
specified               variable (rekursiv) pnfderivsv(r,F,P,n) polynomial 
			over number field derivation, 
specified               variable (rekursiv) pnfevalsv(r,F,P,n,a) polynomial 
			over number field evaluation, 
specified               variable (rekursiv) prderivsv(r,P,n) polynomial 
			over rationals derivation, 
specified               variable (rekursiv) prevalsv(r,P,n,A) polynomial 
			over rationals evaluation, 
specified               variable (rekursiv) prsubstsv(r,P1,n,P2) polynomial 
			over rationals substitution, 
specified               variable diphomogsv(r,P,n) distributive polynomial 
			homogenize 
spgen(a,b)              single prime generator 
spifact(r,P)            squarefree polynomial over integers factorization 
sprod(a,b,pc,pd)        single-precision product 
sputa(a,str)            (MACRO) string put atom 
sputflsp(prec,f,str)    string put floating point special version 
sputi(A,str)            string put integer 
sputl(l,str)            string put list 
sputr(R,str)            string put rational number 
sqrem(a,b,d,pq,pr)      single-precision quotient and remainder 
square                  (rekursiv) pgf2square(r,G,P) polynomial over 
			Galois-field with characteristic 2 
square                  ? isisqr(A) is integer 
square                  ? ismisquare(M,A) is modular integer 
square                  ? isrsqr(R) is rational number 
square                  csqr(v) complex 
square                  gf2squ(G,a) Galois-field with characteristic 2 
square                  mipfnsquare(p) modular integer prime find non 
square                  mipfsquare(p) modular integer prime find 
square                  qffmspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
			field over modular singles primitive ideal 
square                  qffmsspidsqu(m,D,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, sparse representation, 
			primitive ideal 
square                  qnfidsquare(D,A) quadratic number field ideal 
square                  qnfsquare(D,a) quadratic number field element 
square                  root ( lists only ) isqrt_lo(A) integer 
square                  root all solutions misqrtas(N,r) modular integer 
square                  root csqrt(z) complex 
square                  root flsqrt(f) floating point 
square                  root isqrt(A) integer 
square                  root mipsqrt(p,r) modular integer prime 
square                  root misqrt(m,a) modular integer 
square                  root mppsqrt(p,n,r,xk,k) modular prime power 
square                  root mpsqrt(p,a) modular primes 
square                  root nf3sqrt(F,el) number field of degree 3 
square                  root power series upmssrpser(m,P,i) univariate 
			polynomial over modular singles 
square                  root principal part upmssrpp(m,P) univariate 
			polynomial over modular singles 
square                  root search misqrtsrch(m,a) modular integer 
square                  root ssqrt(n) single-precision 
square                  sxsqu(a,pc,pd) single XOR 
square                  with arithmetic list gf2squAL(AL,a) Galois-field 
			with characteristic 2 
square,                 special version qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) 
			quadratic function field over modular singles 
			primitive ideal 
square,                 special version qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) 
			quadratic function field over modular singles, 
			sparse representation, primitive ideal 
squarefree              divisor (rekursiv) upgfsgsd(p,AL,P) univariate 
			polynomial over Galois-field with single 
			characteristic greatest 
squarefree              divisor (rekursiv) upmigsd(ip,P) univariate 
			polynomial over modular integers greatest 
squarefree              divisor (rekursiv) upmsgsd(m,P) univariate 
			polynomial over modular singles greatest 
squarefree              factorization (rekursiv) upgf2sfact(G,P) univariate 
			polynomial over Galois-field with characteristic 2 
squarefree              factorization (rekursiv) upgfssfact(p,AL,P) 
			univariate polynomial over Galois-field with single 
			characteristic 
squarefree              factorization (rekursiv) upmisfact(ip,P) univariate 
			polynomial over modular integers 
squarefree              factorization (rekursiv) upmssfact(m,P) univariate 
			polynomial over modular singles 
squarefree              factorization pisfact(r,P) polynomial over integers 
squarefree              factorization upnfsfact(F,P) univariate polynomial 
			over number field 
squarefree              part isfp(A) integer 
squarefree              part upgfssfp(p,AL,P) univariate polynomial over 
			Galois-field with single characteristic 
squarefree              part upmisfp(m,P) univariate polynomial over 
			modular integers 
squarefree              part upmssfp(m,P) univariate polynomial over 
			modular singles 
squarefree              polynomial over integers ? isiuspi(P) is 
			irreducible univariate 
squarefree              polynomial over integers factorization spifact(r,P) 
squarefree              polynomial over integers factorization uspifact(P) 
			univariate 
squarefree              polynomial over integers isuspi(P) is univariate 
ssign(a)                (MACRO) single-precision signum 
ssqrt(n)                single-precision square root 
standard                representation of projective point ecgf2srpp(G,P) 
			elliptic curve over Galois-field with 
			characteristic 2, 
standard                representation of projective point ecmpsrpp(p,P) 
			elliptic curve over modular primes, 
standard                representation of projective point ecnfsrpp(F,P) 
			elliptic curve over number field 
static                  variables globbind(pL) bind for global and 
static                  variables globinit(pL) init for global and 
step                    - giant step version qffmsregbg(m,D) quadratic 
			function field over modular singles regulator, baby 
step                    - giant step version qffmsregobg(m,D) quadratic 
			function field over modular singles regulator, 
			original baby 
step                    - giant step version, first case qffmsregbg1(m,D,s) 
			quadratic function field over modular singles 
			regulator, baby 
step                    - giant step version, fourth case 
			qffmsregbg4(m,D,s) quadratic function field over 
			modular singles regulator, baby 
step                    - giant step version, second case 
			qffmsregbg2(m,D,s) quadratic function field over 
			modular singles regulator, baby 
step                    - giant step version, third case qffmsregbg3(m,D,s) 
			quadratic function field over modular singles 
			regulator, baby 
step                    for columns maiegsc(M,A,B) matrix of integers 
			Euklid- Gauss- 
step                    for columns maupmipegsc(p,M,A,B) matrix of 
			univariate polynomials over modular integer primes 
			Euklid- Gauss- 
step                    for columns maupmspegsc(p,M,A,B) matrix of 
			univariate polynomials over modular single primes 
			Euklid- Gauss- 
step                    for columns maupregsc(M,A,B) matrix of univariate 
			polynomials over rationals Euklid- Gauss- 
step                    for rows maiegsr(M,A,B) matrix of integers Euklid- 
			Gauss- 
step                    for rows maupmipegsr(p,M,A,B) matrix of univariate 
			polynomials over modular integer primes Euklid- 
			Gauss- 
step                    for rows maupmspegsr(p,M,A,B) matrix of univariate 
			polynomials over modular single primes Euklid- 
			Gauss- 
step                    for rows maupregsr(M,A,B) matrix of univariate 
			polynomials over rationals Euklid- Gauss- 
step                    on a single variable 
			pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
			modular integers, modular ideal, Hensel lemma 
			quadratic 
step                    pimidqhl(r,p,S,P1,P2,F1,F2,M,H,pB) polynomial over 
			integers, modular ideal, Hensel lemma quadratic 
step                    pmimidqhl(r,p,S,P1,P2,F1,F2,M,SL,H,pB) polynomial 
			over modular integers, modular ideal, Hensel lemma 
			quadratic 
step                    upgfsbfls(p,AL,P,B,d) univariate polynomial over 
			Galois-field with single characteristic Berlekamp 
			factorization, last 
step                    upihlqs(p,p_k,p_l,P,L1,L2,A) univariate polynomial 
			over integers, Hensel lemma quadratic 
step                    upmibfls(ip,P,B,d) univariate polynomial over 
			modular integers Berlekamp factorization, last 
step                    upmsbfls(m,P,B,d) univariate polynomial over 
			modular singles Berlekamp factorization, last 
step                    upprmsp1hqs(p,F,T,L1,L2,A) univariate polynomial 
			over polynomial ring over modular single prime, 
			transcendence degree 1, Hensel quadratic 
step                    version qffmsfubs(m,D) quadratic function field 
			over modular singles fundamental unit, baby 
step                    version qffmsregbg(m,D) quadratic function field 
			over modular singles regulator, baby step - giant 
step                    version qffmsregbs(m,D) quadratic function field 
			over modular singles regulator, baby 
step                    version qffmsregobg(m,D) quadratic function field 
			over modular singles regulator, original baby step 
			- giant 
step                    version qffmsregobs(m,D) quadratic function field 
			over modular singles regulator, original baby 
step                    version, first case qffmsregbg1(m,D,s) quadratic 
			function field over modular singles regulator, baby 
			step - giant 
step                    version, fourth case qffmsregbg4(m,D,s) quadratic 
			function field over modular singles regulator, baby 
			step - giant 
step                    version, second case qffmsregbg2(m,D,s) quadratic 
			function field over modular singles regulator, baby 
			step - giant 
step                    version, third case qffmsregbg3(m,D,s) quadratic 
			function field over modular singles regulator, baby 
			step - giant 
step                    with respect to integer prime 
			upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate 
			polynomial over integers, Hensel lemma quadratic 
stop                    and print time stoptime(a) 
stoptime(a)             stop and print time 
string                  StoKstr(str,D,typ,prec) SIMATH to Kant 
string                  fgets(s,n,pf) (MACRO) file get 
string                  fputs(s,pf) (MACRO) file put 
string                  get atom sgeta(ps) 
string                  get character sgetc(ps) 
string                  get character unsgetc(c,ps) undo 
string                  get character, skipping blanks sgetcb(pf) 
string                  get character, skipping space sgetcs(ps) 
string                  get floating point sgetfl(ps) 
string                  get floating point special version sgetflsp(ps) 
string                  get integer sgeti(ps) 
string                  get list (rekursiv) sgetl(ps) 
string                  get rational number sgetr(ps) 
string                  get single sgetsi(ps) 
string                  gets(s) (MACRO) get 
string                  put atom sputa(a,str) (MACRO) 
string                  put floating point special version 
			sputflsp(prec,f,str) 
string                  put integer sputi(A,str) 
string                  put list sputl(l,str) 
string                  put rational number sputr(R,str) 
string                  puts(s) (MACRO) put 
string                  to SIMATH KstrtoS(a) Kant 
strong                  pseudo prime ? isispprime(n,k) is integer 
structure               (rekursiv) fputlstruct(L,pf) file put list 
structure               of torsion group ecrstrtor(E) elliptic curve over 
			rational numbers, 
structure               putlstruct(L) (MACRO) put list 
structure,              imaginary case qffmsicgsti(m,D,L) quadratic 
			function field over modular singles ideal class 
			group 
structure,              real case qffmsicgstr(m,D,d,LG,pHid) quadratic 
			function field over modular singles ideal class 
			group 
subfield                gf2ies(Gm,Gn,n) Galois field with characteristic 2 
			isomorphic embedding of 
subfield                gfsalgenies(p,m,n,ALn) Galois-field with single 
			characteristic arithmetic list generator isomorphic 
			embedding of 
subroutine              1 qffmsdcns1(m,P) quadratic function field over 
			modular singles divisor class number 
subroutine              2 qffmsdcns2(m,P) quadratic function field over 
			modular singles divisor class number 
subroutine              3 qffmsdcns3(m,P) quadratic function field over 
			modular singles divisor class number 
substitution            with respect to a cubic equation 
			bpmisubcubeq(p,P,R) bivariate polynomial over 
			modular integers 
substitution,           main variable pisubst(r,P1,P2) polynomial over 
			integers 
substitution,           main variable pmisubst(r,m,P1,P2) polynomial over 
			modular integers 
substitution,           main variable pmssubst(r,m,P1,P2) polynomial over 
			modular singles 
substitution,           main variable ppfsubst(r,p,P1,P2) polynomial over 
			p-adic field 
substitution,           main variable prsubst(r,P1,P2) polynomial over 
			rationals 
substitution,           selected variable ppfsubstsv(r,p,P1,n,P2) 
			polynomial over p-adic field 
substitution,           specified variable (rekursiv) pisubstsv(r,P1,n,P2) 
			polynomial over integers 
substitution,           specified variable (rekursiv) 
			pmisubstsv(r,m,P1,n,P2) polynomial over modular 
			integers 
substitution,           specified variable (rekursiv) 
			pmssubstsv(r,m,P1,n,P2) polynomial over modular 
			singles 
substitution,           specified variable (rekursiv) prsubstsv(r,P1,n,P2) 
			polynomial over rationals 
subtraction             PAFsub() Papanikolaou floating point package: 
suffix                  lsuffix(L,a) (MACRO) list 
sum                     (rekursiv) dpmisum(r,M,P1,P2) dense polynomial over 
			modular integers 
sum                     (rekursiv) dpmssum(r,m,P1,P2) dense polynomial over 
			modular singles 
sum                     (rekursiv) pflsum(r,P1,P2) polynomial over floating 
			points 
sum                     (rekursiv) pgf2sum(r,G,P1,P2) polynomial over 
			Galois-field with characteristic 2 
sum                     (rekursiv) pgfssum(r,p,AL,P1,P2) polynomial over 
			Galois-field with single characteristic 
sum                     (rekursiv) pisum(r,P1,P2) polynomial over integers 
sum                     (rekursiv) pmisum(r,M,P1,P2) polynomial over 
			modular integers 
sum                     (rekursiv) pmssum(r,m,P1,P2) polynomial over 
			modular singles 
sum                     (rekursiv) pnfsum(r,F,P1,P2) polynomial over number 
			field 
sum                     (rekursiv) prfmsp1sum(r,p,P1,P2) polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1, 
sum                     (rekursiv) prsum(r,P1,P2) polynomial over rationals 
sum                     as function gfssumf(p,AL,a,b) Galois-field with 
			single characteristic 
sum                     as function misumf(M,A,B) modular integer 
sum                     as function mssumf(m,a,b) modular single 
sum                     as function nfssumf(F,a,b) number field, sparse 
			representation, 
sum                     cdprfmsp1sum(p,P1,P2) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, 
sum                     cdprsum(P1,P2) common denominator polynomial over 
			the rationals 
sum                     csum(v,w) complex 
sum                     dipevsum(r,EV1,EV2) distributive polynomial 
			exponent vector 
sum                     dipgfssum(r,p,AL,P1,P2) distributive polynomial 
			over Galois-field with single characteristic 
sum                     dipisum(r,P1,P2) distributive polynomial over 
			integers 
sum                     dipmipsum(r,p,P1,P2) distributive polynomial over 
			modular integer primes 
sum                     dipmspsum(r,p,P1,P2) distributive polynomial over 
			modular single primes 
sum                     dipnfsum(r,F,P1,P2) distributive polynomial over 
			number field 
sum                     dippisum(r1,r2,P1,P2) distributive polynomial over 
			polynomials over integers 
sum                     diprfrsum(r1,r2,P1,P2) distributive polynomial over 
			rational functions over the rationals 
sum                     diprsum(r,P1,P2) distributive polynomial over 
			rationals 
sum                     elcpdssum(N,x1,y1,x2,y2,px3,py3,a) elliptic curve 
			prime divisor search 
sum                     flsum(f,g) floating point 
sum                     gf2sum(G,a,b) Galois-field with characteristic 2 
sum                     gfssum(p,AL,a,b) (MACRO) Galois-field with single 
			characteristic 
sum                     iecpsum(p,P,Q,a) integer elliptic curve point 
sum                     isum(A,B) integer 
sum                     magfssum(p,AL,M,N) (MACRO) matrix of Galois-field 
			with single characteristic elements 
sum                     maisum(M,N) (MACRO) matrix of integers 
sum                     mamisum(m,M,N) (MACRO) matrix of modular integers 
sum                     mamssum(m,M,N) (MACRO) matrix of modular singles 
sum                     manfssum(F,M,N) (MACRO) matrix of number field 
			elements, sparse representation, 
sum                     manfsum(F,M,N) (MACRO) matrix of number field 
			elements 
sum                     mapgfssum(r,p,AL,M,N) (MACRO) matrix of polynomials 
			over Galois-field with single characteristic 
sum                     mapisum(r,M,N) (MACRO) matrix of polynomials over 
			integers 
sum                     mapmisum(r,m,M,N) (MACRO) matrix of polynomials 
			over modular integers 
sum                     mapmssum(r,m,M,N) (MACRO) matrix of polynomials 
			over modular singles 
sum                     mapnfsum(r,F,M,N) (MACRO) matrix of polynomials 
			over number field 
sum                     maprsum(r,M,N) (MACRO) matrix of polynomials over 
			rationals 
sum                     marfmsp1sum(p,M,N) (MACRO) matrix of rational 
			functions over modular single primes, transcendence 
			degree 1, 
sum                     marfrsum(r,M,N) (MACRO) matrix of rational 
			functions over rationals 
sum                     marsum(M,N) (MACRO) matrix of rationals 
sum                     masum(M,N,sum,anzahlargs,arg1,arg2) matrix 
sum                     misum(M,A,B) (MACRO) modular integer 
sum                     mssum(m,a,b) (MACRO) modular single 
sum                     nfssum(F,a,b) (MACRO) number field, sparse 
			representation, 
sum                     nfsum(F,a,b) number field element 
sum                     norm (rekursiv) pisumnorm(r,P) polynomial over 
			integers 
sum                     of points ecgf2sum(G,a1,a2,a3,a4,a6,P1,P2) elliptic 
			curve over Galois-field with characteristic 2, 
sum                     of points eciminsum(E,P,Q) elliptic curve with 
			integer coefficients, minimal model, 
sum                     of points ecisnfsum(E,P,Q) elliptic curve with 
			integer coefficients, short normal form, 
sum                     of points ecmpsnfsum(p,a4,a6,P1,P2) elliptic curve 
			over modular primes, short normal form, 
sum                     of points ecmpsum(p,a1,a2,a3,a4,a6,P1,P2) elliptic 
			curve over modular primes, 
sum                     of points ecnfsnfsum(F,a,b,P1,P2) elliptic curve 
			over number field short normal form 
sum                     of points ecnfsum(F,a1,a2,a3,a4,a6,P1,P2) elliptic 
			curve over number field 
sum                     of points ecracsum(E,P,Q) elliptic curve over the 
			rational numbers, actual curve, 
sum                     of points, special version 
			ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic curve over 
			Galois-field with characteristic 2, special form, 
sum                     of points, special version 
			ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve 
			over modular primes, short normal form, 
sum                     pfsum(p,a,b) p-adic field element 
sum                     ppfsum(r,p,P1,P2) polynomial over p-adic field 
sum                     qnfisum(D,a,b) quadratic number field element, 
			integer, 
sum                     qnfrsum(D,a,b) quadratic number field element, 
			rational number, 
sum                     qnfsum(D,a,b) quadratic number field element 
sum                     rfrsum(r,R1,R2) rational function over the 
			rationals 
sum                     rsum(R,S) rational number 
sum                     special masumspec(M,N,sum,anzahlargs,arg1,...,arg5) 
			matrix 
sum                     special 
			vecsumspec(U,V,sum,anzahlargs,arg1,...,arg5) vector 
sum                     udpisum(P1,P2) univariate dense polynomial over 
			integers 
sum                     udpmisum(m,P1,P2) univariate dense polynomial over 
			modular integers 
sum                     udpmssum(m,P1,P2) univariate dense polynomial over 
			modular singles 
sum                     udppfsum(p,P1,P2) univariate dense polynomial over 
			p-adic field 
sum                     udprsum(P1,P2) univariate dense polynomial over 
			rationals 
sum                     vecgfssum(p,AL,U,V) (MACRO) vector of Galois-field 
			with single characteristic elements 
sum                     vecisum(U,V) (MACRO) vector of integers 
sum                     vecmisum(m,U,V) (MACRO) vector of modular integers 
sum                     vecmssum(m,U,V) (MACRO) vector of modular singles 
sum                     vecnfssum(F,U,V) (MACRO) vector of number field 
			elements, sparse representation, 
sum                     vecnfsum(F,U,V) (MACRO) vector of number field 
			elements 
sum                     vecpgfssum(r,p,AL,U,V) (MACRO) vector of 
			polynomials over Galois-field with single 
			characteristic 
sum                     vecpisum(r,U,V) (MACRO) vector of polynomials over 
			integers 
sum                     vecpmisum(r,m,U,V) (MACRO) vector of polynomials 
			over modular integers 
sum                     vecpmssum(r,m,U,V) (MACRO) vector of polynomials 
			over modular singles 
sum                     vecpnfsum(r,F,U,V) (MACRO) vector of polynomials 
			over number field 
sum                     vecprsum(r,U,V) (MACRO) vector of polynomials over 
			rationals 
sum                     vecrfmsp1sum(p,U,V) (MACRO) vector of rational 
			functions over modular single primes, transcendence 
			degree 1, 
sum                     vecrfrsum(r,U,V) (MACRO) vector of rational 
			functions over rationals 
sum                     vecrsum(U,V) (MACRO) vector of rationals 
sum                     vecsum(U,V,sum,anzahlargs,arg1,arg2) vector 
sum,                    transcendence degree 1 rfmsp1sum(p,R1,R2) rational 
			function over modular single prime 
summation               over Jacobi-symbols udpmssumjs(m,P,n) univariate 
			dense polynomial over modular singles, 
sunion(L1,L2)           set union 
sxprod(a,b,pc,pd)       single XOR product 
sxprods(a,b)            single XOR product special 
sxsqu(a,pc,pd)          single XOR square 
symmetric               remainder system (rekursiv) pmitos(r,M,P) 
			polynomial over modular integers to 
symmetric               remainder system mihoms(M,A) modular integer 
			homomorphism, 
symmetric               remainder system mitos(M,A) modular integer to 
symmetric               remainder system mshoms(m,A) (MACRO) modular 
			single-precision homomorphism, 
symmetrical             difference ussdiff(L1,L2) unordered set 
system                  (rekursiv) pmitos(r,M,P) polynomial over modular 
			integers to symmetric remainder 
system                  fputdippigbs(r1,r2,GS,VL1,VL2,cs,pf) file put 
			distributive polynomial over polynomials over 
			integers Groebner 
system                  mihoms(M,A) modular integer homomorphism, symmetric 
			remainder 
system                  mitos(M,A) modular integer to symmetric remainder 
system                  mshoms(m,A) (MACRO) modular single-precision 
			homomorphism, symmetric remainder 
system                  of linear equations magfsssle(p,AL,A,b,pX,pN) 
			matrix of Galois-field with single characteristic 
			elements solution of a 
system                  of linear equations mamsssle(p,A,b,pX,pN) matrix of 
			modular singles solution of a 
system                  of linear equations manfssle(F,A,b,pX,pN) matrix of 
			number field elements solution of a 
system                  of linear equations manfsssle(F,A,b,pX,pN) matrix 
			of number field elements, sparse representation, 
			solution of a 
system                  of linear equations marfmsp1ssle(p,A,b,pX,pN) 
			matrix of rational functions over modular single 
			primes, transcendence degree 1, solution of a 
system                  of linear equations marfrssle(r,A,b,pX,pN) matrix 
			of rational functions over rationals solution of a 
system                  of linear equations marssle(A,b,pX,pN) matrix of 
			rationals solution of a 
system                  of representatives modulo a prime ideal 
			qnfsysrmodpi(D,P,pi,z,k) quadratic number field 
system                  of representatives qffmsicgrep(m,D,pHid) quadratic 
			function field over modular singles ideal class 
			group 
system                  of representatives, imaginary case 
			qffmsicgri(m,D,pHid) quadratic function field over 
			modular singles ideal class group 
system                  of representatives, real case qffmsicgrr(m,D,d) 
			quadratic function field over modular singles ideal 
			class group 
system                  putdippigbs(r1,r2,GS,VL1,VL2,cs) (MACRO) put 
			distributive polynomial over polynomials over 
