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O abs acos acosh addell(e,z1,z2)=elladd(e,z1,z2); addprimes adj(x)=matadjoint(x); agm akell(e,n)=ellak(e,n); algdep algdep2(x,n,dec)=algdep(x,n,dec); algtobasis(nf,x)=nfalgtobasis(nf,x); allocatemem anell(e,n)=ellan(e,n); apell(e,n)=ellap(e,n); apell2(e,n)=ellap(e,n,1); apprpadic(x,a)=padicappr(x,a); arg asin asinh assmat(x)=matcompanion(x); atan atanh basis(x)=nfbasis(x); basis2(x)=nfbasis(x,2); basistoalg(nf,x)=nfbasistoalg(nf,x); bernreal bernvec bestappr bezout bezoutres bigomega bilhell(e,z1,z2)=ellbil(e,z1,z2); bin(x,y)=binomial(x,y); binary bittest boundcf(x,lmax)=contfrac(x,,lmax); boundfact(x,lim)=factor(x,lim); box(x,a)=plotbox(x,a); buchcertify(bnf)=bnfcertify(bnf); buchfu(bnf)=bnfunit(bnf); buchgen(P)=bnfclassunit(P,2); buchgenforcefu(P)=bnfclassunit(P,1); buchgenfu(P)=bnfclassunit(P); buchimag(D,c1,c2,g)=quadclassunit(D,,[c1,c2,g]); buchinit(P)=bnfinit(P,2); buchinitforcefu(P)=bnfinit(P,1); buchinitfu(P)=bnfinit(P); buchnarrow(bnf)=bnfnarrow(bnf); buchray(bnf,ideal)=bnrclass(bnf,ideal); buchrayinit(bnf,ideal)=bnrclass(bnf,ideal,1); buchrayinitgen(bnf,ideal)=bnrclass(bnf,ideal,2); buchreal(D)=quadclassunit(D); bytesize(x)=sizebyte(x); ceil centerlift cf(x)=contfrac(x); cf2(b,x)=contfrac(x,b); changevar char(x,y)=charpoly(x,y); char1(x,y)=charpoly(x,y,1); char2(x,y)=charpoly(x,y,2); chell(x,y)=ellchangecurve(x,y); chinese chptell(x,y)=ellchangepoint(x,y); classno(x)=qfbclassno(x); classno2(x)=qfbclassno(x,1); coeff(x,s)=polcoeff(x,s); color(w,c)=plotcolor(w,c); compimag(x,y)=x*y; compo(x,s)=component(x,s); compositum(pol1,pol2)=polcompositum(pol1,pol2); compositum2(pol1,pol2)=polcompositum(pol1,pol2,1); comprealraw(x,y)=qfbcompraw(x,y); concat conductor(a1)=bnrconductor(a1); conductorofchar(bnr,chi)=bnrconductorofchar(bnr,chi); conj conjvec content convol(x,y)=serconvol(x,y); core core2(x)=core(x,1); coredisc coredisc2(x)=coredisc(x,1); cos cosh cursor(w)=plotcursor(w); cvtoi(x)=truncate(x,&e); cyclo(n)=polcyclo(n); decodefactor(fa)=factorback(fa); decodemodule(nf,fa)=bnfdecodemodule(nf,fa); default degree(x)=poldegree(x); denom(x)=denominator(x); deplin(x)=lindep(x,-1); deriv det(x)=matdet(x); det2(x)=matdet(x,1); detint(x)=matdetint(x); diagonal(x)=matdiagonal(x); dilog dirdiv direuler dirmul dirzetak disc(x)=poldisc(x); discf(x)=nfdisc(x); discf2(x)=nfdisc(x,2); discrayabs(bnr,subgroup)=bnrdisc(bnr,subgroup); discrayabscond(bnr)=bnrdisc(bnr,,,2); discrayabslist(bnf,list)=bnrdisclist(bnf,list); discrayabslistarch(bnf,arch,bound)=bnrdisclist(bnf,bound,arch); discrayabslistarchall(bnf,bound)=bnrdisclist(bnf,bound,,1); discrayabslistlong(bnf,bound)=bnrdisclist(bnf,bound); discrayrel(bnr,subgroup)=bnrdisc(bnr,subgroup,,1); discrayrelcond(bnr,subgroup)=bnrdisc(bnr,subgroup,,3); divisors