			integers Groebner 
tab(n)                  (MACRO) tabulator 
tabulator               ftab(n,pf) file 
tabulator               tab(n) (MACRO) 
tangens                 hyperbolicus special version flath_sp(f) floating 
			point area 
tangens                 special version flatn_sp(f) floating point arcus 
test                    (rekursiv) igkapt(n,msg) integer Goldwasser Kilian 
			Atkin primality 
test                    and factorization of the defining polynomial or the 
			minimal polynomial afmsp1pptf(p,F,P,Q,Pp,a0,z) 
			algebraic function over modular single prime, 
			transcendence degree 1, P-primality 
test                    and factorization of the defining polynomial or the 
			minimal polynomial infepptfact(F,p,Q,ppot,a0,z) 
			integral number field element p-primality 
test                    and factorization of the defining polynomial or the 
			minimal polynomial with respect to integer primes 
			infepptfip(F,p,Q,ppot,a0,z) integral number field 
			element p-primality 
test                    dipevmt(r,EV1,EV2) distributive polynomial exponent 
			vector multiple 
test                    dippigt(r1,r2,s,PL,CONDS,OPL,pCGB1) distributive 
			polynomial over polynomials over integers Groebner 
test                    dippipim(r1,r2,s,PL,PTL,CONDS,OPL) distributive 
			polynomial over polynomials over integers 
			parametric ideal membership 
test                    fputdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2,pf) file 
			put distributive polynomial over polynomials over 
			integers Groebner 
test                    fputdippipim(r1,r2,NOUT,VL1,VL2,pf) file put 
			distributive polynomial over polynomials over 
			integers parametric ideal membership 
test                    iecpt(n,m,lp,a,b,anz) integer elliptic curve 
			primality 
test                    iftpt(n,L,anz) integer Fermat's theorem primality 
test                    ispt(M,M1,F) integer Selfridge primality 
test                    modielemtest(B,a) module over the integers element 
test                    modprmsp1elt(B,p,a) module over polynomial ring 
			over modular single primes, transcendence degree 1, 
			element 
test                    oupidedekmt(M,P) order of an univariate polynomial 
			over the integers, Dedekind maximality 
test                    ouspprmsp1dm(p,P,F) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			Dedekind maximality 
test                    putdippigt(r1,r2,C,PP,CGB0,CGB1,VL1,VL2) (MACRO) 
			put distributive polynomial over polynomials over 
			integers Groebner 
test                    putdippipim(r1,r2,NOUT,VL1,VL2) (MACRO) put 
			distributive polynomial over polynomials over 
			integers parametric ideal membership 
theorem                 primality test iftpt(n,L,anz) integer Fermat's 
third                   case qffmsregbg3(m,D,s) quadratic function field 
			over modular singles regulator, baby step - giant 
			step version, 
third                   lthird(L) (MACRO) list 
time                    settime() set 
time                    stoptime(a) stop and print 
to                      ( Heidelberg ) Integer itoI(A,h) ( SIMATH ) integer 
to                      ( Heidelberg ) Integer special version 
			itoI_sp(A,lA,h) ( SIMATH ) integer 
to                      ( SIMATH ) floating point PAFtofl(x) Papanikolaou 
			floating point 
to                      ( SIMATH ) integer Itoi(h) ( Heidelberg ) Integer 
to                      C-floating point fltoCfl(f) floating point 
to                      Essen integer itoE(A,e) ( SIMATH ) integer 
to                      Essen integer with upper bound itoEb(A,e,grenze) ( 
			SIMATH ) integer 
to                      Essen integer, sign and upper bound 
			itoEsb(A,e,grenze) ( SIMATH ) integer 
to                      Galois-field with characteristic 2 element 
			gfseltogf2el(G,a) Galois-field with single 
			characteristic element 
to                      Galois-field with characteristic 2 element 
			udpm2togf2el(G,P) univariate dense polynomial over 
			modular 2 
to                      Galois-field with single characteristic element 
			gf2eltogfsel(G,a) (MACRO) Galois-field with 
			characteristic 2 element 
to                      Kant StoK(D,struc,data,type,digits) SIMATH 
to                      Kant string StoKstr(str,D,typ,prec) SIMATH 
to                      Papanikolaou floating point fltoPAF(f,x) ( SIMATH ) 
			floating point 
to                      SIMATH KstrtoS(a) Kant string 
to                      SIMATH KtoS(struc,data,type) Kant 
to                      SIMATH divs(A,B) (MACRO) division with reference 
to                      SIMATH integer Etoi(e) Essen integer 
to                      SIMATH integer negation Etoineg(e) Essen integer 
to                      SIMATH mods(A,B) (MACRO) modulo with reference 
to                      a cubic equation bpmisubcubeq(p,P,R) bivariate 
			polynomial over modular integers substitution with 
			respect 
to                      actual ( rational ) model eciminbtac(E) elliptic 
			curve with integer coefficients, minimal model, 
			birational transformation 
to                      actual ( rational ) model ecisnfbtac(E) elliptic 
			curve with integer coefficients, short normal form, 
			birational transformation 
to                      an integer intppint(P,A) integer P-part with 
			respect 
to                      dense polynomial (rekursiv) ptodp(r,P) polynomial 
to                      distributive polynomial (rekursiv) ptodip(r,P) 
			polynomial 
to                      distributive polynomial over Galois-field with 
			single characteristic in graduated lexicographical 
			order dipgfslotglo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order 
to                      distributive polynomial over Galois-field with 
			single characteristic in lexicographical order with 
			inverse exponent vector dipgfslotlio(r,p,AL,P) 
			distributive polynomial over Galois-field with 
			single characteristic in lexicographical order 
to                      distributive polynomial over Galois-field with 
			single characteristic with total degree ordering 
			dipgfslottdo(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order 
to                      distributive polynomial over integers in graduated 
			lexicographical order dipilotoglo(r,P) distributive 
			polynomial over integers in lexicographical order 
to                      distributive polynomial over integers in 
			lexicographical order with inverse exponent vector 
			dipilotolio(r,P) distributive polynomial over 
			integers in lexicographical order 
to                      distributive polynomial over integers with total 
			degree ordering dipilototdo(r,P) distributive 
			polynomial over integers in lexicographical order 
to                      distributive polynomial over modular integer primes 
			in graduated lexicographical order 
			dipmiplotglo(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order 
to                      distributive polynomial over modular integer primes 
			in lexicographical order with inverse exponent 
			vector dipmiplotlio(r,p,P) distributive polynomial 
			over modular integer primes in lexicographical 
			order 
to                      distributive polynomial over modular integer primes 
			with total degree ordering dipmiplottdo(r,p,P) 
			distributive polynomial over modular integer primes 
			in lexicographical order 
to                      distributive polynomial over modular single primes 
			in graduated lexicographical order 
			dipmsplotglo(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order 
to                      distributive polynomial over modular single primes 
			in lexicographical order with inverse exponent 
			vector dipmsplotlio(r,p,P) distributive polynomial 
			over modular single primes in lexicographical order 
to                      distributive polynomial over modular single primes 
			with total degree ordering dipmsplottdo(r,p,P) 
			distributive polynomial over modular single primes 
			in lexicographical order 
to                      distributive polynomial over number field in 
			graduated lexicographical order dipnflotoglo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order 
to                      distributive polynomial over number field in 
			lexicographical order with inverse exponent vector 
			dipnflotolio(r,F,P) distributive polynomial over 
			number field in lexicographical order 
to                      distributive polynomial over number field with 
			total degree ordering dipnflototdo(r,F,P) 
			distributive polynomial over number field in 
			lexicographical order 
to                      distributive polynomial over polynomials over 
			integers in graduated lexicographical order 
			dippilotoglo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
to                      distributive polynomial over polynomials over 
			integers in lexicographical order with inverse 
			exponent vector dippilotolio(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order 
to                      distributive polynomial over polynomials over 
			integers with total degree ordering 
			dippilototdo(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
to                      distributive polynomial over rational functions 
			over the rationals in graduated lexicographical 
			order diprfrlotglo(r1,r2,P) distributive polynomial 
			over rational functions over the rationals in 
			lexicographical order 
to                      distributive polynomial over rational functions 
			over the rationals in lexicographical order with 
			inverse exponent vector diprfrlotlio(r1,r2,P) 
			distributive polynomial over rational functions 
			over the rationals in lexicographical order 
to                      distributive polynomial over rational functions 
			over the rationals rfrtodiprfr(r1,r2,F) rational 
			function over the rationals 
to                      distributive polynomial over rational functions 
			over the rationals with total degree ordering 
			diprfrlottdo(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order 
to                      distributive polynomial over rationals in graduated 
			lexicographical order diprlotoglo(r,P) distributive 
			polynomial over rationals in lexicographical order 
to                      distributive polynomial over rationals in 
			lexicographical order with inverse exponent vector 
			diprlotolio(r,P) distributive polynomial over 
			rationals in lexicographical order 
to                      distributive polynomial over rationals with total 
			degree ordering diprlototdo(r,P) distributive 
			polynomial over rationals in lexicographical order 
to                      elliptic curve with integral coefficients 
			ecqnftoeci(D,L) elliptic curve over quadratic 
			number field 
to                      equation iecjtoeq(p,j) integer elliptic curve 
			j-invariant 
to                      equation special version iecjtoeqsv(p,j,pi) integer 
			elliptic curve j-invariant 
to                      exact order of the point 
			ecgf2mopto(G,a1,a2,a3,a4,a6,P,N) elliptic curve 
			over Galois-field with characteristic 2, multiple 
			of the order of a point 
to                      exact order of the point 
			ecmpsnfmopto(p,a4,a6,P,mul) elliptic curve over 
			modular primes, short normal form, multiple of the 
			order of a point 
to                      floating point Cfltofl(x) C-floating point 
to                      floating point chartofl(A) character 
to                      floating point fltofl(f) (MACRO) floating point 
to                      floating point itofl(A) (MACRO) integer 
to                      floating point rtofl(r) rational number 
to                      global minimal model ( Laska's algorithm ) 
			ecractoecimin(E) elliptic curve over rational 
			numbers, actual curve 
to                      integer iavalint(M,I) integer additive value with 
			respect 
to                      integer prime upihlfaip(p,P,L,k) univariate 
			polynomial over integers, Hensel lemma 
			factorization approximation with respect 
to                      integer prime upihliip(P,F,L) univariate polynomial 
			over integers, Hensel lemma initialization with 
			respect 
to                      integer prime upihlqsip(P,p_k,p_l,F,L1,L2,A) 
			univariate polynomial over integers, Hensel lemma 
			quadratic step with respect 
to                      integer primes infempmppip(F,a,p,e,Q) integral 
			number field element minimal polynomial modulo 
			p-power with respect 
to                      integer primes infepptfip(F,p,Q,ppot,a0,z) integral 
			number field element p-primality test and 
			factorization of the defining polynomial or the 
			minimal polynomial with respect 
to                      integer primes infepstarvip(P,A) integral number 
			field element p-star valuation with respect 
to                      integer primes ippnfecalip(F,P,Q,mp) integral 
			P-primary number field element, core algorithm with 
			respect 
to                      integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
			denominator of the p-star value with respect 
to                      integer primes ippnferegip(F,p,Q,a0,mpa0,pa1,pa2) 
			integral p-primary number field element regulation 
			with respect 
to                      integer primes ouspibaslmoi(F,P,Q,pk) order of an 
			univariate separable polynomial over the integers 
			basis of a local maximal over-order with respect 
to                      integer ravalint(M,R) rational additive value with 
			respect 
to                      list ptol(pc) (MACRO) pointer 
to                      matrix line nfeltomaln(n,a) number field element 
to                      matrix of dense polynomials maptomadp(r,M) matrix 
			of polynomials 
to                      matrix of modular integers maitomami(m,M) matrix of 
			integers 
to                      matrix of modular integers martomami(m,M) matrix of 
			rationals 
to                      matrix of modular singles maitomams(m,M) matrix of 
			integers 
to                      matrix of number field elements maitomanf(M) matrix 
			of integers 
to                      matrix of number field elements martomanf(M) matrix 
			of rationals 
to                      matrix of number field elements maudprtomnf(M) 
			matrix of univariate dense polynomials over 
			rationals 
to                      matrix of number field elements, sparse 
			representation maitomanfs(M) matrix of integers 
to                      matrix of number field elements, sparse 
			representation martomanfs(M) matrix of rationals 
to                      matrix of polynomials madptomap(r,M) matrix of 
			dense polynomials 
to                      matrix of polynomials modulo polynomial over 
			Galois-field with single characteristic 
			mpgfstompmp(r,p,AL,P,M) matrix of polynomials over 
			Galois-field with single characteristic 
to                      matrix of polynomials modulo polynomial over 
			integers mapitompmpi(r,M,P) matrix of polynomials 
			over integers 
to                      matrix of polynomials modulo polynomial over 
			modular integers mapmitomapmp(r,m,P,M) matrix of 
			polynomials over modular integers 
to                      matrix of polynomials modulo polynomial over 
			modular singles mapmstomapmp(r,m,P,M) matrix of 
			polynomials over modular singles 
to                      matrix of polynomials modulo polynomial over number 
			field mapnftomapmp(r,F,P,M) matrix of polynomials 
			over number field 
to                      matrix of polynomials modulo polynomial over 
			rationals maprtompmpr(r,M,P) matrix of polynomials 
			over rationals 
to                      matrix of polynomials over Galois-field with single 
			characteristic mpmstompgfs(r,p,M) matrix of 
			polynomials over modular singles 
to                      matrix of polynomials over integers maitomapi(r,M) 
			matrix of integers 
to                      matrix of polynomials over modular integers 
			mapitomapmi(r,M,m) matrix of polynomials over 
			integers 
to                      matrix of polynomials over modular integers 
			maprtomapmi(r,M,m) matrix of polynomials over 
			rationals 
to                      matrix of polynomials over modular singles 
			mapitomapms(r,M,m) matrix of polynomials over 
			integers 
to                      matrix of polynomials over number field 
			mapitomapnf(r,M) matrix of polynomials over 
			integers 
to                      matrix of polynomials over number field 
			maprtomapnf(r,M) matrix of polynomials over 
			rationals 
to                      matrix of polynomials over rationals 
			mapnftomapr(r,M) matrix of polynomials over number 
			field 
to                      matrix of polynomials over rationals martomapr(r,M) 
			matrix of rationals 
to                      matrix of rational functions over modular single 
			primes, transcendence degree 1 mpmstmrfmsp1(p,M) 
			matrix of polynomials over modular singles 
to                      matrix of rational functions over rationals 
			mapitomarfr(r,M) matrix of polynomials over 
			integers 
to                      matrix of rational functions over rationals 
			maprtomarfr(r,M) matrix of polynomials over 
			rationals 
to                      matrix of rationals maitomar(M) matrix of integers 
to                      matrix of rationals mapitomapr(r,M) matrix of 
			integers 
to                      matrix of univariate dense polynomials over modular 
			integers mudpitudpmi(M,m) matrix of univariate 
			dense polynomials over integers 
to                      matrix of univariate dense polynomials over 
			rationals manftomudpr(F,M) matrix of number field 
			elements 
to                      matrix of univariate dense polynomials over 
			rationals mudpitmudpr(M) matrix of univariate dense 
			polynomials over integers 
to                      matrix of univariate polynomials maptomaup(r,M) 
			matrix of polynomials 
to                      matrix over Galois-field with single characteristic 
			maitomagfs(p,M) matrix over integers 
to                      minimal model ecisnfbtmin(E) elliptic curve with 
			integer coefficients, short normal form, birational 
			transformation 
to                      minimal model ecracbtmin(E) elliptic curve over the 
			rationals, actual curve, birational transformation 
to                      modular integer rtomi(R,M) rational number 
to                      number field element itonf(A) (MACRO) integer 
to                      number field element rtonf(R) rational number 
to                      number field element udprtonfel(P) univariate dense 
			polynomial over rationals 
to                      number field element uprtonfel(F,P) univariate 
			polynomial over rationals 
to                      number field element, sparse representation 
			itonfs(A) integer 
to                      number field element, sparse representation 
			rtonfs(R) rational number 
to                      number field of degree 3 isnf3eqnf3(F,P,pFD,pPD,pQ) 
			is number field of degree 3 equal 
to                      p-adic field element itopfel(p,d,A) integer 
to                      p-adic field element rtopfel(p,d,R) rational 
to                      pointer ltop(L) (MACRO) list 
to                      polynomial (rekursiv) diptop(r,P) distributive 
			polynomial 
to                      polynomial (rekursiv) dptop(r,P) dense polynomial 
to                      polynomial over Galois-field with characteristic 2 
			(rekursiv) pgfstopgf2(r,G,P) polynomial over 
			Galois-field with single characteristic 
to                      polynomial over Galois-field with characteristic 2 
			(rekursiv) pm2topgf2(r,P) polynomial over modular 2 
to                      polynomial over Galois-field with single 
			characteristic (rekursiv) pgf2topgfs(r,G,P) 
			polynomial over Galois-field with characteristic 2 
to                      polynomial over Galois-field with single 
			characteristic (rekursiv) pmstopgfs(r,p,P) 
			polynomial over modular singles 
to                      polynomial over a number field (rekursiv) 
			pitopnf(r,P) polynomial over the integers 
to                      polynomial over integer itopi(r,A) (MACRO) integer 
to                      polynomial over modular integers (rekursiv) 
			pitopmi(r,P,M) polynomial over integers 
to                      polynomial over modular integers (rekursiv) 
			prtopmi(r,P,M) polynomial over rationals 
to                      polynomial over modular singles (rekursiv) 
			pitopms(r,P,m) polynomial over integers 
to                      polynomial over number field (rekursiv) 
			prtopnf(r,P) polynomial over rationals 
to                      polynomial over p-adic field pitoppf(r,P,p,d) 
			polynomial over integers 
to                      polynomial over p-adic field prtoppf(r,P,p,d) 
			polynomial over rationals 
to                      polynomial over rationals (rekursiv) pitopr(r,P) 
			polynomial over integers 
to                      polynomial over rationals pnftopr(r,P) polynomial 
			over number field 
to                      projective representation ecrptoproj(P) elliptic 
			curve over rational numbers, point 
to                      quadratic number field element itoqnf(D,a) (MACRO) 
			integer 
to                      quadratic number field element rtoqnf(D,A) (MACRO) 
			rational number 
to                      rational function over modular single prime, 
			transcendence degree 1 pmstorfmsp1(p,P) (MACRO) 
			polynomial over modular singles 
to                      rational function over rationals rtorfr(r,R) 
			rational number 
to                      rational function over the rationals 
			diprfrtorfr(r1,r2,P) distributive polynomial over 
			rational functions over the rationals 
to                      rational function over the rationals pitorfr(r,P) 
			polynomial over integers 
to                      rational function over the rationals prtorfr(r,P) 
			polynomial over the rationals 
to                      rational number fltor(f) floating point 
to                      rational number inearesttor(r) integer nearest 
to                      rational number itor(A) integer 
to                      short normal form eciminbtsnf(E) elliptic curve 
			with integer coefficients, minimal model, 
			birational transformation 
to                      short normal form ecimintosnf(E) elliptic curve 
			with integer coefficients, minimal model 
to                      short normal form ecmptosnf(p,a1,a2,a3,a4,a6) 
			elliptic curve over modular primes 
to                      short normal form ecnftosnf(F,a1,a2,a3,a4,a6) 
			elliptic curve over number field 
to                      short normal form ecracbtsnf(E) elliptic curve over 
			rational numbers, actual curve, birational 
			transformation 
to                      special bit-representation udpm2tosb(P) univariate 
			dense polynomial over modular 2 
to                      symmetric remainder system (rekursiv) pmitos(r,M,P) 
			polynomial over modular integers 
to                      symmetric remainder system mitos(M,A) modular 
			integer 
to                      univariate dense polynomial over modular 2 
			gf2eltoudpm2(G,a) Galois-field with characteristic 
			2 element 
to                      univariate dense polynomial over modular 2 
			sbtoudpm2(a) (MACRO) special bit-representation 
to                      univariate dense polynomial over modular integers 
			udpitoudpmi(P,M) univariate dense polynomial over 
			integers 
to                      univariate dense polynomial over p-adic field 
			udpitoudppf(P,p,d) univariate dense polynomial over 
			integers 
to                      univariate dense polynomial over p-adic field 
			udprtoudppf(P,p,d) univariate dense polynomial over 
			rationals 
to                      univariate dense polynomial over rationals 
			nfeltoudpr(a) number field element 
to                      univariate polynomial over rationals udpitoudpr(P) 
			univariate polynomial over integers 
to                      univariate polynomial ptoup(r,P) polynomial 
to                      vector of dense polynomials vecptovecdp(r,V) vector 
			of polynomials 
to                      vector of modular integers vecitovecmi(M,V) vector 
			of integers 
to                      vector of modular integers vecrtovecmi(m,V) vector 
			of rationals 
to                      vector of modular singles vecitovecms(m,V) vector 
			of integers 
to                      vector of number field elements vecitovecnf(V) 
			vector of integers 
to                      vector of number field elements vecrtovecnf(V) 
			vector of rationals 
to                      vector of number field elements vudprtovnf(V) 
			vector of univariate dense polynomials over 
			rationals 
to                      vector of number field elements, sparse 
			representation vecitovnfs(V) vector of integers 
to                      vector of number field elements, sparse 
			representation vecrtovnfs(V) vector of rationals 
to                      vector of polynomials modulo polynomial over 
			Galois-field with single characteristic 
			vpgfstovpmp(r,p,AL,P,V) vector of polynomials over 
			Galois-field with single characteristic 
to                      vector of polynomials modulo polynomial over 
			integers vecpitvpmpi(r,V,P) vector of polynomials 
			over integers 
to                      vector of polynomials modulo polynomial over 
			modular integers vecpmitovpmp(r,m,P,V) vector of 
			polynomials over modular integers 
to                      vector of polynomials modulo polynomial over 
			modular singles vecpmstovpmp(r,m,P,V) vector of 
			polynomials over modular singles 
to                      vector of polynomials modulo polynomial over number 
			field vecpnftovpmp(r,F,P,V) vector of polynomials 
			over number field 
to                      vector of polynomials modulo polynomial over 
			rationals vecprtvpmpr(r,V,P) vector of polynomials 
			over rationals 
to                      vector of polynomials over Galois-field with single 
			characteristic vpmstovpgfs(r,p,V) vector of 
			polynomials over modular singles 
to                      vector of polynomials over integers 
			vecitovecpi(r,V) vector of integers 
to                      vector of polynomials over modular integers 
			vecpitovpmi(r,V,m) vector of polynomials over 
			integers 
to                      vector of polynomials over modular integers 
			vecprtovpmi(r,V,m) vector of polynomials over 
			rationals 
to                      vector of polynomials over modular singles 
			vecpitovpms(r,V,m) vector of polynomials over 
			integers 
to                      vector of polynomials over number field 
			vecpitovpnf(r,V) vector of polynomials over 
			integers 
to                      vector of polynomials over number field 
			vecprtovpnf(r,V) vector of polynomials over 
			rationals 
to                      vector of polynomials over rationals vecpitovpr(V) 
			vector of polynomials over integers 
to                      vector of polynomials over rationals 
			vecpnftovpr(r,V) vector of polynomials over number 
			field 
to                      vector of polynomials over rationals 
			vecrtovecpr(r,V) vector of rationals 
to                      vector of polynomials vecdptovecp(r,V) vector of 
			dense polynomials 
to                      vector of rational functions over modular single 
			primes, transcendence degree 1 vpmstvrfmsp1(p,V) 
			vector of polynomials over modular singles 
to                      vector of rational functions over rationals 
			vecpitovrfr(r,V) vector of polynomials over 
			integers 
to                      vector of rational functions over rationals 
			vecprtovrfr(r,V) vector of polynomials over 
			rationals 
to                      vector of rationals vecitovecr(V) vector of 
			integers 
to                      vector of univariate dense polynomials over modular 
			integers vudpitudpmi(V,M) vector of univariate 
			dense polynomials over integers 
to                      vector of univariate dense polynomials over 
			rationals vnftovudpr(F,V) vector of number field 
			elements 
to                      vector of univariate dense polynomials over 
			rationals vudpitvudpr(V) vector of univariate dense 
			polynomials over integers 
to                      vector of univariate polynomials vecptovecup(r,V) 
			vector of polynomials 
to                      vector over Galois-field with single characteristic 
			vecitovecgfs(p,V) vector over integers 
torsion                 eciminpcompmt(E,P1,P2) elliptic curve with integer 
			coefficients, minimal model, point comparison 
			modulo 
torsion                 group ecimingentor(E) elliptic curve with integer 
			coefficients, minimal model, generators of 
torsion                 group ecimintorgr(E) elliptic curve with integer 
			coefficients, minimal model, 
torsion                 group ecisnfgentor(E) elliptic curve with integer 
			coefficients, short normal form, generators of the 
torsion                 group ecisnftorgr(E) elliptic curve with integer 
			coefficients, short normal form, 
torsion                 group ecracgentor(E) elliptic curve over rational 
			numbers, actual curve, generators of 
torsion                 group ecractorgr(E) elliptic curve over rational 
			numbers, actual curve, 
torsion                 group ecrexptor(E) elliptic curve over rational 
			numbers, exponent of 
torsion                 group ecrordtor(E) elliptic curve over rational 
			numbers, order of 
torsion                 group ecrstrtor(E) elliptic curve over rational 
			numbers, structure of 
torsion                 point on elliptic curve with integer coefficients, 
			minimal model isecimintorp(E,P) is 
total                   degree diptdg(r,P) distributive polynomial 
total                   degree ordering dipgfslottdo(r,p,AL,P) distributive 
			polynomial over Galois-field with single 
			characteristic in lexicographical order to 
			distributive polynomial over Galois-field with 
			single characteristic with 
total                   degree ordering dipilototdo(r,P) distributive 
			polynomial over integers in lexicographical order 
			to distributive polynomial over integers with 
total                   degree ordering dipmiplottdo(r,p,P) distributive 
			polynomial over modular integer primes in 
			lexicographical order to distributive polynomial 
			over modular integer primes with 
total                   degree ordering dipmsplottdo(r,p,P) distributive 
			polynomial over modular single primes in 
			lexicographical order to distributive polynomial 
			over modular single primes with 
total                   degree ordering dipnflototdo(r,F,P) distributive 
			polynomial over number field in lexicographical 
			order to distributive polynomial over number field 
			with 
total                   degree ordering dippilototdo(r1,r2,P) distributive 
			polynomial over polynomials over integers in 
			lexicographical order to distributive polynomial 
			over polynomials over integers with 
total                   degree ordering diprfrlottdo(r1,r2,P) distributive 
			polynomial over rational functions over the 
			rationals in lexicographical order to distributive 
			polynomial over rational functions over the 
			rationals with 
total                   degree ordering diprlototdo(r,P) distributive 
			polynomial over rationals in lexicographical order 
			to distributive polynomial over rationals with 
trace                   function upgfstf(p,AL,G,d,M) univariate polynomial 
			over Galois-field with single characteristic, 
trace                   function, special upgf2tf(G,F,d,M) polynomial over 
			Galois-field with characteristic 2, 
trace                   function, special upmitfsp(ip,G,d,M) univariate 
			polynomial over modular integers, 
trace                   maitrace(M) matrix of integers 
trace                   nftrace(F,a) number field element 
trace                   of an element qnftrace(D,a) quadratic number field 
trailing                base coefficient (rekursiv) ptbc(r,P) polynomial 
trailing                base coefficient udpmstbc(m,P) univariate dense 
			polynomial over modular single 
trailing                base coefficient udptbc(P) univariate dense 
			polynomial 
transcendence           degree 1 ? ismarfmsp1(p,M) (MACRO) is matrix of 
			rational functions over modular single primes, 
transcendence           degree 1 ? isrfmsp1(p,R) is rational function over 
			modular single prime, 
transcendence           degree 1 ? isvecrfmsp1(p,V) (MACRO) is vector of 
			rational functions over modular single primes, 
transcendence           degree 1 cdprfmsp1fup(p,P) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, from 
			univariate polynomial over rational functions over 
			modular single prime, 
transcendence           degree 1 cdprfmsp1lfm(M,p) common denominator 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, list from 
			common denominator matrix of rational functions 
			over modular single prime, 
transcendence           degree 1 clfcdprfmsp1(P,n) coefficient list from 
			common denominator polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1 fgetmarfmsp1(p,V,pf) (MACRO) file get 
			matrix of rational functions over modular single 
			primes, 
transcendence           degree 1 fgetrfmsp1(p,V,pf) file get rational 
			function over modular single primes, 
transcendence           degree 1 fgetvrfmsp1(p,VL,pf) (MACRO) file get 
			vector of rational functions over modular single 
			primes, 
transcendence           degree 1 fputmarfmsp1(p,M,V,pf) (MACRO) file put 
			matrix of rational functions over modular single 
			primes, 
transcendence           degree 1 fputrfmsp1(p,R,V,pf) (MACRO) file put 
			rational function over modular single prime, 
transcendence           degree 1 fputvrfmsp1(p,V,VL,pf) (MACRO) file put 
			vector of rational functions over modular single 
			primes, 
transcendence           degree 1 getmarfmsp1(p,V) (MACRO) get matrix of 
			rational functions over modular single primes, 
transcendence           degree 1 getrfmsp1(p,V) (MACRO) get rational 
			function over modular single primes, 
transcendence           degree 1 getvecrfmsp1(p,VL) (MACRO) get vector of 
			rational functions over modular single primes, 
transcendence           degree 1 mpmstmrfmsp1(p,M) matrix of polynomials 
			over modular singles to matrix of rational 
			functions over modular single primes, 
transcendence           degree 1 nepousppmsp1(p,F,a) norm of an element of 
			the polynomial order of an univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, 
transcendence           degree 1 pmstorfmsp1(p,P) (MACRO) polynomial over 
			modular singles to rational function over modular 
			single prime, 
transcendence           degree 1 putmarfmsp1(p,M,V) (MACRO) put matrix of 
			rational functions over modular single primes, 
transcendence           degree 1 putrfmsp1(p,R,V) (MACRO) put rational 
			function over modular single prime, 
transcendence           degree 1 putvecrfmsp1(p,V,VL) (MACRO) put vector of 
			rational functions over modular single primes, 
transcendence           degree 1 rfmsp1cons(p,P1,P2) rational function over 
			modular single prime construction, 
transcendence           degree 1 rfmsp1dif(p,R1,R2) rational function over 
			modular single prime difference, 
transcendence           degree 1 rfmsp1neg(p,R) rational function over 
			modular single prime negation, 
transcendence           degree 1 rfmsp1prod(p,R1,R2) rational function over 
			modular single prime product, 
transcendence           degree 1 rfmsp1quot(p,R1,R2) rational function over 
			modular single prime quotient, 
transcendence           degree 1 rfmsp1sum(p,R1,R2) rational function over 
			modular single prime sum, 
transcendence           degree 1 sclfuprfmsp1(P,n) special coefficient list 
			from univariate polynomial over rational functions 
			over modular single prime, 
transcendence           degree 1 uprfmsp1fcdp(p,P) univariate polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from common denominator 
			polynomial over rational functions over modular 
			single prime, 
transcendence           degree 1 vepepuspmsp1(p,F,a,P,k,v) values of the 
			extensions of the P-adic valuation of an element of 
			the polynomial order of a univariate separable 
			polynomial over the polynomial ring over modular 
			single prime, 
transcendence           degree 1 vpmstvrfmsp1(p,V) vector of polynomials 
			over modular singles to vector of rational 
			functions over modular single primes, 
transcendence           degree 1, Dedekind maximality test 
			ouspprmsp1dm(p,P,F) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, 
transcendence           degree 1, Hensel factorization approximation 
			upprmsp1hfa(p,F,P,L,k) univariate polynomial over 
			polynomial ring over modular single prime, 
transcendence           degree 1, Hensel lemma initialization 
			upprmsp1hli(p,F,P,L) univariate polynomial over 
			polynomial ring over modular single prime, 
transcendence           degree 1, Hensel quadratic step 
			upprmsp1hqs(p,F,T,L1,L2,A) univariate polynomial 
			over polynomial ring over modular single prime, 
transcendence           degree 1, P-primality test and factorization of the 
			defining polynomial or the minimal polynomial 
			afmsp1pptf(p,F,P,Q,Pp,a0,z) algebraic function over 
			modular single prime, 
transcendence           degree 1, P-star valuation iafmsp1psval(p,P,A) 
			integral algebraic function over modular single 
			prime, 
transcendence           degree 1, algebraic function over modular single 
			prime, transcendence degree 1, evaluation special 
			upprmsp1afes(p,F,P,a) univariate polynomial over 
			polynomial ring over modular single prime, 
transcendence           degree 1, approximation of P-adic factorization 
			uspprmsp1apf(p,P,F,k) univariate separable 
			polynomial over polynomial ring over modular single 
			prime, 
transcendence           degree 1, basis from generators oprmsp1basfg(p,F,L) 
			order over polynomial ring over modular single 
			prime, 
transcendence           degree 1, basis of a local maximal over-order 
			ouspprmsp1bl(p,F,P,Q,pk) order of an univariate 
			separable polynomial over polynomial ring over 
			modular single prime, 
transcendence           degree 1, construction 1 marfmsp1c1(p,n) (MACRO) 
			matrix of rational functions over modular single 
			primes, 
transcendence           degree 1, core algorithm afmsp1coreal(p,F,P,Q,mp) 
			algebraic function over modular single primes, 
transcendence           degree 1, decomposition law affmsp1decl(p,F,P) 
			algebraic function field over modular single prime, 
transcendence           degree 1, decomposition law ouspprmsp1dl(p,F,P,k) 
			order of a univariate separable polynomial over 
			polynomial ring over modular single prime, 
transcendence           degree 1, derivation, main variable 
			prfmsp1deriv(r,p,P) polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1, determinant marfmsp1det(p,M) matrix of 
			rational functions over modular single primes 
transcendence           degree 1, difference (rekursiv) 
			prfmsp1dif(r,p,P1,P2) polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1, difference marfmsp1dif(p,M,N) (MACRO) 
			matrix of rational functions over modular single 
			primes 
transcendence           degree 1, difference vecrfmsp1dif(p,U,V) (MACRO) 
			vector of rational functions over modular single 
			primes, 
transcendence           degree 1, discriminant upprmsp1disc(p,F) univariate 
			polynomial over polynomial ring over modular single 
			prime, 
transcendence           degree 1, element test modprmsp1elt(B,p,a) module 
			over polynomial ring over modular single primes, 
transcendence           degree 1, evaluation special upprmsp1afes(p,F,P,a) 
			univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			algebraic function over modular single prime, 
transcendence           degree 1, exponentiation marfmsp1exp(p,M,n) matrix 
			of rational functions over modular single primes, 
transcendence           degree 1, exponentiation special 
			afmsp1expsp(p,F,a,e,M) algebraic function over 
			modular single prime, 
transcendence           degree 1, extended greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial 
			over rational functions over modular single prime, 
transcendence           degree 1, from coefficient list cdprfmsp1fcl(L,p) 
			common denominator polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1, from common denominator polynomial over 
			rational functions over modular single prime, 
			transcendence degree 1 uprfmsp1fcdp(p,P) univariate 
			polynomial over rational functions over modular 
			single prime, 
transcendence           degree 1, from special coefficient list 
			uprfmsp1fscl(L) univariate polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1, from univariate polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 cdprfmsp1fup(p,P) common denominator 
			polynomial over rational functions over modular 
			single prime, 
transcendence           degree 1, hermitian reduction cdmarfmsp1hr(p,M) 
			common denominator matrix of rational functions 
			over modular single prime, 
transcendence           degree 1, identity construction cdmarfmsp1id(n) 
			common denominator matrix of rational functions 
			over modular single prime, 
transcendence           degree 1, increasing the denominator of the P-star 
			value afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) 
			algebraic function over modular single primes, 
transcendence           degree 1, integral basis ouspprmsp1ib(p,F,pL) order 
			of an univariate separable polynomial over the 
			polynomial ring over modular single prime, 
transcendence           degree 1, inverse cdprfmsp1inv(p,F,A) common 
			denominator polynomial over rational functions over 
			modular single prime, 
transcendence           degree 1, inverse marfmsp1inv(p,M) matrix of 
			rational functions over modular single primes, 
transcendence           degree 1, inverse rfmsp1inv(p,R) rational function 
			over modular single primes, 
transcendence           degree 1, linear combination 
			vecrfmsp1lc(p,F1,F2,V1,V2) vector of rational 
			functions over modular single primes, 
transcendence           degree 1, list from common denominator matrix of 
			rational functions over modular single prime, 
			transcendence degree 1 cdprfmsp1lfm(M,p) common 
			denominator polynomial over rational functions over 
			modular single prime, 
transcendence           degree 1, minimal polynomial afmsp1minpol(p,F,a) 
			algebraic function over modular single primes, 
transcendence           degree 1, minimal polynomial iafmsp1mpol(p,F,a,Q) 
			integral algebraic function over modular single 
			primes, 
transcendence           degree 1, minimal polynomial modulo power of an 
			univariate prime polynomial over modular single 
			primes iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, 
transcendence           degree 1, module homomorphism cdprfmsp1mh(p,P,M) 
			common denominator polynomial over rational 
			functions over modular single primes, 
transcendence           degree 1, negation (rekursiv) prfmsp1neg(r,p,P) 
			polynomial over rational functions over modular 
			single prime, 
transcendence           degree 1, negation marfmsp1neg(p,M) (MACRO) matrix 
			of rational functions over modular single primes, 
transcendence           degree 1, negation vecrfmsp1neg(p,V) (MACRO) vector 
			of rational functions over modular single primes, 
transcendence           degree 1, null space basis marfmsp1nsb(p,M) matrix 
			of rational functions over modular single primes, 
transcendence           degree 1, product (rekursiv) prfmsp1prod(r,p,P1,P2) 
			polynomial over rational functions over modular 
			single prime, 
transcendence           degree 1, product (rekursiv) prfmsp1rfprd(r,p,P,a) 
			polynomial over rational functions over modular 
			single prime, transcendence degree 1, rational 
			function over modular single prime, 
transcendence           degree 1, product marfmsp1prod(p,M,N) (MACRO) 
			matrix of rational functions over modular single 
			primes, 
transcendence           degree 1, product special afmsp1prodsp(p,F,a,b,M) 
			algebraic function over modular single prime, 
transcendence           degree 1, quotient and remainder (rekursiv) 
			prfmsp1qrem(r,p,P1,P2,pR) polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1, rank marfmsp1rk(p,M) matrix of rational 
			functions over modular single primes, 
transcendence           degree 1, rational function over modular single 
			prime, transcendence degree 1, product (rekursiv) 
			prfmsp1rfprd(r,p,P,a) polynomial over rational 
			functions over modular single prime, 
transcendence           degree 1, reduced discriminant upprmsp1redd(p,F) 
			univariate polynomial over polynomial ring over 
			modular single prime, 
transcendence           degree 1, regulation 
			afmsp1regul(p,F,P,Q,a0,mpa0,pa1,pa2) algebraic 
			function over modular single primes, 
transcendence           degree 1, resultant, Sylvester algorithm 
			pprmsp1ress(r,p,P1,P2) polynomial over polynomial 
			ring over modular single prime, 
transcendence           degree 1, resultant, Sylvester algorithm 
			upprmsp1ress(p,P1,P2) univariate polynomial over 
			polynomial ring over modular single prime, 
transcendence           degree 1, scalar multiplication marfmsp1smul(p,M,F) 
			matrix of rational functions over modular single 
			primes, 
transcendence           degree 1, scalar multiplication vecrfmsp1sm(p,F,V) 
			vector of rational functions over modular single 
			primes, 
transcendence           degree 1, scalar product vecrfmsp1sp(p,V,W) vector 
			of rational functions over modular single primes, 
transcendence           degree 1, solution of a system of linear equations 
			marfmsp1ssle(p,A,b,pX,pN) matrix of rational 
			functions over modular single primes, 
transcendence           degree 1, sum (rekursiv) prfmsp1sum(r,p,P1,P2) 
			polynomial over rational functions over modular 
			single prime, 
transcendence           degree 1, sum cdprfmsp1sum(p,P1,P2) common 
			denominator polynomial over rational functions over 
			modular single prime, 
transcendence           degree 1, sum marfmsp1sum(p,M,N) (MACRO) matrix of 
			rational functions over modular single primes, 
transcendence           degree 1, sum vecrfmsp1sum(p,U,V) (MACRO) vector of 
			rational functions over modular single primes, 
transcendence           degree 1, univariate polynomial over modular single 
			prime quotient cdprfmsp1upq(p,F,P) common 
			denominator polynomial over rational functions over 
			modular single prime, 
transcendence           degree 1, vector multiplication marfmsp1vmul(p,A,x) 
			(MACRO) matrix of rational functions over modular 
			single primes, 
transcendental          functions 1 PAFtrans1() Papanikolaou floating point 
			package: 
transcendental          functions 2 PAFtrans2() Papanikolaou floating point 
			package: 
transcendental          functions 3 PAFtrans3() Papanikolaou floating point 
			package: 
transformation          ecrbtinv(BT) elliptic curve over rational numbers, 
			birational transformation, inverse 
transformation          mapgfstransf(r1,p,AL,M1,V1,r2,P2,V2,Vn,pV3) matrix 
			of polynomials over Galois-field with single 
			characteristic 
transformation          mapitransf(r1,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over the integers 
transformation          mapmitransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over modular integers 
transformation          mapmstransf(r1,m,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over modular singles 
transformation          mapnftransf(r1,F,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over number field 
transformation          maprtransf(r1,M1,V1,r2,P2,V2,Vn,pV3) matrix of 
			polynomials over the rationals 
transformation          marfrtransf(r1,M1,V1,r2,R2,V2,Vn,pV3) matrix of 
			rational functions over the rationals 
transformation          of coefficients ecgf2btco(G,a1,a2,a3,a4,a6,r,s,t,u) 
			elliptic curve over Galois-field with 
			characteristic 2, birational 
transformation          of coefficients eciminbtco(E,BT) elliptic curve 
			with integer coefficients, minimal model, 
			birational 
transformation          of coefficients ecisnfbtco(E,BT) elliptic curve 
			with integer coefficients, short normal form, 
			birational 
transformation          of coefficients ecmpbtco(p,a1,a2,a3,a4,a6,r,s,t,u) 
			elliptic curve over modular primes, birational 
transformation          of coefficients ecnfbtco(F,a1,a2,a3,a4,a6,r,s,t,u) 
			elliptic curve over number field birational 
transformation          of coefficients ecracbtco(E,BT) elliptic curve over 
			rational numbers, birational 
transformation          of coefficients ecrbtco(LC,BT) elliptic curve over 
			rational numbers, birational 
transformation          of list of points ecrbtlistp(LP,BT,modus) elliptic 
			curve over rational numbers, birational 
transformation          of point ecrbtp(P,BT) elliptic curve over rational 
			numbers, birational 
transformation          pgf2transf(r1,G,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over Galois-field with characteristic 2 
transformation          pgfstransf(r1,p,AL,P1,V1,r2,P2,V2,Vn,pV3) 
			polynomial over Galois-field with single 
			characteristic 
transformation          pirtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) polynomial over 
			the integers rational 
transformation          pitransf(r1,P1,V1,r2,P2,V2,Vn,pV3) polynomial over 
			the integers 
transformation          pmitransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over modular integers 
transformation          pmstransf(r1,m,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over modular singles 
transformation          pnftransf(r1,F,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over number field 
transformation          ppftransf(r1,p,P1,V1,r2,P2,V2,Vn,pV3) polynomial 
			over p-adic field 
transformation          prrtransf(r1,P1,V1,r2,R2,V2,Vn,pV3) polynomial over 
			the rationals rational 
transformation          prtransf(r1,P1,V1,r2,P2,V2,Vn,pV3) polynomial over 
			the rationals 
transformation          rfrtransf(r1,R1,V1,r2,R2,V2,Vn,pV3) rational 
			function over the rationals 
transformation          to actual ( rational ) model eciminbtac(E) elliptic 
			curve with integer coefficients, minimal model, 
			birational 
transformation          to actual ( rational ) model ecisnfbtac(E) elliptic 
			curve with integer coefficients, short normal form, 
			birational 
transformation          to minimal model ecisnfbtmin(E) elliptic curve with 
			integer coefficients, short normal form, birational 
transformation          to minimal model ecracbtmin(E) elliptic curve over 
			the rationals, actual curve, birational 
transformation          to short normal form eciminbtsnf(E) elliptic curve 