divres(x,y)=divrem(x,y); divsum(n,X,expr)=sumdiv(n,X,expr); draw(list)=plotdraw(list); eigen(x)=mateigen(x); eint1 erfc eta euler=Euler; eval exp extract(x,y)=vecextract(x,y); fact(x)=factorial(x); factcantor(x,p)=factorcantor(x,p); factfq(x,p,a)=factorff(x,p,a); factmod(x,p)=factormod(x,p); factor factoredbasis(x,p)=nfbasis(x,,p); factoreddiscf(x,p)=nfdisc(x,,p); factoredpolred(x,p)=polred(x,,p); factoredpolred2(x,p)=polred(x,2,p); factornf factorpadic factorpadic2(x,p,r)=factorpadic(x,p,r,1); factpol(x,l,hint)=factor(x); factpol2(x,l,hint)=factor(x); fibo(x)=fibonacci(x); floor for fordiv forprime forstep forvec fpn(p,n)=ffinit(p,n); frac galois(x)=polgalois(x); galoisapply(nf,aut,x)=nfgaloisapply(nf,aut,x); galoisconj(nf)=nfgaloisconj(nf); galoisconj1(nf)=nfgaloisconj(nf,2); galoisconjforce=nfgaloisconj(nf,1); gamh(x)=gammah(x); gamma gauss(a,b)=matsolve(a,b); gaussmodulo(M,D,Y)=matsolvemod(M,D,Y); gaussmodulo2(M,D,Y)=matsolvemod(M,D,Y,1); gcd getheap getrand getstack gettime globalred(x,y)=ellglobalred(x,y); goto=; hclassno(x)=qfbhclassno(x); hell(e,x)=ellheight(e,x); hell2(e,x)=ellheight(e,x,1); hermite(x)=mathnf(x); hermite2(x)=mathnf(x,1); hermitehavas(x)=mathnf(x,2); hermitemod(x,d)=mathnfmod(x,d); hermitemodid(x,d)=mathnfmodid(x,d); hermiteperm(x)=mathnf(x,3); hess(x)=mathess(x); hilb(x,y)=hilbert(x,y); hilbert(n)=mathilbert(n); hilbp(x,y,p)=hilbert(x,y,p); hvector(n,X,expr)=vector(n,X,expr); hyperu i=I; idealadd idealaddmultone(nf,list)=idealaddtoone(nf,list); idealaddone(nf,x,y)=idealaddtoone(nf,x,y); idealappr idealapprfact(nf,x)=idealappr(nf,x,1); idealchinese idealcoprime idealdiv idealdivexact(nf,x,y)=idealdiv(nf,x,y,1); idealfactor idealhermite(nf,x)=idealhnf(nf,x); idealhermite2(nf,x)=idealhnf(nf,x); idealintersect idealinv idealinv2(nf,x)=idealinv(nf,x,1); ideallist ideallistarch ideallistarchgen(nf,list,arch)=ideallistarch(nf,list,arch,1); ideallistunit(nf,list)=ideallist(nf,list,2); ideallistunitarch=ideallistarch(nf,list,arch,2); ideallistunitarchgen=ideallistarch(nf,list,arch,3); ideallistunitgen=ideallist(nf,list,3); ideallistzstar(nf,bound)=ideallist(nf,bound); ideallistzstargen(nf,bound)=ideallist(nf,bound,1); ideallllred(nf,x,vdir)=idealred(nf,x,vdir); idealmul idealmulred(nf,x,y)=idealmul(nf,x,y,1); idealnorm idealpow idealpowred(nf,x,y)=idealpow(nf,x,y,1); idealtwoelt idealtwoelt2(nf,x,a)=idealtwoelt(nf,x,a); idealval idmat(n)=matid(n); if imag image(x)=matimage(x); image2(x)=matimage(x,1); imagecompl(x)=matimagecompl(x); incgam