			with integer coefficients, minimal model, 
			birational 
transformation          to short normal form ecracbtsnf(E) elliptic curve 
			over rational numbers, actual curve, birational 
transformation          upmitransf(M,P,r,P1) univariate polynomial over 
			modular integers 
transformation          upmstransf(m,P,r,P1) univariate polynomial over 
			modular singles 
transformation          veciunimtr(V,W,i,pV1,pW1) vector of integers 
			unimodular 
transformation          vecpitransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over the integers 
transformation          vecprtransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over the rationals 
transformation          vecrfrtrnsf(r1,W1,V1,r2,R2,V2,Vn,pV3) vector of 
			rational functions over the rationals 
transformation          vecupmsunimt(p,V,W,i,pV1,pW1) vector of univariate 
			polynomials over modular single prime unimodular 
transformation          version2 upmitransf2(M,P,r,P1) univariate 
			polynomial over modular integers 
transformation          vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) vector 
			of polynomials over Galois-field with single 
			characteristic 
transformation          vpmitransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over modular integers 
transformation          vpmstransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over modular singles 
transformation          vpnftransf(r1,F,W1,V1,r2,P2,V2,Vn,pV3) vector of 
			polynomials over number field 
transformation,         concatenation of transformations ecrbtconc(BT1,BT2) 
			elliptic curve over rational numbers, birational 
transformation,         inverse transformation ecrbtinv(BT) elliptic curve 
			over rational numbers, birational 
transformations         ecrbtconc(BT1,BT2) elliptic curve over rational 
			numbers, birational transformation, concatenation 
			of 
translation,            all variables (rekursiv) pitransav(r,P,LI) 
			polynomial over integers 
translation,            all variables (rekursiv) pmitransav(r,m,P,Lmi) 
			polynomial over modular integers 
translation,            all variables (rekursiv) pmstransav(r,m,P,Lms) 
			polynomial over modular singles 
translation,            all variables (rekursiv) prtransav(r,P,LR) 
			polynomial over rationals 
translation,            all variables ppftransav(r,p,P,Lpf) polynomial over 
			p-adic field 
translation,            main variable pitrans(r,P,A) polynomial over 
			integers 
translation,            main variable pmitrans(r,m,P,a) polynomial over 
			modular integers 
translation,            main variable pmstrans(r,m,P,a) polynomial over 
			modular singles 
translation,            main variable ppftrans(r,p,P,A) polynomial over 
			p-adic field 
translation,            main variable prtrans(r,P,A) polynomial over 
			rationals 
transpose               mactransp(M) matrix constructive 
transpose               matransp(M) matrix 
triangular              form with negative entries ) maihermltne(A) (MACRO) 
			matrix of integers Hermite normal form ( lower 
triangular              form with positive entries ) maihermltpe(A) (MACRO) 
			matrix of integers Hermite normal form ( lower 
trigonometric           functions fltrig(Ffunc,f) (MACRO) floating point 
trinomial,              generator upm2imtgen(n) univariate polynomial over 
			modular 2, irreducible and monic 
trinomial,              generator upmsimtgen(p,n) univariate polynomial 
			over modular singles, irreducible and monic 
truncation              (rekursiv) pitrunc(r,S,P) polynomial over integers 
truncation              itrunc(A,n) (MACRO) integer 
truncation              product (rekursiv) pitrprod(r,S,P1,P2) polynomial 
			over integers 
type                    eciminredtype(E) elliptic curve with integer 
			coefficients, minimal model, reduction 
type                    ecrrt(E,p) elliptic curve over rational numbers 
			reduction 
type                    modulo prime eciminbrtmp(E,p,n) elliptic curve with 
			integer coefficients, minimal model, bad reduction 
type                    modulo prime eciminmrtmp(E,p) elliptic curve with 
			integer coefficients, minimal model, multiplicative 
			reduction 
type,                   imaginary case qffmsicggii(m,D,H,L,pIT) quadratic 
			function field over modular singles ideal class 
			group generators and isomorphy 
type,                   imaginary case qffmszcgiti(m,D,LG,IT) quadratic 
			function field over modular singles zero class 
			group isomorphy 
type,                   real case qffmsicggir(m,D,d,H,L,pIT) quadratic 
			function field over modular singles ideal class 
			group generators and isomorphy 
type,                   real case qffmszcgitr(m,D,d,H,LG,R,IT) quadratic 
			function field over modular singles zero class 
			group isomorphy 
typer                   PAFtype() Papanikolaou floating point package: 
udpgf2remsp(G,P1,P2,ilc) univariate dense polynomial over Galois-field with 
			characteristic 2 remainder, special version 
udpicontpp(P,pPP)       univariate dense polynomial over integers content 
			and primitive part 
udpidif(P1,P2)          univariate dense polynomial over integers 
			difference 
udpiiprod(P,A)          univariate dense polynomial over integers integer 
			product 
udpineg(P)              univariate dense polynomial over integers negation 
udpiprod(P1,P2)         univariate dense polynomial over integers product 
udpipsrem(P1,P2)        univariate dense polynomial over integers pseudo 
			remainder 
udpisum(P1,P2)          univariate dense polynomial over integers sum 
udpitoudpmi(P,M)        univariate dense polynomial over integers to 
			univariate dense polynomial over modular integers 
udpitoudppf(P,p,d)      univariate dense polynomial over integers to 
			univariate dense polynomial over p-adic field 
udpitoudpr(P)           univariate polynomial over integers to univariate 
			polynomial over rationals 
udpm2togf2el(G,P)       univariate dense polynomial over modular 2 to 
			Galois-field with characteristic 2 element 
udpm2tosb(P)            univariate dense polynomial over modular 2 to 
			special bit-representation 
udpmideriv(m,P)         univariate dense polynomial over modular integers 
			derivation 
udpmidif(m,P1,P2)       univariate dense polynomial over modular integers 
			difference 
udpmiegcd(m,P1,P2,pPX,pPY) univariate dense polynomial over modular integers 
			extended greatest common divisor 
udpmigcd(m,P1,P2)       univariate dense polynomial over modular integers 
			greatest common divisor 
udpmihegcd(m,P1,P2,pP3) univariate dense polynomial over modular integers 
			half extended greatest common divisor 
udpmijacsym(m,P1,P2)    univariate dense polynomial over modular integers 
			Jacobi-symbol 
udpmimiprod(m,P,a)      univariate dense polynomial over modular integers, 
			modular integer product 
udpmimonic(m,P)         univariate dense polynomial over modular integers 
			monic 
udpmineg(m,P)           univariate dense polynomial over modular integers 
			negation 
udpmiprod(m,P1,P2)      univariate dense polynomial over modular integers 
			product 
udpmiqrem(m,P1,P2,pP3)  univariate dense polynomial over modular integers 
			quotient and remainder 
udpmiquot(m,P1,P2)      (MACRO) univariate dense polynomial over modular 
			integers quotient 
udpmirem(ip,P,P2)       univariate dense polynomial over modular integers 
			remainder 
udpmisum(m,P1,P2)       univariate dense polynomial over modular integers 
			sum 
udpmsderiv(m,P)         univariate dense polynomial over modular singles 
			derivation 
udpmsdif(m,P1,P2)       univariate dense polynomial over modular singles 
			difference 
udpmsegcd(m,P1,P2,pPX,pPY) univariate dense polynomial over modular singles 
			extended greatest common divisor 
udpmsgcd(m,P1,P2)       univariate dense polynomial over modular singles 
			greatest common divisor 
udpmshegcd(m,P1,P2,pP3) univariate dense polynomial over modular singles 
			half extended greatest common divisor 
udpmsjacsym(m,P1,P2)    univariate dense polynomial over modular singles 
			Jacobi-symbol 
udpmsmonic(m,P)         univariate dense polynomial over modular singles 
			monic 
udpmsmsprod(m,P,a)      univariate dense polynomial over modular singles, 
			modular single product 
udpmsneg(m,P)           univariate dense polynomial over modular singles 
			negation 
udpmsprod(m,P1,P2)      univariate dense polynomial over modular singles 
			product 
udpmsqrem(m,P1,P2,pP3)  univariate dense polynomial over modular singles 
			quotient and remainder 
udpmsquot(m,P1,P2)      (MACRO) univariate dense polynomial over modular 
			singles quotient 
udpmsrem(m,P1,P2)       univariate dense polynomial over modular singles 
			remainder 
udpmssum(m,P1,P2)       univariate dense polynomial over modular singles 
			sum 
udpmssumjs(m,P,n)       univariate dense polynomial over modular singles, 
			summation over Jacobi-symbols 
udpmstbc(m,P)           univariate dense polynomial over modular single 
			trailing base coefficient 
udppfdif(p,P1,P2)       univariate dense polynomial over p-adic field 
			difference 
udppfexp(p,P,n)         univariate dense polynomial over p-adic field 
			exponentiation 
udppffit(p,P,Pd)        univariate dense polynomial over p-adic field 
			fitting 
udppfneg(p,P)           univariate dense polynomial over p-adic field 
			negation 
udppfpfprod(p,P,a)      univariate dense polynomial over p-adic field 
			p-adic field element product 
udppfpprod(p,P,i)       univariate dense polynomial over p-adic field prime 
			power product 
udppfprod(p,P1,P2)      univariate dense polynomial over p-adic field 
			product 
udppfsum(p,P1,P2)       univariate dense polynomial over p-adic field sum 
udprdif(P1,P2)          univariate dense polynomial over rationals 
			difference 
udprneg(P)              univariate dense polynomial over rationals negation 
udprprod(P1,P2)         univariate dense polynomial over rationals product 
udprqrem(P1,P2,pP3)     univariate dense polynomial over rationals quotient 
			and remainder 
udprrprod(P,A)          univariate dense polynomial over rationals, 
			rational number product 
udprsum(P1,P2)          univariate dense polynomial over rationals sum 
udprtonfel(P)           univariate dense polynomial over rationals to 
			number field element 
udprtoudppf(P,p,d)      univariate dense polynomial over rationals to 
			univariate dense polynomial over p-adic field 
udptbc(P)               univariate dense polynomial trailing base 
			coefficient 
undo                    string get character unsgetc(c,ps) 
unimodular              transformation veciunimtr(V,W,i,pV1,pW1) vector of 
			integers 
unimodular              transformation vecupmsunimt(p,V,W,i,pV1,pW1) vector 
			of univariate polynomials over modular single prime 
union                   csetunion(S,T) characteristic set 
union                   eciminplunion(E,L1,L2,modus) elliptic curve with 
			integer coefficients, minimal model, point list 
union                   sunion(L1,L2) set 
union                   usunion(L1,L2) (MACRO) unordered set 
unit                    ball volunitball(r) volume of the 
unit                    group qnfunit(D) quadratic number field 
unit                    ismiunit(M,A) is modular integer 
unit                    rqnffu(D,pl) real quadratic number field 
			fundamental 
unit,                   baby step version qffmsfubs(m,D) quadratic function 
			field over modular singles fundamental 
unit,                   original version qffmsfuobs(m,D) quadratic function 
			field over modular singles fundamental 
unit?                   ispmiunit(r,m,P) is polynomial over modular 
			integers 
unit?                   ispmsunit(r,m,P) is polynomial over modular singles 
units                   msunits(m) modular single 
univariate              content (rekursiv) pmiucont(r,m,P) polynomial over 
			modular integers 
univariate              content (rekursiv) pmsucont(r,m,P) polynomial over 
			modular singles 
univariate              dense polynomial over Galois-field with 
			characteristic 2 remainder, special version 
			udpgf2remsp(G,P1,P2,ilc) 
univariate              dense polynomial over integers content and 
			primitive part udpicontpp(P,pPP) 
univariate              dense polynomial over integers difference 
			udpidif(P1,P2) 
univariate              dense polynomial over integers integer product 
			udpiiprod(P,A) 
univariate              dense polynomial over integers negation udpineg(P) 
univariate              dense polynomial over integers product 
			udpiprod(P1,P2) 
univariate              dense polynomial over integers pseudo remainder 
			udpipsrem(P1,P2) 
univariate              dense polynomial over integers sum udpisum(P1,P2) 
univariate              dense polynomial over integers to univariate dense 
			polynomial over modular integers udpitoudpmi(P,M) 
univariate              dense polynomial over integers to univariate dense 
			polynomial over p-adic field udpitoudppf(P,p,d) 
univariate              dense polynomial over modular 2 gf2eltoudpm2(G,a) 
			Galois-field with characteristic 2 element to 
univariate              dense polynomial over modular 2 in special 
			bit-representation ? isudpm2sb(A) is 
univariate              dense polynomial over modular 2 sbtoudpm2(a) 
			(MACRO) special bit-representation to 
univariate              dense polynomial over modular 2 to Galois-field 
			with characteristic 2 element udpm2togf2el(G,P) 
univariate              dense polynomial over modular 2 to special 
			bit-representation udpm2tosb(P) 
univariate              dense polynomial over modular integers 
			Jacobi-symbol udpmijacsym(m,P1,P2) 
univariate              dense polynomial over modular integers derivation 
			udpmideriv(m,P) 
univariate              dense polynomial over modular integers difference 
			udpmidif(m,P1,P2) 
univariate              dense polynomial over modular integers extended 
			greatest common divisor udpmiegcd(m,P1,P2,pPX,pPY) 
univariate              dense polynomial over modular integers greatest 
			common divisor udpmigcd(m,P1,P2) 
univariate              dense polynomial over modular integers half 
			extended greatest common divisor 
			udpmihegcd(m,P1,P2,pP3) 
univariate              dense polynomial over modular integers monic 
			udpmimonic(m,P) 
univariate              dense polynomial over modular integers negation 
			udpmineg(m,P) 
univariate              dense polynomial over modular integers product 
			udpmiprod(m,P1,P2) 
univariate              dense polynomial over modular integers quotient and 
			remainder udpmiqrem(m,P1,P2,pP3) 
univariate              dense polynomial over modular integers quotient 
			udpmiquot(m,P1,P2) (MACRO) 
univariate              dense polynomial over modular integers remainder 
			udpmirem(ip,P,P2) 
univariate              dense polynomial over modular integers sum 
			udpmisum(m,P1,P2) 
univariate              dense polynomial over modular integers 
			udpitoudpmi(P,M) univariate dense polynomial over 
			integers to 
univariate              dense polynomial over modular integers, modular 
			integer product udpmimiprod(m,P,a) 
univariate              dense polynomial over modular single trailing base 
			coefficient udpmstbc(m,P) 
univariate              dense polynomial over modular singles Jacobi-symbol 
			udpmsjacsym(m,P1,P2) 
univariate              dense polynomial over modular singles derivation 
			udpmsderiv(m,P) 
univariate              dense polynomial over modular singles difference 
			udpmsdif(m,P1,P2) 
univariate              dense polynomial over modular singles extended 
			greatest common divisor udpmsegcd(m,P1,P2,pPX,pPY) 
univariate              dense polynomial over modular singles greatest 
			common divisor udpmsgcd(m,P1,P2) 
univariate              dense polynomial over modular singles half extended 
			greatest common divisor udpmshegcd(m,P1,P2,pP3) 
univariate              dense polynomial over modular singles monic 
			udpmsmonic(m,P) 
univariate              dense polynomial over modular singles negation 
			udpmsneg(m,P) 
univariate              dense polynomial over modular singles product 
			udpmsprod(m,P1,P2) 
univariate              dense polynomial over modular singles quotient and 
			remainder udpmsqrem(m,P1,P2,pP3) 
univariate              dense polynomial over modular singles quotient 
			udpmsquot(m,P1,P2) (MACRO) 
univariate              dense polynomial over modular singles remainder 
			udpmsrem(m,P1,P2) 
univariate              dense polynomial over modular singles sum 
			udpmssum(m,P1,P2) 
univariate              dense polynomial over modular singles, modular 
			single product udpmsmsprod(m,P,a) 
univariate              dense polynomial over modular singles, summation 
			over Jacobi-symbols udpmssumjs(m,P,n) 
univariate              dense polynomial over p-adic field difference 
			udppfdif(p,P1,P2) 
univariate              dense polynomial over p-adic field exponentiation 
			udppfexp(p,P,n) 
univariate              dense polynomial over p-adic field fitting 
			udppffit(p,P,Pd) 
univariate              dense polynomial over p-adic field negation 
			udppfneg(p,P) 
univariate              dense polynomial over p-adic field p-adic field 
			element product udppfpfprod(p,P,a) 
univariate              dense polynomial over p-adic field prime power 
			product udppfpprod(p,P,i) 
univariate              dense polynomial over p-adic field product 
			udppfprod(p,P1,P2) 
univariate              dense polynomial over p-adic field sum 
			udppfsum(p,P1,P2) 
univariate              dense polynomial over p-adic field 
			udpitoudppf(P,p,d) univariate dense polynomial over 
			integers to 
univariate              dense polynomial over p-adic field 
			udprtoudppf(P,p,d) univariate dense polynomial over 
			rationals to 
univariate              dense polynomial over rationals difference 
			udprdif(P1,P2) 
univariate              dense polynomial over rationals negation udprneg(P) 
univariate              dense polynomial over rationals nfeltoudpr(a) 
			number field element to 
univariate              dense polynomial over rationals product 
			udprprod(P1,P2) 
univariate              dense polynomial over rationals quotient and 
			remainder udprqrem(P1,P2,pP3) 
univariate              dense polynomial over rationals sum udprsum(P1,P2) 
univariate              dense polynomial over rationals to number field 
			element udprtonfel(P) 
univariate              dense polynomial over rationals to univariate dense 
			polynomial over p-adic field udprtoudppf(P,p,d) 
univariate              dense polynomial over rationals, rational number 
			product udprrprod(P,A) 
univariate              dense polynomial trailing base coefficient 
			udptbc(P) 
univariate              dense polynomials over integers to matrix of 
			univariate dense polynomials over modular integers 
			mudpitudpmi(M,m) matrix of 
univariate              dense polynomials over integers to matrix of 
			univariate dense polynomials over rationals 
			mudpitmudpr(M) matrix of 
univariate              dense polynomials over integers to vector of 
			univariate dense polynomials over modular integers 
			vudpitudpmi(V,M) vector of 
univariate              dense polynomials over integers to vector of 
			univariate dense polynomials over rationals 
			vudpitvudpr(V) vector of 
univariate              dense polynomials over modular integers 
			mudpitudpmi(M,m) matrix of univariate dense 
			polynomials over integers to matrix of 
univariate              dense polynomials over modular integers 
			vudpitudpmi(V,M) vector of univariate dense 
			polynomials over integers to vector of 
univariate              dense polynomials over rationals manftomudpr(F,M) 
			matrix of number field elements to matrix of 
univariate              dense polynomials over rationals mudpitmudpr(M) 
			matrix of univariate dense polynomials over 
			integers to matrix of 
univariate              dense polynomials over rationals to matrix of 
			number field elements maudprtomnf(M) matrix of 
univariate              dense polynomials over rationals to vector of 
			number field elements vudprtovnf(V) vector of 
univariate              dense polynomials over rationals vnftovudpr(F,V) 
			vector of number field elements to vector of 
univariate              dense polynomials over rationals vudpitvudpr(V) 
			vector of univariate dense polynomials over 
			integers to vector of 
univariate              polynomial distinct degree factorization 
			upmsddfact(p,F) 
univariate              polynomial over Galois-field with characteristic 2 
			Ben-Or factorization, special upgf2bofacts(G,P) 
univariate              polynomial over Galois-field with characteristic 2 
			Berlekamp Q polynomials construction upgf2bqp(G,P) 
univariate              polynomial over Galois-field with characteristic 2 
			distinct degree factorization upgf2ddfact(G,P) 
univariate              polynomial over Galois-field with characteristic 2 
			greatest common divisor upgf2gcd(G,P1,P2) 
univariate              polynomial over Galois-field with characteristic 2 
			squarefree factorization (rekursiv) upgf2sfact(G,P) 
univariate              polynomial over Galois-field with characteristic 2, 
			2^m-th power of variable, polynomial, remainder 
			upgf22pvprem(G,m,P) 
univariate              polynomial over Galois-field with characteristic 2, 
			Ben-Or factorization upgf2bofact(G,P) 
univariate              polynomial over Galois-field with characteristic 2, 
			modular exponentiation, special version 
			upgf2modexps(G,F,m,P,pM) 
univariate              polynomial over Galois-field with characteristic 2, 
			monomial, polynomial, remainder upgf2mprem(G,a,T,P) 
univariate              polynomial over Galois-field with characteristic 2, 
			random generator upgf2gen(G,m) 
univariate              polynomial over Galois-field with characteristic 2, 
			separate factor of equal degree upgf2sfed(G,H,d) 
univariate              polynomial over Galois-field with single 
			characteristic Berlekamp Q polynomials construction 
			upgfsbqp(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic Berlekamp factorization 
			upgfsbfact(p,AL,P,d) 
univariate              polynomial over Galois-field with single 
			characteristic Berlekamp factorization, Zassenhaus 
			method upgfsbfzm(p,AL,s,P,G) 
univariate              polynomial over Galois-field with single 
			characteristic Berlekamp factorization, last step 
			upgfsbfls(p,AL,P,B,d) 
univariate              polynomial over Galois-field with single 
			characteristic complete factorization special 
			upgfscfacts(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic complete factorization 
			upgfscfact(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic distinct degree factorization 
			upgfsddfact(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic extended greatest common divisor 
			upgfsegcd(p,AL,P1,P2,pP3,pP4) 
univariate              polynomial over Galois-field with single 
			characteristic greatest common divisor 
			upgfsgcd(p,AL,P1,P2) 
univariate              polynomial over Galois-field with single 
			characteristic greatest squarefree divisor 
			(rekursiv) upgfsgsd(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic half extended greatest common 
			divisor upgfshegcd(p,AL,P1,P2,pP3) 
univariate              polynomial over Galois-field with single 
			characteristic number of irreducible factors 
			upgfsnif(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic randomize upgfsrand(p,AL,m) 
univariate              polynomial over Galois-field with single 
			characteristic randomize, positive degree 
			upgfsrandpd(p,AL,m) 
univariate              polynomial over Galois-field with single 
			characteristic relative prime factorization 
			upgfsrelpfac(p,AL,P,Fak,pA2) 
univariate              polynomial over Galois-field with single 
			characteristic root finding (rekursiv) 
			upgfsrf(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic squarefree factorization (rekursiv) 
			upgfssfact(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic squarefree part upgfssfp(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic, Ben-Or factorization 
			upgfsbofact(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic, Ben-Or factorization, special 
			upgfsbofacts(p,AL,P) 
univariate              polynomial over Galois-field with single 
			characteristic, separate factors of equal degree 
			upgfssfed(p,AL,G,d) 
univariate              polynomial over Galois-field with single 
			characteristic, trace function upgfstf(p,AL,G,d,M) 
univariate              polynomial over Galois-field, monomial, integer 
			exponentiation, polynomial, remainder 
			upgfsmieprem(p,AL,a,t,P) 
univariate              polynomial over Galois-field, monomial, polynomial, 
			remainder upgfsmprem(p,AL,a,T,P) 
univariate              polynomial over a number field evaluation 
			upnfeval(F,P,A) 
univariate              polynomial over integers ? isiupi(P) is irreducible 
univariate              polynomial over integers factorization upifact(P) 
univariate              polynomial over integers number field element 
			evaluation upinfeval(P,F,a) 
univariate              polynomial over integers number field element, 
			sparse representation, evaluation upinfseval(P,F,a) 
univariate              polynomial over integers of degree 4 cubic 
			resolvent upid4cubres(P) 
univariate              polynomial over integers of degree 4 real ? 
			isupid4real(P) is 
univariate              polynomial over integers to univariate polynomial 
			over rationals udpitoudpr(P) 
univariate              polynomial over integers, Hensel lemma 
			factorization approximation with respect to integer 
			prime upihlfaip(p,P,L,k) 
univariate              polynomial over integers, Hensel lemma 
			initialization upihli(p,P,L) 
univariate              polynomial over integers, Hensel lemma 
			initialization with respect to integer prime 
			upihliip(P,F,L) 
univariate              polynomial over integers, Hensel lemma quadratic 
			step upihlqs(p,p_k,p_l,P,L1,L2,A) 
univariate              polynomial over integers, Hensel lemma quadratic 
			step with respect to integer prime 
			upihlqsip(P,p_k,p_l,F,L1,L2,A) 
univariate              polynomial over modular 2, irreducible and monic 
			trinomial, generator upm2imtgen(n) 
univariate              polynomial over modular 2, irreducible and monic, 
			generator upm2imgen(n) 
univariate              polynomial over modular integer prime additive 
			valuation upmiaddval(p,P1,P) 
univariate              polynomial over modular integers ? isimupmi(p,A) is 
			irreducible, monic, 
univariate              polynomial over modular integers Ben-Or 
			factorization upmibofact(ip,P) 
univariate              polynomial over modular integers Ben-Or 
			factorization, special upmibofacts(ip,P) 
univariate              polynomial over modular integers Berlekamp 
			factorization, last step upmibfls(ip,P,B,d) 
univariate              polynomial over modular integers Jacobi-symbol 
			upmijacsym(m,P1,P2) 
univariate              polynomial over modular integers complete 
			factorization upmicfact(ip,P) 
univariate              polynomial over modular integers distinct degree 
			factorization upmiddfact(ip,P) 
univariate              polynomial over modular integers extended greatest 
			common divisor upmiegcd(P,P1,P2,pP3,pP4) 
univariate              polynomial over modular integers factorization, 
			Berlekamp algorithm upmibfact(ip,P,d) 
univariate              polynomial over modular integers greatest common 
			divisor upmigcd(ip,P1,P2) 
univariate              polynomial over modular integers greatest 
			squarefree divisor (rekursiv) upmigsd(ip,P) 
univariate              polynomial over modular integers half extended 
			greatest common divisor upmihegcd(P,P1,P2,pP3) 
univariate              polynomial over modular integers modular polynomial 
			exponentiation upmimpexp(ip,K,E,P) 
univariate              polynomial over modular integers product (rekursiv) 
			pmiupmiprod(r,m,P1,P2) polynomial over modular 
			integers, 
univariate              polynomial over modular integers quotient 
			(rekursiv) pmiupmiquot(r,m,P1,P2) polynomial over 
			modular integers, 
univariate              polynomial over modular integers randomize 
			upmirand(ip,m) 
univariate              polynomial over modular integers relative prime 
			factorization upmirelpfact(P,F,Fak,pA2) 
univariate              polynomial over modular integers remainder 
			upmirem(M,P1,P2) 
univariate              polynomial over modular integers resultant and 
			cofactor of resultant equation 
			upmiresulc(m,P1,P2,pC) 
univariate              polynomial over modular integers resultant 
			upmires(m,P1,P2) 
univariate              polynomial over modular integers separate factor of 
			equal degree upmisfed(ip,G,d) 
univariate              polynomial over modular integers squarefree 
			factorization (rekursiv) upmisfact(ip,P) 
univariate              polynomial over modular integers squarefree part 
			upmisfp(m,P) 
univariate              polynomial over modular integers transformation 
			upmitransf(M,P,r,P1) 
univariate              polynomial over modular integers transformation 
			version2 upmitransf2(M,P,r,P1) 
univariate              polynomial over modular integers, Berlekamp Q 
			polynomials construction upmibqp(ip,P) 
univariate              polynomial over modular integers, Berlekamp 
			factorization, Zassenhaus method upmibfzm(ip,s,P,G) 
univariate              polynomial over modular integers, complete 
			factorization special upmicfacts(P,F) 
univariate              polynomial over modular integers, monomial, 
			polynomial, remainder upmimprem(ip,K,E,P) 
univariate              polynomial over modular integers, number of 
			irreducible factors upminif(m,P) 
univariate              polynomial over modular integers, root finding 
			(rekursiv) upmirf(ip,P) 
univariate              polynomial over modular integers, root finding, 
			special (rekursiv) upmirfspec(ip,P) 
univariate              polynomial over modular integers, trace function, 
			special upmitfsp(ip,G,d,M) 
univariate              polynomial over modular single prime quotient 
			cdprfmsp1upq(p,F,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, 
univariate              polynomial over modular single prime, complete 
			factorization special upmscfacts(p,A) 
univariate              polynomial over modular singles ? isimupms(p,A) is 
			irreducible, monic, 
univariate              polynomial over modular singles Berlekamp 
			factorization, last step upmsbfls(m,P,B,d) 
univariate              polynomial over modular singles Jacobi-symbol 
			upmsjacsym(m,P1,P2) 
univariate              polynomial over modular singles additive valuation 
			upmsaddval(p,P1,P) 
univariate              polynomial over modular singles complete 
			factorization upmscfact(p,A) 
univariate              polynomial over modular singles extended greatest 
			common divisor upmsegcd(m,P1,P2,pP3,pP4) 
univariate              polynomial over modular singles factorization, 
			Berlekamp algorithm upmsbfact(p,A,d) 
univariate              polynomial over modular singles greatest common 
			divisor upmsgcd(m,P1,P2) 
univariate              polynomial over modular singles greatest squarefree 
			divisor (rekursiv) upmsgsd(m,P) 
univariate              polynomial over modular singles half extended 
			greatest common divisor upmshegcd(m,P1,P2,pP3) 
univariate              polynomial over modular singles product (rekursiv) 
			pmsupmsprod(r,m,P1,P2) polynomial over modular 
			singles, 
univariate              polynomial over modular singles quotient (rekursiv) 
			pmsupmsquot(r,m,P1,P2) polynomial over modular 
			singles, 
univariate              polynomial over modular singles relative prime 
			factorization upmsrelpfact(p,P,Fak,pA2) 
univariate              polynomial over modular singles remainder 
			upmsrem(m,P1,P2) 
univariate              polynomial over modular singles resultant and 
			cofactor of resultant equation 
			upmsresulc(m,P1,P2,pC) 
univariate              polynomial over modular singles resultant 
			upmsres(m,P1,P2) 
univariate              polynomial over modular singles square root power 
			series upmssrpser(m,P,i) 
univariate              polynomial over modular singles square root 
			principal part upmssrpp(m,P) 
univariate              polynomial over modular singles squarefree 
			factorization (rekursiv) upmssfact(m,P) 
univariate              polynomial over modular singles squarefree part 
			upmssfp(m,P) 
univariate              polynomial over modular singles transformation 
			upmstransf(m,P,r,P1) 
univariate              polynomial over modular singles, Berlekamp Q 
			polynomials construction upmsbqp(p,A) 
univariate              polynomial over modular singles, Berlekamp 
			factorization, Zassenhaus method upmsbfzm(m,s,P,G) 
univariate              polynomial over modular singles, irreducible and 
			monic trinomial, generator upmsimtgen(p,n) 
univariate              polynomial over modular singles, irreducible and 
			monic, generator upmsimgen(p,n) 
univariate              polynomial over modular singles, monomial, 
			polynomial, remainder upmsmprem(m,k,T,P) 
univariate              polynomial over modular singles, number of 
			irreducible factors upmsnif(m,P) 
univariate              polynomial over modular singles, root finding 
			(rekursiv) upmsrf(m,P) 
univariate              polynomial over number field greatest common 
			divisor and cofactors upnfgcdcf(F,P1,P2,pQ1,pQ2) 
univariate              polynomial over number field greatest common 
			divisor upnfgcd(F,P1,P2) 
univariate              polynomial over number field squarefree 
			factorization upnfsfact(F,P) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Hensel factorization 
			approximation upprmsp1hfa(p,F,P,L,k) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Hensel lemma 
			initialization upprmsp1hli(p,F,P,L) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, Hensel quadratic 
			step upprmsp1hqs(p,F,T,L1,L2,A) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, algebraic function 
			over modular single prime, transcendence degree 1, 
			evaluation special upprmsp1afes(p,F,P,a) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, discriminant 
			upprmsp1disc(p,F) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, reduced discriminant 
			upprmsp1redd(p,F) 
univariate              polynomial over polynomial ring over modular single 
			prime, transcendence degree 1, resultant, Sylvester 
			algorithm upprmsp1ress(p,P1,P2) 
univariate              polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			cdprfmsp1fup(p,P) common denominator polynomial 
			over rational functions over modular single prime, 
			transcendence degree 1, from 
univariate              polynomial over rational functions over modular 
			single prime, transcendence degree 1 
			sclfuprfmsp1(P,n) special coefficient list from 
univariate              polynomial over rational functions over modular 
			single prime, transcendence degree 1, extended 
			greatest common divisor 
			uprfmsp1egcd(p,P1,P2,pF1,pF2) 
univariate              polynomial over rational functions over modular 
			single prime, transcendence degree 1, from common 
			denominator polynomial over rational functions over 
			modular single prime, transcendence degree 1 
			uprfmsp1fcdp(p,P) 
univariate              polynomial over rational functions over modular 
			single prime, transcendence degree 1, from special 
			coefficient list uprfmsp1fscl(L) 
univariate              polynomial over rationals ? isiupr(P) is 
			irreducible 
univariate              polynomial over rationals factorization uprfact(P) 
univariate              polynomial over rationals number field element 
			evaluation uprnfeval(P,F,a) 
univariate              polynomial over rationals number field element, 
			sparse representation, evaluation uprnfseval(P,F,a) 
univariate              polynomial over rationals to number field element 
			uprtonfel(F,P) 
univariate              polynomial over rationals udpitoudpr(P) univariate 
			polynomial over integers to 
univariate              polynomial over the integers factorization 
			rdiscupifact(rd,c,pL) reduced discriminant and 
			discriminant of an 
univariate              polynomial over the integers from special 
			coefficient list upifscl(L) 
univariate              polynomial over the integers number field element 
			evaluation special upinfeevals(F,P,a) 
univariate              polynomial over the integers reduced discriminant 
			and content of resultant equation upireddiscc(P,pc) 
univariate              polynomial over the integers resultant and cofactor 
			of resultant equation upiresulc(P1,P2,pB) 
univariate              polynomial over the integers sclfupi(P,n) special 
			coefficient list from 
univariate              polynomial over the integers, Dedekind maximality 
			test oupidedekmt(M,P) order of an 
univariate              polynomial over the integers, Hensel lemma 
			factorization approximation upihlfa(p,P,L,k) 
univariate              polynomial over the rationals cdprfupr(P) common 
			denominator polynomial over the rationals from 
univariate              polynomial over the rationals from common 
			denominator polynomial over the rationals 
			uprfcdpr(PC) 
univariate              polynomial ptoup(r,P) polynomial to 
univariate              polynomials macup(n,L) matrix of coefficients of 
univariate              polynomials maptomaup(r,M) matrix of polynomials to 
			matrix of 
univariate              polynomials over modular integer primes Euklid- 
			Gauss- step for columns maupmipegsc(p,M,A,B) matrix 
			of 
univariate              polynomials over modular integer primes Euklid- 
			Gauss- step for rows maupmipegsr(p,M,A,B) matrix of 
univariate              polynomials over modular integer primes elementary 
			divisor form and cofactors maupmipedfcf(p,M,pA,pB) 
			matrix of 
univariate              polynomials over modular single prime unimodular 
			transformation vecupmsunimt(p,V,W,i,pV1,pW1) vector 
			of 
univariate              polynomials over modular single primes Euklid- 
			Gauss- step for columns maupmspegsc(p,M,A,B) matrix 
			of 
univariate              polynomials over modular single primes Euklid- 
			Gauss- step for rows maupmspegsr(p,M,A,B) matrix of 
univariate              polynomials over modular single primes elementary 
			divisor form and cofactors maupmspedfcf(p,M,pA,pB) 
			matrix of 
univariate              polynomials over modular single primes hermitian 
			reduction, special maupmshermsp(p,M,r,pD) matrix of 
univariate              polynomials over rationals Euklid- Gauss- step for 
			columns maupregsc(M,A,B) matrix of 
univariate              polynomials over rationals Euklid- Gauss- step for 
			rows maupregsr(M,A,B) matrix of 
univariate              polynomials over rationals elementary divisor form 
			and cofactors maupredfcf(M,pA,pB) matrix of 
univariate              polynomials vecptovecup(r,V) vector of polynomials 
			to vector of 
univariate              prime polynomial over modular single primes 
			iafmsp1mpmpp(p,F,a,P,e,Q) integral algebraic 
			function over modular single primes, transcendence 
			degree 1, minimal polynomial modulo power of an 
univariate              separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			Dedekind maximality test ouspprmsp1dm(p,P,F) order 
			of an 
univariate              separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			approximation of P-adic factorization 
			uspprmsp1apf(p,P,F,k) 
univariate              separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, basis 
			of a local maximal over-order 
			ouspprmsp1bl(p,F,P,Q,pk) order of an 
univariate              separable polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			decomposition law ouspprmsp1dl(p,F,P,k) order of a 
univariate              separable polynomial over the integers 
			approximation of p-adic factorization of the 
			defining polynomial, generators of p-maximal orders 
			of the p-adic divisors of the defining polynomial 
			and p-minimal polynomials of the generators 
			ouspiapfgmic(p,P,k) order of an 
univariate              separable polynomial over the integers basis of a 
			local maximal over-order ouspibaslmo(F,p,Q,pk) 
			order of an 
univariate              separable polynomial over the integers basis of a 
			local maximal over-order with respect to integer 
			primes ouspibaslmoi(F,P,Q,pk) order of an 
univariate              separable polynomial over the integers basis of the 
			integral closure ( ORDMAX, Ordmax, ordmax, integral 
			basis ) ouspibasisic(F,pL) order of an 
univariate              separable polynomial over the integers 
			normelpruspi(P,a) norm of an element of the 
			polynomial ring of an 
univariate              separable polynomial over the integers 
			vepvelpruspi(F,a,p,k,v) values of the extensions of 
			the p-adic valuation of an element of the 
			polynomial ring of an 
univariate              separable polynomial over the integers, 
			approximation of p-adic factorization 
			uspiapf(p,P,k) 
univariate              separable polynomial over the polynomial ring over 
			modular single prime, transcendence degree 1 
			nepousppmsp1(p,F,a) norm of an element of the 
			polynomial order of an 
univariate              separable polynomial over the polynomial ring over 
			modular single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) values of the extensions 
			of the P-adic valuation of an element of the 
			polynomial order of a 
univariate              separable polynomial over the polynomial ring over 
			modular single prime, transcendence degree 1, 
			integral basis ouspprmsp1ib(p,F,pL) order of an 
univariate              squarefree polynomial over integers ? isiuspi(P) is 
			irreducible 
univariate              squarefree polynomial over integers factorization 
			uspifact(P) 
univariate              squarefree polynomial over integers isuspi(P) is 
unordered               set difference usdiff(L1,L2) 
unordered               set intersection usinter(L1,L2) 
unordered               set symmetrical difference ussdiff(L1,L2) 
unordered               set union usunion(L1,L2) (MACRO) 
unsgetc(c,ps)           undo string get character 
upgf22pvprem(G,m,P)     univariate polynomial over Galois-field with 
			characteristic 2, 2^m-th power of variable, 
			polynomial, remainder 
upgf2bofact(G,P)        univariate polynomial over Galois-field with 
			characteristic 2, Ben-Or factorization 
upgf2bofacts(G,P)       univariate polynomial over Galois-field with 
			characteristic 2 Ben-Or factorization, special 
upgf2bqp(G,P)           univariate polynomial over Galois-field with 
			characteristic 2 Berlekamp Q polynomials 
			construction 
upgf2ddfact(G,P)        univariate polynomial over Galois-field with 
			characteristic 2 distinct degree factorization 
upgf2eval(G,P,a)        polynomial over Galois-field with characteristic 2 
			evaluation 
upgf2gcd(G,P1,P2)       univariate polynomial over Galois-field with 
			characteristic 2 greatest common divisor 
upgf2gen(G,m)           univariate polynomial over Galois-field with 
			characteristic 2, random generator 
upgf2modexps(G,F,m,P,pM) univariate polynomial over Galois-field with 
			characteristic 2, modular exponentiation, special 
			version 
upgf2mprem(G,a,T,P)     univariate polynomial over Galois-field with 
			characteristic 2, monomial, polynomial, remainder 
upgf2sfact(G,P)         univariate polynomial over Galois-field with 
			characteristic 2 squarefree factorization 
			(rekursiv) 
upgf2sfed(G,H,d)        univariate polynomial over Galois-field with 
			characteristic 2, separate factor of equal degree 
upgf2tf(G,F,d,M)        polynomial over Galois-field with characteristic 2, 
			trace function, special 
upgfsbfact(p,AL,P,d)    univariate polynomial over Galois-field with single 
			characteristic Berlekamp factorization 
upgfsbfls(p,AL,P,B,d)   univariate polynomial over Galois-field with single 
			characteristic Berlekamp factorization, last step 
upgfsbfzm(p,AL,s,P,G)   univariate polynomial over Galois-field with single 
			characteristic Berlekamp factorization, Zassenhaus 
			method 
upgfsbofact(p,AL,P)     univariate polynomial over Galois-field with single 
			characteristic, Ben-Or factorization 
upgfsbofacts(p,AL,P)    univariate polynomial over Galois-field with single 
			characteristic, Ben-Or factorization, special 
upgfsbqp(p,AL,P)        univariate polynomial over Galois-field with single 
			characteristic Berlekamp Q polynomials construction 
upgfscfact(p,AL,P)      univariate polynomial over Galois-field with single 
			characteristic complete factorization 
upgfscfacts(p,AL,P)     univariate polynomial over Galois-field with single 
			characteristic complete factorization special 
upgfsddfact(p,AL,P)     univariate polynomial over Galois-field with single 
			characteristic distinct degree factorization 
upgfsegcd(p,AL,P1,P2,pP3,pP4) univariate polynomial over Galois-field with 
			single characteristic extended greatest common 
			divisor 
upgfsgcd(p,AL,P1,P2)    univariate polynomial over Galois-field with single 
			characteristic greatest common divisor 
upgfsgsd(p,AL,P)        univariate polynomial over Galois-field with single 
			characteristic greatest squarefree divisor 
			(rekursiv) 
upgfshegcd(p,AL,P1,P2,pP3) univariate polynomial over Galois-field with 
			single characteristic half extended greatest common 
			divisor 
upgfsmieprem(p,AL,a,t,P) univariate polynomial over Galois-field, monomial, 
			integer exponentiation, polynomial, remainder 
upgfsmprem(p,AL,a,T,P)  univariate polynomial over Galois-field, monomial, 
			polynomial, remainder 
upgfsnif(p,AL,P)        univariate polynomial over Galois-field with single 
			characteristic number of irreducible factors 
upgfsrand(p,AL,m)       univariate polynomial over Galois-field with single 
			characteristic randomize 
upgfsrandpd(p,AL,m)     univariate polynomial over Galois-field with single 
			characteristic randomize, positive degree 
upgfsrelpfac(p,AL,P,Fak,pA2) univariate polynomial over Galois-field with 
			single characteristic relative prime factorization 
upgfsrf(p,AL,P)         univariate polynomial over Galois-field with single 
			characteristic root finding (rekursiv) 
upgfssfact(p,AL,P)      univariate polynomial over Galois-field with single 
			characteristic squarefree factorization (rekursiv) 
upgfssfed(p,AL,G,d)     univariate polynomial over Galois-field with single 
			characteristic, separate factors of equal degree 
upgfssfp(p,AL,P)        univariate polynomial over Galois-field with single 
			characteristic squarefree part 
upgfstf(p,AL,G,d,M)     univariate polynomial over Galois-field with single 
			characteristic, trace function 
upid4cubres(P)          univariate polynomial over integers of degree 4 
			cubic resolvent 
upifact(P)              univariate polynomial over integers factorization 
upifscl(L)              univariate polynomial over the integers from 
			special coefficient list 
upihlfa(p,P,L,k)        univariate polynomial over the integers, Hensel 
			lemma factorization approximation 
upihlfaip(p,P,L,k)      univariate polynomial over integers, Hensel lemma 
			factorization approximation with respect to integer 
			prime 
upihli(p,P,L)           univariate polynomial over integers, Hensel lemma 
			initialization 
upihliip(P,F,L)         univariate polynomial over integers, Hensel lemma 
			initialization with respect to integer prime 
upihlqs(p,p_k,p_l,P,L1,L2,A) univariate polynomial over integers, Hensel 
			lemma quadratic step 
upihlqsip(P,p_k,p_l,F,L1,L2,A) univariate polynomial over integers, Hensel 
			lemma quadratic step with respect to integer prime 
upinfeevals(F,P,a)      univariate polynomial over the integers number 
			field element evaluation special 
upinfeval(P,F,a)        univariate polynomial over integers number field 
			element evaluation 
upinfseval(P,F,a)       univariate polynomial over integers number field 
			element, sparse representation, evaluation 
upireddiscc(P,pc)       univariate polynomial over the integers reduced 
			discriminant and content of resultant equation 
upiresulc(P1,P2,pB)     univariate polynomial over the integers resultant 
			and cofactor of resultant equation 
upm2imgen(n)            univariate polynomial over modular 2, irreducible 
			and monic, generator 
upm2imtgen(n)           univariate polynomial over modular 2, irreducible 
			and monic trinomial, generator 
upmiaddval(p,P1,P)      univariate polynomial over modular integer prime 
			additive valuation 
upmibfact(ip,P,d)       univariate polynomial over modular integers 
			factorization, Berlekamp algorithm 
upmibfls(ip,P,B,d)      univariate polynomial over modular integers 
			Berlekamp factorization, last step 
upmibfzm(ip,s,P,G)      univariate polynomial over modular integers, 
			Berlekamp factorization, Zassenhaus method 
upmibofact(ip,P)        univariate polynomial over modular integers Ben-Or 
			factorization 
upmibofacts(ip,P)       univariate polynomial over modular integers Ben-Or 
			factorization, special 
upmibqp(ip,P)           univariate polynomial over modular integers, 
			Berlekamp Q polynomials construction 
upmicfact(ip,P)         univariate polynomial over modular integers 
			complete factorization 
upmicfacts(P,F)         univariate polynomial over modular integers, 
			complete factorization special 
upmiddfact(ip,P)        univariate polynomial over modular integers 
			distinct degree factorization 
upmiegcd(P,P1,P2,pP3,pP4) univariate polynomial over modular integers 
			extended greatest common divisor 
upmigcd(ip,P1,P2)       univariate polynomial over modular integers 
			greatest common divisor 
upmigsd(ip,P)           univariate polynomial over modular integers 
			greatest squarefree divisor (rekursiv) 
upmihegcd(P,P1,P2,pP3)  univariate polynomial over modular integers half 
			extended greatest common divisor 
upmijacsym(m,P1,P2)     univariate polynomial over modular integers 
			Jacobi-symbol 
upmimpexp(ip,K,E,P)     univariate polynomial over modular integers modular 
			polynomial exponentiation 
upmimprem(ip,K,E,P)     univariate polynomial over modular integers, 
			monomial, polynomial, remainder 
upminif(m,P)            univariate polynomial over modular integers, number 
			of irreducible factors 
upmirand(ip,m)          univariate polynomial over modular integers 
			randomize 
upmirelpfact(P,F,Fak,pA2) univariate polynomial over modular integers 
			relative prime factorization 
upmirem(M,P1,P2)        univariate polynomial over modular integers 
			remainder 
upmires(m,P1,P2)        univariate polynomial over modular integers 
			resultant 
upmiresulc(m,P1,P2,pC)  univariate polynomial over modular integers 
			resultant and cofactor of resultant equation 
upmirf(ip,P)            univariate polynomial over modular integers, root 
			finding (rekursiv) 
upmirfspec(ip,P)        univariate polynomial over modular integers, root 
			finding, special (rekursiv) 
upmisfact(ip,P)         univariate polynomial over modular integers 
			squarefree factorization (rekursiv) 
upmisfed(ip,G,d)        univariate polynomial over modular integers 
			separate factor of equal degree 
upmisfp(m,P)            univariate polynomial over modular integers 
			squarefree part 