incgam1(s,x)=; incgam2(s,x)=; incgam3(s,x)=; incgam4(s,x,y)=incgam(s,x,y); indexrank(x)=matindexrank(x); indsort(x)=vecsort(x,,1); initalg(pol)=nfinit(pol); initalgred(x)=nfinit(x,2); initalgred2(x)=nfinit(x,3); initell(x)=ellinit(x); initrect(w,x,y)=plotinit(w,x,y); initzeta(x)=zetakinit(x); integ(x,y)=intformal(x,y); intersect(x,y)=matintersect(x,y); intgen(x=a,b,s)=intnum(x=a,b,s,1); intinf(x=a,b,s)=intnum(x=a,b,s,2); intnum intopen(x=a,b,s)=intnum(x=a,b,s,3); inverseimage(x,y)=matinverseimage(x,y); isdiagonal(x)=matisdiagonal(x); isfund(x)=isfundamental(x); isideal(nf,x)=nfisideal(nf,x); isincl(x,y)=nfisincl(x,y); isinclfast(nf1,nf2)=nfisincl(nf1,nf2,1); isirreducible(x)=polisirreducible(x); isisom(x,y)=nfisisom(x,y); isisomfast(x,y)=nfisisom(x,y); isoncurve(e,x)=ellisoncurve(e,x); isprime isprincipal(bnf,x)=bnfisprincipal(bnf,x,0); isprincipalforce(bnf,x)=bnfisprincipal(bnf,x,2); isprincipalgen(bnf,x)=bnfisprincipal(bnf,x); isprincipalgenforce(bnf,x)=bnfisprincipal(bnf,x,3); isprincipalray(bnf,x)=bnrisprincipal(bnf,x); isprincipalraygen ispsp(x)=ispseudoprime(x); isqrt(x)=sqrtint(x); isset(x)=setisset(x); issqfree(x)=issquarefree(x); issquare isunit(bnf,x)=bnfisunit(bnf,x); jacobi(x)=qfjacobi(x); jbesselh(n,x)=besseljh(n,x); jell(x)=ellj(x); karamul(x,y,k)=; kbessel(nu,x)=besselk(nu,x); kbessel2(nu,x)=besselk(nu,x,1); ker(x)=matker(x); keri(x)=matker(x,1); kerint(x)=matkerint(x); kerint1(x)=matkerint(x,1); kerint2(x)=matkerint(x,2); kill killrect(w)=plotkill(w); kro(x,y)=kronecker(x,y); label=; lambdak(nfz,s)=zetak(nfz,s,1); laplace(x)=serlaplace(x); lcm legendre(n)=pollegendre(n); length lex lexsort(x)=vecsort(x,,2); lift lindep lindep2(x)=lindep(x,1); line(w,x2,y2)=plotlines(w,x2,y2); lines(w,x2,y2)=plotlines(w,x2,y2); lll(x)=qflll(x); lll1(x)=qflll(x,7); lllgen(x)=qflll(x,8); lllgram(x)=qflllgram(x); lllgram1(x)=qflllgram(x,7); lllgramgen(x)=qflllgram(x,8); lllgramint(x)=qflllgram(x,1); lllgramkerim(x)=qflllgram(x,4); lllgramkerimgen(x)=qflllgram(x,5); lllint(x)=qflll(x,1); lllintpartial(x)=qflll(x,2); lllkerim(x)=qflll(x,4); lllkerimgen(x)=qflll(x,5); lllrat(x)=qflll(x,3); ln(x)=log(x); lngamma localred(e)=elllocalred(e); log logagm(x)=log(x,1); lseriesell(e,s,N,A)=elllseries(e,s,A); makebigbnf(sbnf)=bnfmake(sbnf); mat(x)=Mat(x); matextract(x,y,z)=vecextract(x,y,z); mathell(e,x)=ellheightmatrix(e,x); matrix matrixqz matrixqz2(x,p)=matrixqz(x,-1); matrixqz3(x,p)=matrixqz(x,-2); matsize max min minideal(nf,ix,vdir)=idealmin(nf,ix,vdir); minim(x,bound,maxnum)=qfminim(x,bound,maxnum); minim2(x,bound)=qfminim(x,bound,,1); mod(x,y)=Mod(x,y); modp(x,y,p)=Mod(x,y,1); modreverse