upmitfsp(ip,G,d,M)      univariate polynomial over modular integers, trace 
			function, special 
upmitransf(M,P,r,P1)    univariate polynomial over modular integers 
			transformation 
upmitransf2(M,P,r,P1)   univariate polynomial over modular integers 
			transformation version2 
upmsaddval(p,P1,P)      univariate polynomial over modular singles additive 
			valuation 
upmsbfact(p,A,d)        univariate polynomial over modular singles 
			factorization, Berlekamp algorithm 
upmsbfls(m,P,B,d)       univariate polynomial over modular singles 
			Berlekamp factorization, last step 
upmsbfzm(m,s,P,G)       univariate polynomial over modular singles, 
			Berlekamp factorization, Zassenhaus method 
upmsbqp(p,A)            univariate polynomial over modular singles, 
			Berlekamp Q polynomials construction 
upmscfact(p,A)          univariate polynomial over modular singles complete 
			factorization 
upmscfacts(p,A)         univariate polynomial over modular single prime, 
			complete factorization special 
upmsddfact(p,F)         univariate polynomial distinct degree factorization 
upmsegcd(m,P1,P2,pP3,pP4) univariate polynomial over modular singles 
			extended greatest common divisor 
upmsgcd(m,P1,P2)        univariate polynomial over modular singles greatest 
			common divisor 
upmsgsd(m,P)            univariate polynomial over modular singles greatest 
			squarefree divisor (rekursiv) 
upmshegcd(m,P1,P2,pP3)  univariate polynomial over modular singles half 
			extended greatest common divisor 
upmsimgen(p,n)          univariate polynomial over modular singles, 
			irreducible and monic, generator 
upmsimtgen(p,n)         univariate polynomial over modular singles, 
			irreducible and monic trinomial, generator 
upmsjacsym(m,P1,P2)     univariate polynomial over modular singles 
			Jacobi-symbol 
upmsmprem(m,k,T,P)      univariate polynomial over modular singles, 
			monomial, polynomial, remainder 
upmsnif(m,P)            univariate polynomial over modular singles, number 
			of irreducible factors 
upmsrelpfact(p,P,Fak,pA2) univariate polynomial over modular singles 
			relative prime factorization 
upmsrem(m,P1,P2)        univariate polynomial over modular singles 
			remainder 
upmsres(m,P1,P2)        univariate polynomial over modular singles 
			resultant 
upmsresulc(m,P1,P2,pC)  univariate polynomial over modular singles 
			resultant and cofactor of resultant equation 
upmsrf(m,P)             univariate polynomial over modular singles, root 
			finding (rekursiv) 
upmssfact(m,P)          univariate polynomial over modular singles 
			squarefree factorization (rekursiv) 
upmssfp(m,P)            univariate polynomial over modular singles 
			squarefree part 
upmssrpp(m,P)           univariate polynomial over modular singles square 
			root principal part 
upmssrpser(m,P,i)       univariate polynomial over modular singles square 
			root power series 
upmstransf(m,P,r,P1)    univariate polynomial over modular singles 
			transformation 
upnfeval(F,P,A)         univariate polynomial over a number field 
			evaluation 
upnfgcd(F,P1,P2)        univariate polynomial over number field greatest 
			common divisor 
upnfgcdcf(F,P1,P2,pQ1,pQ2) univariate polynomial over number field greatest 
			common divisor and cofactors 
upnfsfact(F,P)          univariate polynomial over number field squarefree 
			factorization 
upper                   bound itoEb(A,e,grenze) ( SIMATH ) integer to Essen 
			integer with 
upper                   bound itoEsb(A,e,grenze) ( SIMATH ) integer to 
			Essen integer, sign and 
upprmsp1afes(p,F,P,a)   univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			algebraic function over modular single prime, 
			transcendence degree 1, evaluation special 
upprmsp1disc(p,F)       univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			discriminant 
upprmsp1hfa(p,F,P,L,k)  univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			Hensel factorization approximation 
upprmsp1hli(p,F,P,L)    univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			Hensel lemma initialization 
upprmsp1hqs(p,F,T,L1,L2,A) univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			Hensel quadratic step 
upprmsp1redd(p,F)       univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			reduced discriminant 
upprmsp1ress(p,P1,P2)   univariate polynomial over polynomial ring over 
			modular single prime, transcendence degree 1, 
			resultant, Sylvester algorithm 
uprfact(P)              univariate polynomial over rationals factorization 
uprfcdpr(PC)            univariate polynomial over the rationals from 
			common denominator polynomial over the rationals 
uprfmsp1egcd(p,P1,P2,pF1,pF2) univariate polynomial over rational functions 
			over modular single prime, transcendence degree 1, 
			extended greatest common divisor 
uprfmsp1fcdp(p,P)       univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			common denominator polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1 
uprfmsp1fscl(L)         univariate polynomial over rational functions over 
			modular single prime, transcendence degree 1, from 
			special coefficient list 
uprnfeval(P,F,a)        univariate polynomial over rationals number field 
			element evaluation 
uprnfseval(P,F,a)       univariate polynomial over rationals number field 
			element, sparse representation, evaluation 
uprtonfel(F,P)          univariate polynomial over rationals to number 
			field element 
usdiff(L1,L2)           unordered set difference 
using                   Heidelberg arithmetic functions 
			iHDfu(func,anzahlargs,arg1,arg2) integer 
using                   Papanikolaou floating point functions 
			flPAFfu(func,anzahlargs,arg1,arg2) floating point 
using                   the algorithm of cornaccia cornaccia(m,q,x0,pX,pY) 
			determine a solution of the diophantine equation 
			x^2+q*y^2=m 
usinter(L1,L2)          unordered set intersection 
uspiapf(p,P,k)          univariate separable polynomial over the integers, 
			approximation of p-adic factorization 
uspifact(P)             univariate squarefree polynomial over integers 
			factorization 
uspprmsp1apf(p,P,F,k)   univariate separable polynomial over polynomial 
			ring over modular single prime, transcendence 
			degree 1, approximation of P-adic factorization 
ussdiff(L1,L2)          unordered set symmetrical difference 
usunion(L1,L2)          (MACRO) unordered set union 
utilities               HDiutil() Heidelberg arithmetic package: 
utilities               PAFutil() Papanikolaou floating point package: 
valuation               iafmsp1psval(p,P,A) integral algebraic function 
			over modular single prime, transcendence degree 1, 
			P-star 
valuation               infepstarval(p,A) integral number field element 
			p-star 
valuation               of an element of the polynomial order of a 
			univariate separable polynomial over the polynomial 
			ring over modular single prime, transcendence 
			degree 1 vepepuspmsp1(p,F,a,P,k,v) values of the 
			extensions of the P-adic 
valuation               of an element of the polynomial ring of an 
			univariate separable polynomial over the integers 
			vepvelpruspi(F,a,p,k,v) values of the extensions of 
			the p-adic 
valuation               pfaval(p,a) p-adic field additive 
valuation               qnfaval(D,p,a) quadratic number field additive 
valuation               upmiaddval(p,P1,P) univariate polynomial over 
			modular integer prime additive 
valuation               upmsaddval(p,P1,P) univariate polynomial over 
			modular singles additive 
valuation               with respect to integer primes infepstarvip(P,A) 
			integral number field element p-star 
value                   afmsp1idpval(p,F,P,a0,a2,wa,b2,wb,py,pwy) algebraic 
			function over modular single primes, transcendence 
			degree 1, increasing the denominator of the P-star 
value                   b2 ecqnfacb2(E) elliptic curve over quadratic 
			number field, actual model, Tate 
value                   b4 ecqnfacb4(E) elliptic curve over quadratic 
			number field, actual model, Tate 
value                   b6 ecqnfacb6(E) elliptic curve over quadratic 
			number field, actual model, Tate 
value                   b8 ecqnfacb8(E) elliptic curve over quadratic 
			number field, actual model, Tate 
value                   c4 ecqnfacc4(E) elliptic curve over quadratic 
			number field, actual model, Tate 
value                   c6 ecqnfacc6(E) elliptic curve over quadratic 
			number field, actual model, Tate 
value                   cabsv(z) complex absolute 
value                   eciminlhaav(E,P) elliptic curve with integer 
			coefficients, minimal model, local height at the 
			archimedean absolute 
value                   flabs(f) (MACRO) floating point absolute 
value                   iabs(A) (MACRO) integer absolute 
value                   iaval(m,A) integer additive m-adic 
value                   ippnfeidpval(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
			denominator of the p-star 
value                   piabs(r,P) polynomial over integers absolute 
value                   rabs(R) (MACRO) rational number absolute 
value                   raval(m,R) rational additive m-adic 
value                   sabs(a) (MACRO) single-precision absolute 
value                   with respect to integer iavalint(M,I) integer 
			additive 
value                   with respect to integer primes 
			ippnfeidpvip(F,p,a0,a2,wa,b2,wb,py,pwy) integral 
			p-primary number field element, increasing the 
			denominator of the p-star 
value                   with respect to integer ravalint(M,R) rational 
			additive 
values                  b2, b4, b6 ecgf2tavb6(G,a1,a2,a3,a4,a6) elliptic 
			curve over Galois-field with characteristic 2, 
			Tate's 
values                  b2, b4, b6 ecmptavb6(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular primes Tate's 
values                  b2, b4, b6 ecnftavb6(F,a1,a2,a3,a4,a6) elliptic 
			curve over number field Tate's 
values                  b2, b4, b6, b8 ecgf2tavb8(G,a1,a2,a3,a4,a6) 
			elliptic curve over Galois-field with 
			characteristic 2, Tate's 
values                  b2, b4, b6, b8 ecitavalb(a1,a2,a3,a4,a6) elliptic 
			curve with integer coefficients, Tate's 
values                  b2, b4, b6, b8 ecmptavb8(p,a1,a2,a3,a4,a6) elliptic 
			curve over modular primes Tate's 
values                  b2, b4, b6, b8 ecnftavb8(F,a1,a2,a3,a4,a6) elliptic 
			curve over number field Tate's 
values                  b2, b4, b6, b8 ecrtavalb(a1,a2,a3,a4,a6) elliptic 
			curve over rational numbers, Tate's 
values                  c4, c6 ecgf2tavc6(G,a1,a2,a3,a4,a6) elliptic curve 
			over Galois-field with characteristic 2, Tate's 
values                  c4, c6 ecitavalc(a1,a2,a3,a4,a6) elliptic curve 
			with integer coefficients, minimal model, Tate's 
values                  c4, c6 ecmptavc6(p,a1,a2,a3,a4,a6) elliptic curve 
			over modular primes Tate's 
values                  c4, c6 ecnftavc6(F,a1,a2,a3,a4,a6) elliptic curve 
			over number field Tate's 
values                  c4, c6 ecrtavalc(a1,a2,a3,a4,a6) elliptic curve 
			over the rationals Tate's 
values                  eciminlhnaav(E,P) elliptic curve with integer 
			coefficients, minimal model, local heights at all 
			non archimedean absolute 
values                  ecrprodcp(E) elliptic curve over the rationals, 
			product over all c_p- 
values                  of the extensions of the P-adic valuation of an 
			element of the polynomial order of a univariate 
			separable polynomial over the polynomial ring over 
			modular single prime, transcendence degree 1 
			vepepuspmsp1(p,F,a,P,k,v) 
values                  of the extensions of the p-adic valuation of an 
			element of the polynomial ring of an univariate 
			separable polynomial over the integers 
			vepvelpruspi(F,a,p,k,v) 
variable                (rekursiv) pdegreesv(r,P,n) polynomial degree, 
			specified 
variable                (rekursiv) pgf2derivsv(r,G,P,i) polynomial over 
			Galois-field with characteristic 2 derivation, 
			specified 
variable                (rekursiv) pgfsderivsv(r,p,AL,P,i) polynomial over 
			Galois-field with single characteristic derivation, 
			specified 
variable                (rekursiv) pgfsevalsv(r,p,AL,P,d,a) polynomial over 
			Galois-field with single characteristic evaluation, 
			specified 
variable                (rekursiv) piderivsv(r,P,n) polynomial over 
			integers derivation, specified 
variable                (rekursiv) pievalsv(r,P,n,A) polynomial over 
			integers evaluation, specified 
variable                (rekursiv) pisubstsv(r,P1,n,P2) polynomial over 
			integers substitution, specified 
variable                (rekursiv) pmiderivsv(r,m,P,n) polynomial over 
			modular integers derivation, specified 
variable                (rekursiv) pmievalsv(r,m,P,n,a) polynomial over 
			modular integers evaluation, specified 
variable                (rekursiv) pmisubstsv(r,m,P1,n,P2) polynomial over 
			modular integers substitution, specified 
variable                (rekursiv) pmsderivsv(r,m,P,n) polynomial over 
			modular singles derivation, specified 
variable                (rekursiv) pmsevalsv(r,m,P,n,a) polynomial over 
			modular singles evaluation, specified 
variable                (rekursiv) pmssubstsv(r,m,P1,n,P2) polynomial over 
			modular singles substitution, specified 
variable                (rekursiv) pnfderivsv(r,F,P,n) polynomial over 
			number field derivation, specified 
variable                (rekursiv) pnfevalsv(r,F,P,n,a) polynomial over 
			number field evaluation, specified 
variable                (rekursiv) ppfderiv(r,p,P) polynomial over p-adic 
			field derivation, main 
variable                (rekursiv) ppvquot(r,P,i,n) polynomial quotient by 
			power of 
variable                (rekursiv) prderivsv(r,P,n) polynomial over 
			rationals derivation, specified 
variable                (rekursiv) prevalsv(r,P,n,A) polynomial over 
			rationals evaluation, specified 
variable                (rekursiv) prsubstsv(r,P1,n,P2) polynomial over 
			rationals substitution, specified 
variable                diphomogsv(r,P,n) distributive polynomial 
			homogenize specified 
variable                dipnmv(r,P,n) distributive polynomial new main 
variable                list ? isvarl(r,V) is 
variable                list extension pvext(r,P,V,VN) polynomial 
variable                list fgetvl(pf) file get 
variable                list getvl() (MACRO) get 
variable                list merge pvmerge(LV,LP,pLP) polynomial 
variable                list sort vlsort(V,pPI) 
variable                name comparison vncomp(Vn1,Vn2) 
variable                pdegree(r,P) (MACRO) polynomial degree, main 
variable                permutation mavpermut(r,M,PI) matrix of polynomials 
variable                permutation pvpermut(r,P,PI) polynomial 
variable                permutation vecvpermut(r,V,PI) vector of 
			polynomials 
variable                pgf2deriv(r,G,P) polynomial over Galois-field with 
			characteristic 2 derivation, main 
variable                pgf2eval(r,G,P,a) polynomial over Galois-field with 
			characteristic 2 evaluation, main 
variable                pgfsderiv(r,p,AL,P) polynomial over Galois-field 
			with single characteristic derivation, main 
variable                pgfseval(r,p,AL,P,a) polynomial over Galois-field 
			with single characteristic evaluation, main 
variable                pideriv(r,P) polynomial over integers derivation, 
			main 
variable                pieval(r,P,A) polynomial over integers evaluation, 
			main 
variable                pisign(r,P) polynomial over integers sign, base 
variable                pisubst(r,P1,P2) polynomial over integers 
			substitution, main 
variable                pitrans(r,P,A) polynomial over integers 
			translation, main 
variable                plbc(r,P) polynomial leading base coefficient, main 
variable                plc(r,P) (MACRO) polynomial leading coefficient, 
			main 
variable                pmideriv(r,M,P) polynomial over modular integers 
			derivation, main 
variable                pmieval(r,M,P,A) polynomial over modular integers 
			evaluation, main 
variable                pmimidqhls(r,M,S,P1,P2,F1,F2,i,l,H) polynomial over 
			modular integers, modular ideal, Hensel lemma 
			quadratic step on a single 
variable                pmisubst(r,m,P1,P2) polynomial over modular 
			integers substitution, main 
variable                pmitrans(r,m,P,a) polynomial over modular integers 
			translation, main 
variable                pmsderiv(r,m,P) polynomial over modular singles 
			derivation, main 
variable                pmseval(r,m,P,a) polynomial over modular singles 
			evaluation, main 
variable                pmssubst(r,m,P1,P2) polynomial over modular singles 
			substitution, main 
variable                pmstrans(r,m,P,a) polynomial over modular singles 
			translation, main 
variable                pnfderiv(r,F,P) polynomial over number field 
			derivation, main 
variable                pnfeval(r,F,P,a) polynomial over number field 
			evaluation, main 
variable                ppfderivsv(r,p,P,n) polynomial over p-adic field 
			derivation, selected 
variable                ppfeval(r,p,P,A) polynomial over p-adic field 
			evaluation, main 
variable                ppfevalsv(r,p,P,n,A) polynomial over p-adic field 
			evaluation, selected 
variable                ppfsubst(r,p,P1,P2) polynomial over p-adic field 
			substitution, main 
variable                ppfsubstsv(r,p,P1,n,P2) polynomial over p-adic 
			field substitution, selected 
variable                ppftrans(r,p,P,A) polynomial over p-adic field 
			translation, main 
variable                ppmvprod(r,P,n) polynomial product by power of main 
variable                ppmvquot(r,P,n) polynomial quotient by power of 
			main 
variable                prderiv(r,P) polynomial over rationals derivation, 
			main 
variable                preval(r,P,A) polynomial over rationals evaluation, 
			main 
variable                prfmsp1deriv(r,p,P) polynomial over rational 
			functions over modular single prime, transcendence 
			degree 1, derivation, main 
variable                printegr(r,P) polynomial over rationals 
			integration, main 
variable                prsubst(r,P1,P2) polynomial over rationals 
			substitution, main 
variable                prtrans(r,P,A) polynomial over rationals 
			translation, main 
variable                special version (rekursiv) pigf2evalfvs(r,G,P) 
			polynomial over integers Galois-field with 
			characteristic 2 element evaluation first 
variable                special version (rekursiv) pigfsevalfvs(r,p,AL,P) 
			polynomial over integers Galois-field with single 
			characteristic element evaluation first 
variable                special version mapigfsevfvs(r,p,AL,M) matrix over 
			polynomials over integers Galois-field with single 
			characteristic element evaluation first 
variable                special version mapinfevlfvs(r,F,M) matrix of 
			polynomials over integers number field element 
			evaluation first 
variable                special version maprnfevlfvs(r,F,M) matrix of 
			polynomials over rationals number field element 
			evaluation first 
variable                special version pinfevalfvs(r,F,P) polynomial over 
			integers number field element evaluation first 
variable                special version prnfevalfvs(r,F,P) polynomial over 
			rationals number field element evaluation first 
variable                special version vecpigfsefvs(r,p,AL,V) vector over 
			polynomials over integers Galois-field with single 
			characteristic element evaluation first 
variable                special version vpinfevalfvs(r,F,V) vector of 
			polynomials over integers number field element 
			evaluation first 
variable                special version vprnfevalfvs(r,F,V) vector of 
			polynomials over rationals number field element 
			evaluation first 
variable,               polynomial, remainder upgf22pvprem(G,m,P) 
			univariate polynomial over Galois-field with 
			characteristic 2, 2^m-th power of 
variables               (rekursiv) pitransav(r,P,LI) polynomial over 
			integers translation, all 
variables               (rekursiv) pmitransav(r,m,P,Lmi) polynomial over 
			modular integers translation, all 
variables               (rekursiv) pmstransav(r,m,P,Lms) polynomial over 
			modular singles translation, all 
variables               (rekursiv) prtransav(r,P,LR) polynomial over 
			rationals translation, all 
variables               (rekursiv) pvinsert(r,P,k) polynomial insertion of 
			new 
variables               globbind(pL) bind for global and static 
variables               globinit(pL) init for global and static 
variables               pmakevl(s) polynomial make list of 
variables               ppftransav(r,p,P,Lpf) polynomial over p-adic field 
			translation, all 
variables               pvred(r,P,V,pV) reduction of polynomial 
vecdptovecp(r,V)        vector of dense polynomials to vector of 
			polynomials 
vecgf2sprod(G,V,W)      vector of Galois-field with characteristic 2 
			elements scalar product 
vecgfsdif(p,AL,U,V)     (MACRO) vector of Galois-field with single 
			characteristic elements difference 
vecgfsefe(p,ALm,V,g)    vector over Galois-field with single characteristic 
			embedding in field extension 
vecgfslc(p,AL,s1,s2,L1,L2) vector of Galois-field with single characteristic 
			elements linear combination 
vecgfsneg(p,AL,V)       (MACRO) vector of Galois-field with single 
			characteristic elements negation 
vecgfssmul(p,AL,V,el)   vector of Galois-field with single characteristic 
			elements scalar multiplication 
vecgfssprod(p,AL,V,W)   vector of Galois-field with single characteristic 
			elements scalar product 
vecgfssum(p,AL,U,V)     (MACRO) vector of Galois-field with single 
			characteristic elements sum 
vecidif(U,V)            (MACRO) vector of integers difference 
vecilc(s1,s2,V1,V2)     vector of integers linear combination 
vecineg(V)              (MACRO) vector of integers negation 
vecismul(s,V)           vector of integers scalar multiplication 
vecisprod(V,W)          vector of integers scalar product 
vecisum(U,V)            (MACRO) vector of integers sum 
vecitovecgfs(p,V)       vector over integers to vector over Galois-field 
			with single characteristic 
vecitovecmi(M,V)        vector of integers to vector of modular integers 
vecitovecms(m,V)        vector of integers to vector of modular singles 
vecitovecnf(V)          vector of integers to vector of number field 
			elements 
vecitovecpi(r,V)        vector of integers to vector of polynomials over 
			integers 
vecitovecr(V)           vector of integers to vector of rationals 
vecitovnfs(V)           vector of integers to vector of number field 
			elements, sparse representation 
veciunimtr(V,W,i,pV1,pW1) vector of integers unimodular transformation 
veclength(V)            (MACRO) vector length 
vecmidif(m,U,V)         (MACRO) vector of modular integers difference 
vecmilc(M,S1,S2,L1,L2)  vector of modular integers linear combination 
vecmineg(m,V)           (MACRO) vector of modular integers negation 
vecmismul(m,s,V)        vector of modular integers scalar multiplication 
vecmisprod(M,V,W)       vector of modular integers scalar product 
vecmisum(m,U,V)         (MACRO) vector of modular integers sum 
vecmsdif(m,U,V)         (MACRO) vector of modular singles difference 
vecmslc(m,s1,s2,L1,L2)  vector of modular singles linear combination 
vecmsneg(m,V)           (MACRO) vector of modular singles negation 
vecmssmul(m,s,V)        vector of modular singles scalar multiplication 
vecmssprod(m,V,W)       vector of modular singles scalar product 
vecmssum(m,U,V)         (MACRO) vector of modular singles sum 
vecneg(V,neg,anzahlargs,arg1,arg2) vector negation 
vecnegspec(V,neg,anzahlargs,arg1,...,arg5) vector negation special 
vecnfdif(F,U,V)         (MACRO) vector of number field elements difference 
vecnflc(F,s1,s2,L1,L2)  vector of number field elements linear combination 
vecnfneg(F,V)           (MACRO) vector of number field elements negation 
vecnfsdif(F,U,V)        (MACRO) vector of number field elements, sparse 
			representation, difference 
vecnfslc(F,s1,s2,L1,L2) vector of number field elements, sparse 
			representation, linear combination 
vecnfsmul(F,V,el)       vector of number field elements scalar 
			multiplication 
vecnfsneg(F,V)          (MACRO) vector of number field elements, sparse 
			representation, negation 
vecnfsprod(F,V,W)       vector of number field elements scalar product 
vecnfssmul(F,V,el)      vector of number field elements, sparse 
			representation, scalar multiplication 
vecnfssprod(F,V,W)      vector of number field elements, sparse 
			representation, scalar product 
vecnfssum(F,U,V)        (MACRO) vector of number field elements, sparse 
			representation, sum 
vecnfsum(F,U,V)         (MACRO) vector of number field elements sum 
vecpgfsdif(r,p,AL,U,V)  (MACRO) vector of polynomials over Galois-field 
			with single characteristic difference 
vecpgfsefe(r,p,ALm,V,g) vector over polynomials over Galois-field with 
			single characteristic embedding in field extension 
vecpgfslc(r,p,AL,s1,s2,L1,L2) vector of polynomials over Galois-field with 
			single characteristic linear combination 
vecpgfsneg(r,p,AL,V)    (MACRO) vector of polynomials over Galois-field 
			with single characteristic negation 
vecpgfssmul(r,p,AL,V,el) vector of polynomials over Galois-field with single 
			characteristic scalar multiplication 
vecpgfssum(r,p,AL,U,V)  (MACRO) vector of polynomials over Galois-field 
			with single characteristic sum 
vecpidif(r,U,V)         (MACRO) vector of polynomials over integers 
			difference 
vecpigfsefvs(r,p,AL,V)  vector over polynomials over integers Galois-field 
			with single characteristic element evaluation first 
			variable special version 
vecpilc(r,P1,P2,V1,V2)  vector of polynomials over integers linear 
			combination 
vecpineg(r,V)           (MACRO) vector of polynomials over integers 
			negation 
vecpismul(r,P,V)        vector of polynomials over integers scalar 
			multiplication 
vecpisprod(r,V,W)       vector of polynomials over integers scalar product 
vecpisum(r,U,V)         (MACRO) vector of polynomials over integers sum 
vecpitovpmi(r,V,m)      vector of polynomials over integers to vector of 
			polynomials over modular integers 
vecpitovpms(r,V,m)      vector of polynomials over integers to vector of 
			polynomials over modular singles 
vecpitovpnf(r,V)        vector of polynomials over integers to vector of 
			polynomials over number field 
vecpitovpr(V)           vector of polynomials over integers to vector of 
			polynomials over rationals 
vecpitovrfr(r,V)        vector of polynomials over integers to vector of 
			rational functions over rationals 
vecpitransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of polynomials over the 
			integers transformation 
vecpitvpmpi(r,V,P)      vector of polynomials over integers to vector of 
			polynomials modulo polynomial over integers 
vecpmidif(r,m,U,V)      (MACRO) vector of polynomials over modular integers 
			difference 
vecpmilc(r,m,P1,P2,V1,V2) vector of polynomials over modular integers linear 
			combination 
vecpmineg(r,m,V)        (MACRO) vector of polynomials over modular integers 
			negation 
vecpmismul(r,m,P,V)     vector of polynomials over modular integers scalar 
			multiplication 
vecpmisprod(r,m,V,W)    vector of polynomials over modular integers scalar 
			product 
vecpmisum(r,m,U,V)      (MACRO) vector of polynomials over modular integers 
			sum 
vecpmitovpmp(r,m,P,V)   vector of polynomials over modular integers to 
			vector of polynomials modulo polynomial over 
			modular integers 
vecpmsdif(r,m,U,V)      (MACRO) vector of polynomials over modular singles 
			difference 
vecpmslc(r,m,P1,P2,V1,V2) vector of polynomials over modular singles linear 
			combination 
vecpmsneg(r,m,V)        (MACRO) vector of polynomials over modular singles 
			negation 
vecpmssmul(r,m,P,V)     vector of polynomials over modular singles scalar 
			multiplication 
vecpmssprod(r,m,V,W)    vector of polynomials over modular singles scalar 
			product 
vecpmssum(r,m,U,V)      (MACRO) vector of polynomials over modular singles 
			sum 
vecpmstovpmp(r,m,P,V)   vector of polynomials over modular singles to 
			vector of polynomials modulo polynomial over 
			modular singles 
vecpnfdif(r,F,U,V)      (MACRO) vector of polynomials over number field 
			difference 
vecpnflc(r,F,s1,s2,L1,L2) vector of polynomials over number field linear 
			combination 
vecpnfneg(r,F,U)        (MACRO) vector of polynomials over number field 
			negation 
vecpnfsmul(r,F,U,el)    vector of polynomials over number field scalar 
			multiplication 
vecpnfsum(r,F,U,V)      (MACRO) vector of polynomials over number field sum 
vecpnftovpmp(r,F,P,V)   vector of polynomials over number field to vector 
			of polynomials modulo polynomial over number field 
vecpnftovpr(r,V)        vector of polynomials over number field to vector 
			of polynomials over rationals 
vecprdif(r,U,V)         (MACRO) vector of polynomials over rationals 
			difference 
vecprlc(r,P1,P2,V1,V2)  vector of polynomials over rationals linear 
			combination 
vecprneg(r,V)           (MACRO) vector of polynomials over rationals 
			negation 
vecprsmul(r,P,V)        vector of polynomials over rationals scalar 
			multiplication 
vecprsprod(r,V,W)       vector of polynomials over rationals scalar product 
vecprsum(r,U,V)         (MACRO) vector of polynomials over rationals sum 
vecprtovpmi(r,V,m)      vector of polynomials over rationals to vector of 
			polynomials over modular integers 
vecprtovpnf(r,V)        vector of polynomials over rationals to vector of 
			polynomials over number field 
vecprtovrfr(r,V)        vector of polynomials over rationals to vector of 
			rational functions over rationals 
vecprtransf(r1,W1,V1,r2,P2,V2,Vn,pV3) vector of polynomials over the 
			rationals transformation 
vecprtvpmpr(r,V,P)      vector of polynomials over rationals to vector of 
			polynomials modulo polynomial over rationals 
vecptovecdp(r,V)        vector of polynomials to vector of dense 
			polynomials 
vecptovecup(r,V)        vector of polynomials to vector of univariate 
			polynomials 
vecrdif(U,V)            (MACRO) vector of rationals difference 
vecrfmsp1dif(p,U,V)     (MACRO) vector of rational functions over modular 
			single primes, transcendence degree 1, difference 
vecrfmsp1lc(p,F1,F2,V1,V2) vector of rational functions over modular single 
			primes, transcendence degree 1, linear combination 
vecrfmsp1neg(p,V)       (MACRO) vector of rational functions over modular 
			single primes, transcendence degree 1, negation 
vecrfmsp1sm(p,F,V)      vector of rational functions over modular single 
			primes, transcendence degree 1, scalar 
			multiplication 
vecrfmsp1sp(p,V,W)      vector of rational functions over modular single 
			primes, transcendence degree 1, scalar product 
vecrfmsp1sum(p,U,V)     (MACRO) vector of rational functions over modular 
			single primes, transcendence degree 1, sum 
vecrfrdif(r,U,V)        (MACRO) vector of rational functions over rationals 
			difference 
vecrfrlc(r,F1,F2,V1,V2) vector of rational functions over rationals linear 
			combination 
vecrfrneg(r,V)          (MACRO) vector of rational functions over rationals 
			negation 
vecrfrsmul(r,F,V)       vector of rational functions over rationals scalar 
			multiplication 
vecrfrsprod(r,V,W)      vector of rational functions over rationals scalar 
			product 
vecrfrsum(r,U,V)        (MACRO) vector of rational functions over rationals 
			sum 
vecrfrtrnsf(r1,W1,V1,r2,R2,V2,Vn,pV3) vector of rational functions over the 
			rationals transformation 
vecrlc(s1,s2,V1,V2)     vector of rationals linear combination 
vecrneg(V)              (MACRO) vector of rationals negation 
vecrsmul(s,V)           vector of rationals scalar multiplication 
vecrsprod(V,W)          vector of rationals scalar product 
vecrsum(U,V)            (MACRO) vector of rationals sum 
vecrtovecmi(m,V)        vector of rationals to vector of modular integers 
vecrtovecnf(V)          vector of rationals to vector of number field 
			elements 
vecrtovecpr(r,V)        vector of rationals to vector of polynomials over 
			rationals 
vecrtovnfs(V)           vector of rationals to vector of number field 
			elements, sparse representation 
vecsum(U,V,sum,anzahlargs,arg1,arg2) vector sum 
vecsumspec(U,V,sum,anzahlargs,arg1,...,arg5) vector sum special 
vector                  (rekursiv) dpdegvec(r,P) dense polynomial degree 
vector                  (rekursiv) pdegvec(r,P) polynomial degree 
vector                  ? isvec(V) (MACRO) is 
vector                  compare dipevcomp(r,EV1,EV2) distributive 
			polynomial exponent 
vector                  difference dipevdif(r,EV1,EV2) distributive 
			polynomial exponent 
vector                  dipgfslotlio(r,p,AL,P) distributive polynomial over 
			Galois-field with single characteristic in 
			lexicographical order to distributive polynomial 
			over Galois-field with single characteristic in 
			lexicographical order with inverse exponent 
vector                  dipilotolio(r,P) distributive polynomial over 
			integers in lexicographical order to distributive 
			polynomial over integers in lexicographical order 
			with inverse exponent 
vector                  dipmiplotlio(r,p,P) distributive polynomial over 
			modular integer primes in lexicographical order to 
			distributive polynomial over modular integer primes 
			in lexicographical order with inverse exponent 
vector                  dipmsplotlio(r,p,P) distributive polynomial over 
			modular single primes in lexicographical order to 
			distributive polynomial over modular single primes 
			in lexicographical order with inverse exponent 
vector                  dipnflotolio(r,F,P) distributive polynomial over 
			number field in lexicographical order to 
			distributive polynomial over number field in 
			lexicographical order with inverse exponent 
vector                  dippilotolio(r1,r2,P) distributive polynomial over 
			polynomials over integers in lexicographical order 
			to distributive polynomial over polynomials over 
			integers in lexicographical order with inverse 
			exponent 
vector                  diprfrlotlio(r1,r2,P) distributive polynomial over 
			rational functions over the rationals in 
			lexicographical order to distributive polynomial 
			over rational functions over the rationals in 
			lexicographical order with inverse exponent 
vector                  diprlotolio(r,P) distributive polynomial over 
			rationals in lexicographical order to distributive 
			polynomial over rationals in lexicographical order 
			with inverse exponent 
vector                  fgetvec(pf,fgetfkt,anzahlargs,arg1,arg2,arg3) file 
			get 
vector                  fputvec(V,pf,fputfkt,anzahlargs,arg1,arg2,arg3) 
			file put 
vector                  functions HDidigitvec() Heidelberg arithmetic 
			package: 
vector                  least common multiple dipevlcm(r,EV1,EV2) 
			distributive polynomial exponent 
vector                  length veclength(V) (MACRO) 
vector                  multiple test dipevmt(r,EV1,EV2) distributive 
			polynomial exponent 
vector                  multiplication magfsvecmul(p,AL,A,x) (MACRO) matrix 
			of Galois-field with single characteristic elements 
vector                  multiplication maivecmul(A,x) (MACRO) matrix of 
			integers 
vector                  multiplication mamivecmul(m,A,x) (MACRO) matrix of 
			modular integers 
vector                  multiplication mamsvecmul(m,A,x) (MACRO) matrix of 
			modular singles 
vector                  multiplication manfsvecmul(F,A,x) (MACRO) matrix of 
			number field elements, sparse representation, 
vector                  multiplication manfvecmul(F,A,x) (MACRO) matrix of 
			number field elements 
vector                  multiplication mapgfsvmul(r,p,AL,A,x) (MACRO) 
			matrix of polynomials over Galois-field with single 
			characteristic 
vector                  multiplication mapivecmul(r,A,x) (MACRO) matrix of 
			polynomials over integers 
vector                  multiplication mapmivecmul(r,m,A,x) (MACRO) matrix 
			of polynomials over modular integers 
vector                  multiplication mapmsvecmul(r,m,A,x) (MACRO) matrix 
			of polynomials over modular singles 
vector                  multiplication mapnfvecmul(r,F,A,x) (MACRO) matrix 
			of polynomials over number field 
vector                  multiplication maprvecmul(r,A,x) (MACRO) matrix of 
			polynomials over rationals 
vector                  multiplication marfmsp1vmul(p,A,x) (MACRO) matrix 
			of rational functions over modular single primes, 
			transcendence degree 1, 
vector                  multiplication marfrvecmul(r,A,x) (MACRO) matrix of 
			rational functions over rationals 
vector                  multiplication marvecmul(A,x) (MACRO) matrix of 
			rationals 
vector                  multiplication 
			mavecmul(A,x,prod,sum,anzahlargs,arg1,arg2) matrix 
vector                  multiplication special 
			mavmulspec(A,x,prod,sum,anzahlargs,arg1,...,arg5) 
			matrix 
vector                  negation special 
			vecnegspec(V,neg,anzahlargs,arg1,...,arg5) 
vector                  negation vecneg(V,neg,anzahlargs,arg1,arg2) 
vector                  of Galois-field with characteristic 2 elements 
			scalar product vecgf2sprod(G,V,W) 
vector                  of Galois-field with single characteristic elements 
			? isvecgfs(p,AL,A) (MACRO) is 
vector                  of Galois-field with single characteristic elements 
			difference vecgfsdif(p,AL,U,V) (MACRO) 
vector                  of Galois-field with single characteristic elements 
			fgetvecgfs(p,AL,VL,pf) (MACRO) file get 
vector                  of Galois-field with single characteristic elements 
			fputvecgfs(p,AL,V,VL,pf) (MACRO) file put 
vector                  of Galois-field with single characteristic elements 
			getvecgfs(p,AL,VL) (MACRO) get 
vector                  of Galois-field with single characteristic elements 
			linear combination vecgfslc(p,AL,s1,s2,L1,L2) 
vector                  of Galois-field with single characteristic elements 
			negation vecgfsneg(p,AL,V) (MACRO) 
vector                  of Galois-field with single characteristic elements 
			putvecgfs(p,AL,V,VL) (MACRO) put 
vector                  of Galois-field with single characteristic elements 
			scalar multiplication vecgfssmul(p,AL,V,el) 
vector                  of Galois-field with single characteristic elements 
			scalar product vecgfssprod(p,AL,V,W) 
vector                  of Galois-field with single characteristic elements 
			sum vecgfssum(p,AL,U,V) (MACRO) 
vector                  of ____ ? isvec_(V,is,anzahlargs,arg1,arg2) is 
vector                  of ____, special ? 
			isvecspec_(V,is,anzahlargs,arg1,...,arg5) is 
vector                  of dense polynomials ? isvecdp(r,V) (MACRO) is 
vector                  of dense polynomials over integers ? isvecdpi(r,V) 
			(MACRO) is 
vector                  of dense polynomials over modular singles ? 
			isvecdpms(r,m,V) (MACRO) is 
vector                  of dense polynomials over rationals ? isvecdpr(r,V) 
			(MACRO) is 
vector                  of dense polynomials to vector of polynomials 
			vecdptovecp(r,V) 
vector                  of dense polynomials vecptovecdp(r,V) vector of 
			polynomials to 
vector                  of integers ? isveci(V) (MACRO) is 
vector                  of integers difference vecidif(U,V) (MACRO) 
vector                  of integers fgetveci(pf) (MACRO) file get 
vector                  of integers fputveci(V,pf) (MACRO) file put 
vector                  of integers getveci() (MACRO) get 
vector                  of integers linear combination vecilc(s1,s2,V1,V2) 
vector                  of integers negation vecineg(V) (MACRO) 
vector                  of integers putveci(V) (MACRO) put 
vector                  of integers scalar multiplication vecismul(s,V) 
vector                  of integers scalar product vecisprod(V,W) 
vector                  of integers sum vecisum(U,V) (MACRO) 
vector                  of integers to vector of modular integers 
			vecitovecmi(M,V) 
vector                  of integers to vector of modular singles 
			vecitovecms(m,V) 
vector                  of integers to vector of number field elements 
			vecitovecnf(V) 
vector                  of integers to vector of number field elements, 
			sparse representation vecitovnfs(V) 
vector                  of integers to vector of polynomials over integers 
			vecitovecpi(r,V) 
vector                  of integers to vector of rationals vecitovecr(V) 
vector                  of integers unimodular transformation 
			veciunimtr(V,W,i,pV1,pW1) 
vector                  of modular integers difference vecmidif(m,U,V) 
			(MACRO) 
vector                  of modular integers fgetvecmi(m,pf) (MACRO) file 
			get 
vector                  of modular integers fputvecmi(m,V,pf) (MACRO) file 
			put 
vector                  of modular integers getvecmi(m) (MACRO) get 
vector                  of modular integers linear combination 
			vecmilc(M,S1,S2,L1,L2) 
vector                  of modular integers negation vecmineg(m,V) (MACRO) 
vector                  of modular integers putvecmi(m,V) (MACRO) put 
vector                  of modular integers scalar multiplication 
			vecmismul(m,s,V) 
vector                  of modular integers scalar product 
			vecmisprod(M,V,W) 
vector                  of modular integers sum vecmisum(m,U,V) (MACRO) 
vector                  of modular integers vecitovecmi(M,V) vector of 
			integers to 
vector                  of modular integers vecrtovecmi(m,V) vector of 
			rationals to 
vector                  of modular singles ? isvecms(m,A) (MACRO) is 
vector                  of modular singles difference vecmsdif(m,U,V) 
			(MACRO) 
vector                  of modular singles fgetvecms(m,pf) (MACRO) file get 
vector                  of modular singles fputvecms(m,V,pf) (MACRO) file 
			put 
vector                  of modular singles getvecms(m) (MACRO) get 
vector                  of modular singles linear combination 
			vecmslc(m,s1,s2,L1,L2) 
vector                  of modular singles negation vecmsneg(m,V) (MACRO) 
vector                  of modular singles putvecms(m,V) (MACRO) put 
vector                  of modular singles scalar multiplication 
			vecmssmul(m,s,V) 
vector                  of modular singles scalar product vecmssprod(m,V,W) 
vector                  of modular singles sum vecmssum(m,U,V) (MACRO) 
vector                  of modular singles vecitovecms(m,V) vector of 
			integers to 
vector                  of number field elements ? isvecnf(F,V) (MACRO) is 
vector                  of number field elements difference vecnfdif(F,U,V) 
			(MACRO) 
vector                  of number field elements fgetvecnf(F,VL,pf) (MACRO) 
			file get 
vector                  of number field elements fputvecnf(F,V,VL,pf) 
			(MACRO) file put 
vector                  of number field elements getvecnf(F,VL) (MACRO) get 
vector                  of number field elements linear combination 
			vecnflc(F,s1,s2,L1,L2) 
vector                  of number field elements negation vecnfneg(F,V) 
			(MACRO) 
vector                  of number field elements putvecnf(F,V,VL) (MACRO) 
			put 
vector                  of number field elements scalar multiplication 
			vecnfsmul(F,V,el) 
vector                  of number field elements scalar product 
			vecnfsprod(F,V,W) 
vector                  of number field elements sum vecnfsum(F,U,V) 
			(MACRO) 
vector                  of number field elements to vector of univariate 
			dense polynomials over rationals vnftovudpr(F,V) 
vector                  of number field elements vecitovecnf(V) vector of 
			integers to 
vector                  of number field elements vecrtovecnf(V) vector of 
			rationals to 
vector                  of number field elements vudprtovnf(V) vector of 
			univariate dense polynomials over rationals to 
vector                  of number field elements, sparse representation ? 
			isvecnfs(F,V) (MACRO) is 
vector                  of number field elements, sparse representation 
			fgetvecnfs(F,VL,pf) (MACRO) file get 
vector                  of number field elements, sparse representation 
			fputvecnfs(F,V,VL,pf) (MACRO) file put 
vector                  of number field elements, sparse representation 
			getvecnfs(F,VL) (MACRO) get 
vector                  of number field elements, sparse representation 
			putvecnfs(F,V,VL) (MACRO) put 
vector                  of number field elements, sparse representation 
			vecitovnfs(V) vector of integers to 
vector                  of number field elements, sparse representation 
			vecrtovnfs(V) vector of rationals to 
vector                  of number field elements, sparse representation, 
			difference vecnfsdif(F,U,V) (MACRO) 
vector                  of number field elements, sparse representation, 
			linear combination vecnfslc(F,s1,s2,L1,L2) 
vector                  of number field elements, sparse representation, 
			negation vecnfsneg(F,V) (MACRO) 
vector                  of number field elements, sparse representation, 
			scalar multiplication vecnfssmul(F,V,el) 
vector                  of number field elements, sparse representation, 
			scalar product vecnfssprod(F,V,W) 
vector                  of number field elements, sparse representation, 
			sum vecnfssum(F,U,V) (MACRO) 
vector                  of polynomials ? isvecp(r,V) (MACRO) is 
vector                  of polynomials modulo polynomial over Galois-field 
			with single characteristic vpgfstovpmp(r,p,AL,P,V) 
			vector of polynomials over Galois-field with single 
			characteristic to 
vector                  of polynomials modulo polynomial over integers 
			vecpitvpmpi(r,V,P) vector of polynomials over 
			integers to 
vector                  of polynomials modulo polynomial over modular 
			integers vecpmitovpmp(r,m,P,V) vector of 
			polynomials over modular integers to 
vector                  of polynomials modulo polynomial over modular 
			singles vecpmstovpmp(r,m,P,V) vector of polynomials 
			over modular singles to 
vector                  of polynomials modulo polynomial over number field 
			vecpnftovpmp(r,F,P,V) vector of polynomials over 
			number field to 
vector                  of polynomials modulo polynomial over rationals 
			vecprtvpmpr(r,V,P) vector of polynomials over 
			rationals to 
vector                  of polynomials over Galois-field with single 
			characteristic ? isvecpgfs(r,p,AL,V) (MACRO) is 
vector                  of polynomials over Galois-field with single 
			characteristic difference vecpgfsdif(r,p,AL,U,V) 
			(MACRO) 
vector                  of polynomials over Galois-field with single 
			characteristic fgetvpgfs(r,p,AL,V,Vgfs,pf) (MACRO) 
			file get 
vector                  of polynomials over Galois-field with single 
			characteristic fputvpgfs(r,p,AL,W,V,Vgfs,pf) 
			(MACRO) file put 
vector                  of polynomials over Galois-field with single 
			characteristic getvpgfs(r,p,AL,V,Vgfs) (MACRO) get 
vector                  of polynomials over Galois-field with single 
			characteristic linear combination 
			vecpgfslc(r,p,AL,s1,s2,L1,L2) 
vector                  of polynomials over Galois-field with single 
			characteristic negation vecpgfsneg(r,p,AL,V) 
			(MACRO) 
vector                  of polynomials over Galois-field with single 
			characteristic putvpgfs(r,p,AL,W,V,Vgfs) (MACRO) 
			put 
vector                  of polynomials over Galois-field with single 
			characteristic scalar multiplication 
			vecpgfssmul(r,p,AL,V,el) 
vector                  of polynomials over Galois-field with single 
			characteristic scalar product 
			vpgfssprod(r,p,AL,V,W) 
vector                  of polynomials over Galois-field with single 
			characteristic sum vecpgfssum(r,p,AL,U,V) (MACRO) 
vector                  of polynomials over Galois-field with single 
			characteristic to vector of polynomials modulo 
			polynomial over Galois-field with single 
			characteristic vpgfstovpmp(r,p,AL,P,V) 
vector                  of polynomials over Galois-field with single 
			characteristic transformation 
			vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) 
vector                  of polynomials over Galois-field with single 
			characteristic vpmstovpgfs(r,p,V) vector of 
			polynomials over modular singles to 
vector                  of polynomials over integers ? isvecpi(r,V) (MACRO) 
			is 
vector                  of polynomials over integers difference 
			vecpidif(r,U,V) (MACRO) 
vector                  of polynomials over integers fgetvecpi(r,VL,pf) 
			(MACRO) file get 
vector                  of polynomials over integers fputvecpi(r,V,VL,pf) 
			(MACRO) file put 
vector                  of polynomials over integers getvecpi(r,VL) (MACRO) 
			get 
vector                  of polynomials over integers linear combination 
			vecpilc(r,P1,P2,V1,V2) 
vector                  of polynomials over integers negation vecpineg(r,V) 
			(MACRO) 
vector                  of polynomials over integers number field element 
			evaluation first variable special version 
			vpinfevalfvs(r,F,V) 
vector                  of polynomials over integers putvecpi(r,V,VL) 
			(MACRO) put 
vector                  of polynomials over integers scalar multiplication 
			vecpismul(r,P,V) 
vector                  of polynomials over integers scalar product 
			vecpisprod(r,V,W) 
vector                  of polynomials over integers sum vecpisum(r,U,V) 
			(MACRO) 
vector                  of polynomials over integers to vector of 
			polynomials modulo polynomial over integers 
			vecpitvpmpi(r,V,P) 
vector                  of polynomials over integers to vector of 
			polynomials over modular integers 
			vecpitovpmi(r,V,m) 
vector                  of polynomials over integers to vector of 
			polynomials over modular singles vecpitovpms(r,V,m) 
vector                  of polynomials over integers to vector of 
			polynomials over number field vecpitovpnf(r,V) 
vector                  of polynomials over integers to vector of 
			polynomials over rationals vecpitovpr(V) 
vector                  of polynomials over integers to vector of rational 
			functions over rationals vecpitovrfr(r,V) 
vector                  of polynomials over integers vecitovecpi(r,V) 
			vector of integers to 
vector                  of polynomials over modular integers difference 
			vecpmidif(r,m,U,V) (MACRO) 
vector                  of polynomials over modular integers 
			fgetvecpmi(r,m,VL,pf) (MACRO) file get 
vector                  of polynomials over modular integers 
			fputvecpmi(r,m,V,VL,pf) (MACRO) file put 
vector                  of polynomials over modular integers 
			getvecpmi(r,m,VL) (MACRO) get 
vector                  of polynomials over modular integers linear 
			combination vecpmilc(r,m,P1,P2,V1,V2) 
vector                  of polynomials over modular integers negation 
			vecpmineg(r,m,V) (MACRO) 
vector                  of polynomials over modular integers 
			putvecpmi(r,m,V,VL) (MACRO) put 
vector                  of polynomials over modular integers scalar 
			multiplication vecpmismul(r,m,P,V) 
vector                  of polynomials over modular integers scalar product 
			vecpmisprod(r,m,V,W) 
vector                  of polynomials over modular integers sum 
			vecpmisum(r,m,U,V) (MACRO) 
vector                  of polynomials over modular integers to vector of 
			polynomials modulo polynomial over modular integers 
			vecpmitovpmp(r,m,P,V) 
vector                  of polynomials over modular integers transformation 
			vpmitransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) 
vector                  of polynomials over modular integers 
			vecpitovpmi(r,V,m) vector of polynomials over 
			integers to 
vector                  of polynomials over modular integers 
			vecprtovpmi(r,V,m) vector of polynomials over 
			rationals to 
vector                  of polynomials over modular singles ? 