modulargcd(x,y)=gcd(x,y,1); move(w,x,y)=plotmove(w,x,y); mu(n)=moebius(n); newtonpoly nextprime nfdetint nfdiv(nf,a,b)=nfeltdiv(nf,a,b); nfdiveuc(nf,a,b)=nfeltdiveuc(nf,a,b); nfdivres(nf,a,b)=nfeltdivrem(nf,a,b); nfhermite(nf,x)=nfhnf(nf,x); nfhermitemod(nf,x,detx)=nfhnfmod(nf,x,detx); nfmod(nf,a,b)=nfeltmod(nf,a,b); nfmul(nf,a,b)=nfeltmul(nf,a,b); nfpow(nf,a,k)=nfeltpow(nf,a,k); nfreduce(nf,a,id)=nfeltreduce(nf,a,id); nfsmith(nf,x)=nfsnf(nf,x); nfval(nf,a,pr)=nfeltval(nf,a,pr); norm norml2 nucomp(x,y,l)=qfbnucomp(x,y,l); numdiv numer(x)=numerator(x); nupow(x,n)=qfbnupow(x,n); o(x)=O(x); omega ordell(e,x)=ellordinate(e,x); order(x)=znorder(x); orderell(e,x)=ellorder(e,x); ordred(x)=polredord(x); padicprec pascal(n)=matpascal(n); perf(a)=qfperfection(a); permutation(n,k)=numtoperm(n,k); permutation2num(vect)=permtonum(vect); pf(x,p)=qfbprimeform(x,p); phi(x)=eulerphi(x); pi=Pi; plot ploth ploth2(X=a,b,expr)=ploth(X=a,b,expr,1); plothmult(X=a,b,expr)=ploth(X=a,b,expr); plothraw pnqn(x)=contfracpnqn(x); point(w,x,y)=plotpoints(w,x,y); pointell(e,z)=ellztopoint(e,z); points(w,x,y)=plotpoints(w,x,y); polint(xa,ya,x)=polinterpolate(xa,ya,p); polred polred2(x)=polred(x,2); polredabs polredabs2(x)=polredabs(x,1); polredabsall(x)=polredabs(x,4); polredabsfast(x)=polredabs(x,8); polredabsnored(x)=polredabs(x,2); polsym polvar(x)=variable(x); poly(x,v)=Pol(x,v); polylog polylogd(m,x)=polylog(m,x,1); polylogdold(m,x)=polylog(m,x,2); polylogp(m,x)=polylog(m,x,3); polyrev(x,v)=Polrev(x,v); polzag(n,m)=polzagier(n,m); postdraw(list)=psdraw(list); postploth(X=a,b,expr)=psploth(X=a,b,expr); postploth2(X=a,b,expr)=psploth(X=a,b,expr,1); postplothraw(listx,listy)=psplothraw(listx,listy); powell(e,x,n)=ellpow(e,x,n); powrealraw(x,n)=qfbpowraw(x,n); pprint(x)=printp(x); pprint1(x)=printp1(x); prec(x,n)=precision(x,n); precision prime primedec(nf,p)=idealprimedec(nf,p); primes primroot(n)=znprimroot(n); principalideal(nf,x)=idealprincipal(nf,x); principalidele(nf,x)=ideleprincipal(nf,x); print print1 prod(x,X=a,b,expr)=prod(X=a,b,expr,x); prodeuler prodinf prodinf1(X=a,expr)=prodinf(X=a,expr,1); psi qfi(a,b,c)=Qfb(a,b,c); qfr(a,b,c,d)=Qfb(a,b,c,d); quaddisc quadgen quadpoly random rank(x)=matrank(x); rayclassno(bnf,x)=bnrclassno(bnf,x); rayclassnolist(bnf,liste)=bnrclassnolist(bnf,liste); rbox(w,dx,dy)=plotrbox(w,dx,dy); read(x)=input(x); real recip(x)=polrecip(x); redimag(x)=qfbred(x); redreal(x)=qfbred(x); redrealnod(x,d)=qfbred(x,2,,d); reduceddisc(f)=poldiscreduced(f); regula(x)=quadregulator(x); reorder