			isvecpms(r,m,V) (MACRO) is 
vector                  of polynomials over modular singles difference 
			vecpmsdif(r,m,U,V) (MACRO) 
vector                  of polynomials over modular singles 
			fgetvecpms(r,m,VL,pf) (MACRO) file get 
vector                  of polynomials over modular singles 
			fputvecpms(r,m,V,VL,pf) (MACRO) file put 
vector                  of polynomials over modular singles 
			getvecpms(r,m,VL) (MACRO) get 
vector                  of polynomials over modular singles linear 
			combination vecpmslc(r,m,P1,P2,V1,V2) 
vector                  of polynomials over modular singles negation 
			vecpmsneg(r,m,V) (MACRO) 
vector                  of polynomials over modular singles 
			putvecpms(r,m,V,VL) (MACRO) put 
vector                  of polynomials over modular singles scalar 
			multiplication vecpmssmul(r,m,P,V) 
vector                  of polynomials over modular singles scalar product 
			vecpmssprod(r,m,V,W) 
vector                  of polynomials over modular singles sum 
			vecpmssum(r,m,U,V) (MACRO) 
vector                  of polynomials over modular singles to vector of 
			polynomials modulo polynomial over modular singles 
			vecpmstovpmp(r,m,P,V) 
vector                  of polynomials over modular singles to vector of 
			polynomials over Galois-field with single 
			characteristic vpmstovpgfs(r,p,V) 
vector                  of polynomials over modular singles to vector of 
			rational functions over modular single primes, 
			transcendence degree 1 vpmstvrfmsp1(p,V) 
vector                  of polynomials over modular singles transformation 
			vpmstransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) 
vector                  of polynomials over modular singles 
			vecpitovpms(r,V,m) vector of polynomials over 
			integers to 
vector                  of polynomials over number field difference 
			vecpnfdif(r,F,U,V) (MACRO) 
vector                  of polynomials over number field 
			fgetvecpnf(r,F,VL,VLnf,pf) (MACRO) file get 
vector                  of polynomials over number field 
			fputvecpnf(r,F,W,VL,VLnf,pf) (MACRO) file put 
vector                  of polynomials over number field 
			getvecpnf(r,F,VL,VLnf) (MACRO) get 
vector                  of polynomials over number field linear combination 
			vecpnflc(r,F,s1,s2,L1,L2) 
vector                  of polynomials over number field negation 
			vecpnfneg(r,F,U) (MACRO) 
vector                  of polynomials over number field 
			putvecpnf(r,F,W,VL,VLnf) (MACRO) put 
vector                  of polynomials over number field scalar 
			multiplication vecpnfsmul(r,F,U,el) 
vector                  of polynomials over number field scalar product 
			vpnfsprod(r,F,V,W) 
vector                  of polynomials over number field sum 
			vecpnfsum(r,F,U,V) (MACRO) 
vector                  of polynomials over number field to vector of 
			polynomials modulo polynomial over number field 
			vecpnftovpmp(r,F,P,V) 
vector                  of polynomials over number field to vector of 
			polynomials over rationals vecpnftovpr(r,V) 
vector                  of polynomials over number field transformation 
			vpnftransf(r1,F,W1,V1,r2,P2,V2,Vn,pV3) 
vector                  of polynomials over number field vecpitovpnf(r,V) 
			vector of polynomials over integers to 
vector                  of polynomials over number field vecprtovpnf(r,V) 
			vector of polynomials over rationals to 
vector                  of polynomials over rationals ? isvecpr(r,V) 
			(MACRO) is 
vector                  of polynomials over rationals difference 
			vecprdif(r,U,V) (MACRO) 
vector                  of polynomials over rationals fgetvecpr(r,VL,pf) 
			(MACRO) file get 
vector                  of polynomials over rationals fputvecpr(r,V,VL,pf) 
			(MACRO) file put 
vector                  of polynomials over rationals getvecpr(r,VL) 
			(MACRO) get 
vector                  of polynomials over rationals linear combination 
			vecprlc(r,P1,P2,V1,V2) 
vector                  of polynomials over rationals negation 
			vecprneg(r,V) (MACRO) 
vector                  of polynomials over rationals number field element 
			evaluation first variable special version 
			vprnfevalfvs(r,F,V) 
vector                  of polynomials over rationals putvecpr(r,V,VL) 
			(MACRO) put 
vector                  of polynomials over rationals scalar multiplication 
			vecprsmul(r,P,V) 
vector                  of polynomials over rationals scalar product 
			vecprsprod(r,V,W) 
vector                  of polynomials over rationals sum vecprsum(r,U,V) 
			(MACRO) 
vector                  of polynomials over rationals to vector of 
			polynomials modulo polynomial over rationals 
			vecprtvpmpr(r,V,P) 
vector                  of polynomials over rationals to vector of 
			polynomials over modular integers 
			vecprtovpmi(r,V,m) 
vector                  of polynomials over rationals to vector of 
			polynomials over number field vecprtovpnf(r,V) 
vector                  of polynomials over rationals to vector of rational 
			functions over rationals vecprtovrfr(r,V) 
vector                  of polynomials over rationals vecpitovpr(V) vector 
			of polynomials over integers to 
vector                  of polynomials over rationals vecpnftovpr(r,V) 
			vector of polynomials over number field to 
vector                  of polynomials over rationals vecrtovecpr(r,V) 
			vector of rationals to 
vector                  of polynomials over the integers transformation 
			vecpitransf(r1,W1,V1,r2,P2,V2,Vn,pV3) 
vector                  of polynomials over the rationals transformation 
			vecprtransf(r1,W1,V1,r2,P2,V2,Vn,pV3) 
vector                  of polynomials to vector of dense polynomials 
			vecptovecdp(r,V) 
vector                  of polynomials to vector of univariate polynomials 
			vecptovecup(r,V) 
vector                  of polynomials variable permutation 
			vecvpermut(r,V,PI) 
vector                  of polynomials vecdptovecp(r,V) vector of dense 
			polynomials to 
vector                  of rational functions over modular single primes, 
			transcendence degree 1 ? isvecrfmsp1(p,V) (MACRO) 
			is 
vector                  of rational functions over modular single primes, 
			transcendence degree 1 fgetvrfmsp1(p,VL,pf) (MACRO) 
			file get 
vector                  of rational functions over modular single primes, 
			transcendence degree 1 fputvrfmsp1(p,V,VL,pf) 
			(MACRO) file put 
vector                  of rational functions over modular single primes, 
			transcendence degree 1 getvecrfmsp1(p,VL) (MACRO) 
			get 
vector                  of rational functions over modular single primes, 
			transcendence degree 1 putvecrfmsp1(p,V,VL) (MACRO) 
			put 
vector                  of rational functions over modular single primes, 
			transcendence degree 1 vpmstvrfmsp1(p,V) vector of 
			polynomials over modular singles to 
vector                  of rational functions over modular single primes, 
			transcendence degree 1, difference 
			vecrfmsp1dif(p,U,V) (MACRO) 
vector                  of rational functions over modular single primes, 
			transcendence degree 1, linear combination 
			vecrfmsp1lc(p,F1,F2,V1,V2) 
vector                  of rational functions over modular single primes, 
			transcendence degree 1, negation vecrfmsp1neg(p,V) 
			(MACRO) 
vector                  of rational functions over modular single primes, 
			transcendence degree 1, scalar multiplication 
			vecrfmsp1sm(p,F,V) 
vector                  of rational functions over modular single primes, 
			transcendence degree 1, scalar product 
			vecrfmsp1sp(p,V,W) 
vector                  of rational functions over modular single primes, 
			transcendence degree 1, sum vecrfmsp1sum(p,U,V) 
			(MACRO) 
vector                  of rational functions over rationals ? 
			isvecrfr(r,V) (MACRO) is 
vector                  of rational functions over rationals difference 
			vecrfrdif(r,U,V) (MACRO) 
vector                  of rational functions over rationals 
			fgetvecrfr(r,VL,pf) (MACRO) file get 
vector                  of rational functions over rationals 
			fputvecrfr(r,V,VL,pf) (MACRO) file put 
vector                  of rational functions over rationals 
			getvecrfr(r,VL) (MACRO) get 
vector                  of rational functions over rationals linear 
			combination vecrfrlc(r,F1,F2,V1,V2) 
vector                  of rational functions over rationals negation 
			vecrfrneg(r,V) (MACRO) 
vector                  of rational functions over rationals 
			putvecrfr(r,V,VL) (MACRO) put 
vector                  of rational functions over rationals scalar 
			multiplication vecrfrsmul(r,F,V) 
vector                  of rational functions over rationals scalar product 
			vecrfrsprod(r,V,W) 
vector                  of rational functions over rationals sum 
			vecrfrsum(r,U,V) (MACRO) 
vector                  of rational functions over rationals 
			vecpitovrfr(r,V) vector of polynomials over 
			integers to 
vector                  of rational functions over rationals 
			vecprtovrfr(r,V) vector of polynomials over 
			rationals to 
vector                  of rational functions over the rationals 
			transformation 
			vecrfrtrnsf(r1,W1,V1,r2,R2,V2,Vn,pV3) 
vector                  of rationals ? isvecr(V) (MACRO) is 
vector                  of rationals difference vecrdif(U,V) (MACRO) 
vector                  of rationals fgetvecr(pf) (MACRO) file get 
vector                  of rationals fputvecr(V,pf) (MACRO) file put 
vector                  of rationals getvecr() (MACRO) get 
vector                  of rationals linear combination vecrlc(s1,s2,V1,V2) 
vector                  of rationals negation vecrneg(V) (MACRO) 
vector                  of rationals putvecr(V) (MACRO) put 
vector                  of rationals scalar multiplication vecrsmul(s,V) 
vector                  of rationals scalar product vecrsprod(V,W) 
vector                  of rationals sum vecrsum(U,V) (MACRO) 
vector                  of rationals to vector of modular integers 
			vecrtovecmi(m,V) 
vector                  of rationals to vector of number field elements 
			vecrtovecnf(V) 
vector                  of rationals to vector of number field elements, 
			sparse representation vecrtovnfs(V) 
vector                  of rationals to vector of polynomials over 
			rationals vecrtovecpr(r,V) 
vector                  of rationals vecitovecr(V) vector of integers to 
vector                  of the leading monomial dipevl(r,P) distributive 
			polynomial exponent 
vector                  of univariate dense polynomials over integers to 
			vector of univariate dense polynomials over modular 
			integers vudpitudpmi(V,M) 
vector                  of univariate dense polynomials over integers to 
			vector of univariate dense polynomials over 
			rationals vudpitvudpr(V) 
vector                  of univariate dense polynomials over modular 
			integers vudpitudpmi(V,M) vector of univariate 
			dense polynomials over integers to 
vector                  of univariate dense polynomials over rationals to 
			vector of number field elements vudprtovnf(V) 
vector                  of univariate dense polynomials over rationals 
			vnftovudpr(F,V) vector of number field elements to 
vector                  of univariate dense polynomials over rationals 
			vudpitvudpr(V) vector of univariate dense 
			polynomials over integers to 
vector                  of univariate polynomials over modular single prime 
			unimodular transformation 
			vecupmsunimt(p,V,W,i,pV1,pW1) 
vector                  of univariate polynomials vecptovecup(r,V) vector 
			of polynomials to 
vector                  over Galois-field with single characteristic 
			embedding in field extension vecgfsefe(p,ALm,V,g) 
vector                  over Galois-field with single characteristic 
			vecitovecgfs(p,V) vector over integers to 
vector                  over integers to vector over Galois-field with 
			single characteristic vecitovecgfs(p,V) 
vector                  over polynomials over Galois-field with single 
			characteristic embedding in field extension 
			vecpgfsefe(r,p,ALm,V,g) 
vector                  over polynomials over integers Galois-field with 
			single characteristic element evaluation first 
			variable special version vecpigfsefvs(r,p,AL,V) 
vector                  signum dipevsign(r,EV) distributive polynomial 
			exponent 
vector                  special 
			fgetvecspec(pf,fgetfkt,anzahlargs,arg1,...,arg8) 
			file get 
vector                  special 
			fputvecspec(V,pf,fputfkt,anzahlargs,arg1,...,arg8) 
			file put 
vector                  sum dipevsum(r,EV1,EV2) distributive polynomial 
			exponent 
vector                  sum special 
			vecsumspec(U,V,sum,anzahlargs,arg1,...,arg5) 
vector                  sum vecsum(U,V,sum,anzahlargs,arg1,arg2) 
vecupmsunimt(p,V,W,i,pV1,pW1) vector of univariate polynomials over modular 
			single prime unimodular transformation 
vecvpermut(r,V,PI)      vector of polynomials variable permutation 
vepepuspmsp1(p,F,a,P,k,v) values of the extensions of the P-adic valuation 
			of an element of the polynomial order of a 
			univariate separable polynomial over the polynomial 
			ring over modular single prime, transcendence 
			degree 1 
vepvelpruspi(F,a,p,k,v) values of the extensions of the p-adic valuation of 
			an element of the polynomial ring of an univariate 
			separable polynomial over the integers 
version                 (rekursiv) ifact_o(N) integer factorization, old 
version                 (rekursiv) pigf2evalfvs(r,G,P) polynomial over 
			integers Galois-field with characteristic 2 element 
			evaluation first variable special 
version                 (rekursiv) pigfsevalfvs(r,p,AL,P) polynomial over 
			integers Galois-field with single characteristic 
			element evaluation first variable special 
version                 1 ecgf2npmspv1(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a single prime determined with the 
			Schoof algorithm, 
version                 2 ecgf2npmspv2(G,a6,p,L) elliptic curve over 
			Galois-field with characteristic 2, number of 
			points modulo a single prime determined with the 
			Schoof algorithm, 
version                 3 iqrem_3(A,B,pQ,pR) integer quotient and remainder 
			special 
version                 cexpsv(z,n) complex exponential function special 
version                 ecgf2sfmuls(p,a6,x1,y1,n) elliptic curve over 
			Galois-field with characteristic 2, special form, 
			multiplication-map, special 
version                 ecgf2sfsums(G,a6,x1,y1,x2,y2) elliptic curve over 
			Galois-field with characteristic 2, special form, 
			sum of points, special 
version                 ecimindivs(E,P,h,ug,PL,n) elliptic curve with 
			integer coefficients, minimal model, division of a 
			point by an integer, special 
version                 ecmipsnfnpsv(p,a4,a6) elliptic curve over modular 
			integer primes short normal form number of points 
			special 
version                 ecmpsnfmuls(p,a4,a6,x1,y1,n) elliptic curve over 
			modular primes, short normal form, 
			multiplication-map, special 
version                 ecmpsnfsums(p,a4,a6,x1,y1,x2,y2) elliptic curve 
			over modular primes, short normal form, sum of 
			points, special 
version                 ecrlserfds(E,A,result) elliptic curve over the 
			rationals, L-series, first derivative, special 
version                 ecrlsers(E,A,result) elliptic curve over the 
			rationals, L-series, special 
version                 ecrsigns(E,A,C) elliptic curve over the rationals, 
			sign of the functional equation, special 
version                 flath_sp(f) floating point area tangens 
			hyperbolicus special 
version                 flatn_sp(f) floating point arcus tangens special 
version                 flcos_sp(f) floating point cosinus special 
version                 flsin_sp(f) floating point sinus special 
version                 iecjtoeqsv(p,j,pi) integer elliptic curve 
			j-invariant to equation special 
version                 iqrem_2(A,B,pQ,pR) integer quotient and remainder, 
			old 
version                 irand_2(u) integer randomize, alternative 
version                 itoI_sp(A,lA,h) ( SIMATH ) integer to ( Heidelberg 
			) Integer special 
version                 lscomps(L1,L2) list of singles comparison special 
version                 lsmaxs(L1,L2) list of singles maximum special 
version                 lsmins(L1,L2) list of singles minimum special 
version                 mapigfsevfvs(r,p,AL,M) matrix over polynomials over 
			integers Galois-field with single characteristic 
			element evaluation first variable special 
version                 mapinfevlfvs(r,F,M) matrix of polynomials over 
			integers number field element evaluation first 
			variable special 
version                 maprnfevlfvs(r,F,M) matrix of polynomials over 
			rationals number field element evaluation first 
			variable special 
version                 pinfevalfvs(r,F,P) polynomial over integers number 
			field element evaluation first variable special 
version                 prnfevalfvs(r,F,P) polynomial over rationals number 
			field element evaluation first variable special 
version                 qffmsfubs(m,D) quadratic function field over 
			modular singles fundamental unit, baby step 
version                 qffmsfuobs(m,D) quadratic function field over 
			modular singles fundamental unit, original 
version                 qffmspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles primitive ideal 
			product, special 
version                 qffmspidsqus(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles primitive ideal square, 
			special 
version                 qffmsregbg(m,D) quadratic function field over 
			modular singles regulator, baby step - giant step 
version                 qffmsregbs(m,D) quadratic function field over 
			modular singles regulator, baby step 
version                 qffmsregobg(m,D) quadratic function field over 
			modular singles regulator, original baby step - 
			giant step 
version                 qffmsregobs(m,D) quadratic function field over 
			modular singles regulator, original baby step 
version                 qffmsspidprs(m,D,C1,Q1,P1,Q2,P2,pQ,pP) quadratic 
			function field over modular singles, sparse 
			representation, primitive ideal product, special 
version                 qffmsspidsqs(m,D,C1,Q1,P1,pQ,pP) quadratic function 
			field over modular singles, sparse representation, 
			primitive ideal square, special 
version                 qnfielpifacts(D,a,L) quadratic number field 
			integral element prime ideal factorization, special 
version                 sgetflsp(ps) string get floating point special 
version                 sputflsp(prec,f,str) string put floating point 
			special 
version                 udpgf2remsp(G,P1,P2,ilc) univariate dense 
			polynomial over Galois-field with characteristic 2 
			remainder, special 
version                 upgf2modexps(G,F,m,P,pM) univariate polynomial over 
			Galois-field with characteristic 2, modular 
			exponentiation, special 
version                 vecpigfsefvs(r,p,AL,V) vector over polynomials over 
			integers Galois-field with single characteristic 
			element evaluation first variable special 
version                 vpinfevalfvs(r,F,V) vector of polynomials over 
			integers number field element evaluation first 
			variable special 
version                 vprnfevalfvs(r,F,V) vector of polynomials over 
			rationals number field element evaluation first 
			variable special 
version,                first case qffmsregbg1(m,D,s) quadratic function 
			field over modular singles regulator, baby step - 
			giant step 
version,                fourth case qffmsregbg4(m,D,s) quadratic function 
			field over modular singles regulator, baby step - 
			giant step 
version,                second case qffmsregbg2(m,D,s) quadratic function 
			field over modular singles regulator, baby step - 
			giant step 
version,                third case qffmsregbg3(m,D,s) quadratic function 
			field over modular singles regulator, baby step - 
			giant step 
version1                ippnferegul1(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field element regulation, 
version1                nfespecmpc1(F,a) number field element special 
			minimal polynomial, Collins algorithm, 
version2                ippnferegul2(F,p,Q,a0,mpa0,pa1,pa2) integral 
			p-primary number field element regulation, 
version2                nfespecmpc2(F,a) number field element special 
			minimal polynomial, Collins algorithm, 
version2                upmitransf2(M,P,r,P1) univariate polynomial over 
			modular integers transformation 
via                     Hankel matrix pmidiscrhank(r,M,P) polynomial over 
			modular integers discriminant 
via                     Hankel- matrix pidiscrhank(r,P) polynomial over 
			integers discriminant 
vlsort(V,pPI)           variable list sort 
vncomp(Vn1,Vn2)         variable name comparison 
vnftovudpr(F,V)         vector of number field elements to vector of 
			univariate dense polynomials over rationals 
volume                  of the unit ball volunitball(r) 
volunitball(r)          volume of the unit ball 
vpgfssprod(r,p,AL,V,W)  vector of polynomials over Galois-field with single 
			characteristic scalar product 
vpgfstovpmp(r,p,AL,P,V) vector of polynomials over Galois-field with single 
			characteristic to vector of polynomials modulo 
			polynomial over Galois-field with single 
			characteristic 
vpgfstransf(r1,p,AL,W1,V1,r2,P2,V2,Vn,pV3) vector of polynomials over 
			Galois-field with single characteristic 
			transformation 
vpinfevalfvs(r,F,V)     vector of polynomials over integers number field 
			element evaluation first variable special version 
vpmitransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of polynomials over modular 
			integers transformation 
vpmstovpgfs(r,p,V)      vector of polynomials over modular singles to 
			vector of polynomials over Galois-field with single 
			characteristic 
vpmstransf(r1,m,W1,V1,r2,P2,V2,Vn,pV3) vector of polynomials over modular 
			singles transformation 
vpmstvrfmsp1(p,V)       vector of polynomials over modular singles to 
			vector of rational functions over modular single 
			primes, transcendence degree 1 
vpnfsprod(r,F,V,W)      vector of polynomials over number field scalar 
			product 
vpnftransf(r1,F,W1,V1,r2,P2,V2,Vn,pV3) vector of polynomials over number 
			field transformation 
vprnfevalfvs(r,F,V)     vector of polynomials over rationals number field 
			element evaluation first variable special version 
vudpitudpmi(V,M)        vector of univariate dense polynomials over 
			integers to vector of univariate dense polynomials 
			over modular integers 
vudpitvudpr(V)          vector of univariate dense polynomials over 
			integers to vector of univariate dense polynomials 
			over rationals 
vudprtovnf(V)           vector of univariate dense polynomials over 
			rationals to vector of number field elements 
x^2+q*y^2=m             using the algorithm of cornaccia 
			cornaccia(m,q,x0,pX,pY) determine a solution of the 
			diophantine equation 
zero                    class group isomorphy type, imaginary case 
			qffmszcgiti(m,D,LG,IT) quadratic function field 
			over modular singles 
zero                    class group isomorphy type, real case 
			qffmszcgitr(m,D,d,H,LG,R,IT) quadratic function 
			field over modular singles 
zero                    maconszero(m,n) matrix construction 
zero?                   isqnfppihom0(D,P,k,pi,z,a) is quadratic number 
			field element power of prime ideal homomorphism 
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