resultant(x,y)=polresultant(x,y); resultant2(x,y)=polresultant(x,y,1); reverse(x)=serreverse(x); rhoreal(x)=qfbred(x,1); rhorealnod(x,d)=qfbred(x,3,,d); rline(w,dx,dy)=plotrline(w,dx,dy); rlines(w,dx,dy)=plotrlines(w,dx,dy,1); rmove(w,dx,dy)=plotrmove(w,dx,dy); rndtoi(x)=round(x,&e); rnfbasis rnfdiscf(nf,pol)=rnfdisc(nf,pol); rnfequation rnfequation2(nf,pol)=rnfequation(nf,pol,1); rnfhermitebasis(bnf,order)=rnfhnfbasis(bnf,order); rnfisfree rnflllgram rnfpolred rnfpseudobasis rnfsteinitz rootmod(x,p)=polrootsmod(x,p); rootmod2(x,p)=polrootsmod(x,p,1); rootpadic(x,p,r)=polrootspadic(x,p,r); roots(x)=polroots(x); rootsof1(nf)=nfrootsof1(nf); rootsold(x)=polroots(x,1); round rounderror(x)=round(x,&e); rpoint(w,dx,dy)=plotrpoint(w,dx,dy); rpoints(w,dx,dy)=plotrpoints(w,dx,dy); scale(w,x1,x2,y1,y2)=plotscale(w,x1,x2,y1,y2); series(x,v)=Ser(x,v); set(x)=Set(x); setintersect setminus setprecision(n)=default(realprecision,n); setrand setsearch setserieslength(n)=default(seriesprecision,n); settype(x,t)=type(x,t); setunion shift shiftmul sigma sigmak(x,k)=sigma(x,k); sign signat(x)=qfsign(x); signunit(bnf)=bnfsignunit(bnf); simplefactmod(x,p)=factormod(x,p,1); simplify sin sinh size(x)=sizedigit(x); smallbasis(x)=nfbasis(x,1); smallbuchinit(x)=bnfinit(x,3); smalldiscf(x)=nfdisc(x,1); smallfact(x)=factor(x,0); smallinitell(x)=ellinit(x,1); smallpolred(x)=polred(x,1); smallpolred2(x)=polred(x,3); smith(x)=matsnf(x); smith2(x)=matsnf(x,1); smithclean(x)=matsnf(x,4); smithpol(x)=matsnf(x,2); solve sort(x)=vecsort(x); sqr sqred(x)=qfgaussred(x); sqrt srgcd(x,y)=gcd(x,y,2); string(w,x)=plotstring(w,x); sturm(x)=polsturm(x); sturmpart(x,a,b)=polsturm(x,a,b); subcyclo(p,d)=polsubcyclo(p,d); subell(e,a,b)=ellsub(e,a,b); subst sum(x,X=a,b,expr)=sum(X=a,b,expr,x); sumalt sumalt2(X=a,expr)=sumalt(X=a,expr,1); suminf sumpos sumpos2(X=a,expr)=sumpos(X=a,expr,1); supplement(x)=matsupplement(x); sylvestermatrix(x,y)=polsylvestermatrix(x,y); system tan tanh taniyama(e)=elltaniyama(e); taylor tchebi(n)=poltchebi(n); teich(x)=teichmuller(x); texprint(x)=printtex(x); theta thetanullk threetotwo=; threetotwo2=; torsell(e)=elltors(e); trace trans(x)=mattranspose(x); trunc(x)=truncate(x); tschirnhaus(x)=poltschirnhaus(x); twototwo(nf,a,b)=; type unit(x)=quadunit(x); until valuation vec(x)=Vec(x); vecindexsort(x)=vecsort(x,,1); veclexsort(x)=vecsort(x,,2); vecmax vecmin vecsort vector vvector(n,X,expr)=vectorv(n,X,expr); weipell(e)=ellwp(e); wf(x)=weber(x); wf2(x)=weber(x,2); while zell(e,P)=ellpointtoz(e,P); zeta zetak zideallog(nf,x,bid)=ideallog(nf,x,bid); zidealstar(nf,I)=idealstar(nf,I); zidealstarinit(nf,id)=idealstar(nf,id,1); zidealstarinitgen(nf,id)=idealstar(nf,id,2); znstar