\p 38
\e
\\ Initialisations diverses
nfpol=x^5-5*x^3+5*x+25
qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
fa=[11699,6;2392997,2;4987333019653,2]
setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
nf=nfinit(nfpol)
nf1=nfinit(nfpol,2)
nfinit(nfpol,3)
nfinit(nfpol,4)
nf3=nfinit(x^6+108);
nf4=nfinit(x^3-10*x+8)
setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
setrand(1);bnfinit(x^2-x-100000,1)
\p19
setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
\p38
bnrinit(bnf,[[5,3;0,1],[1,0]],1)
bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
rnfinit(nf2,x^5-x-2)
\\
bnfcertify(bnf)
setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
setrand(1);bnfclassunit(x^2-x-100000)
setrand(1);bnfclassunit(x^2-x-100000,1)
setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
setrand(1);bnfclgp(17)
setrand(1);bnfclgp(-31)
setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
bnrconductor(bnf,[[25,13;0,1],[1,1]])
bnrconductorofchar(bnr,[2])
\\ bnfdecodemodule(bnf,
\\ bnfisintnorm
\\ bnfisnorm
bnfisprincipal(bnf,[5,1;0,1],0)
bnfisprincipal(bnf,[5,1;0,1])
\\ bnfissunit
bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
\p19
bnfmake(sbnf)
\p38
bnfnarrow(bnf)
bnfreg(x^2-x-57)
bnfsignunit(bnf)
\\ bnfsunit(bnf,
bnfunit(bnf)
bnrclass(bnf,[[5,3;0,1],[1,0]])
bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
bnrclassno(bnf,[[5,3;0,1],[1,0]])
lu=ideallist(bnf,55,3);
bnrclassnolist(bnf,lu)
bnrdisc(bnr,Mat(6))
bnrdisc(bnr)
bnrdisc(bnr2,,,2)
bnrdisc(bnr,Mat(6),,1)
bnrdisc(bnr,,,1)
bnrdisc(bnr2,,,3)
bnrdisclist(bnf,lu)
bnrdisclist(bnf,20,,1)
bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
dirzetak(nf4,30)
factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
\\
vp=idealprimedec(nf,3)[1]
idx=idealmul(nf,matid(5),vp)
idealinv(nf,idx)
idy=idealred(nf,idx,[1,5,6])
idx2=idealmul(nf,idx,idx)
idt=idealmul(nf,idx,idx,1)
idz=idealintersect(nf,idx,idy)
aid=[idx,idy,idz,matid(5),idx]
bid=idealstar(nf2,54,1)
vaid=[idx,idy,matid(5)]
haid=[matid(5),matid(5),matid(5)]
idealadd(nf,idx,idy)
idealaddtoone(nf,idx,idy)
idealaddtoone(nf,[idy,idx])
idealappr(nf,idy)
idealappr(nf,idealfactor(nf,idy),1)
\\ idealchinese
idealcoprime(nf,idx,idx)
idealdiv(nf,idy,idt)
idealdiv(nf,idx2,idx,1)
idf=idealfactor(nf,idz)
idealhnf(nf,vp)
idealhnf(nf,vp[2],3)
ideallist(bnf,20)
\\ ideallistarch
ideallog(nf2,w,bid)
idealmin(nf,idx,[1,2,3])
idealnorm(nf,idt)
idp=idealpow(nf,idx,7)
idealpow(nf,idx,7,1)
idealprimedec(nf,2)
idealprimedec(nf,3)
idealprimedec(nf,11)
idealprincipal(nf,Mod(x^3+5,nfpol))
idealtwoelt(nf,idy)
idealtwoelt(nf,idy,10)
idealstar(nf2,54)
idealval(nf,idp,vp)
ideleprincipal(nf,Mod(x^3+5,nfpol))
\\
ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
matbasistoalg(nf,bc)
nfbasis(x^3+4*x+5)
nfbasis(x^3+4*x+5,2)
nfbasis(x^3+4*x+12,1)
nfbasistoalg(nf,ba)
nfbasis(p2,0,fa)
da=nfdetint(nf,[a,aid])
nfdisc(x^3+4*x+12)
nfdisc(x^3+4*x+12,1)
nfdisc(p2,0,fa)
nfeltdiv(nf,ba,bb)
nfeltdiveuc(nf,ba,bb)
nfeltdivrem(nf,ba,bb)
nfeltmod(nf,ba,bb)
nfeltmul(nf,ba,bb)
nfeltpow(nf,bb,5)
nfeltreduce(nf,ba,idx)
nfeltval(nf,ba,vp)
nffactor(nf2,x^3+x)
\\ nffactormod
aut=nfgaloisconj(nf3)
nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
nfhilbert(nf,3,5)
nfhilbert(nf,3,5,idf[1,1])
nfhnf(nf,[a,aid])
nfhnfmod(nf,[a,aid],da)
nfisideal(bnf[7],[5,1;0,1])
nfisincl(x^2+1,x^4+1)
nfisincl(x^2+1,nfinit(x^4+1))
nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
nfroots(nf2,x+2)
nfrootsof1(nf)
nfsnf(nf,[as,haid,vaid])
nfsubfields(nf)
polcompositum(x^4-4*x+2,x^3-x-1)
polcompositum(x^4-4*x+2,x^3-x-1,1)
polgalois(x^6-3*x^2-1)
polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
polred(x^4+576,1)
polred(x^4+576,3)
polred(p2,0,fa)
polred(p2,1,fa)
polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
polredord(x^3-12*x+45*x-1)
polsubcyclo(31,5)
setrand(1);poltschirnhaus(x^5-x-1)
\\
\\ rnfalgtobasis
aa=rnfpseudobasis(nf2,p)
rnfbasis(bnf2,aa)
\\ rnfbasis
\\ rnfcharpoly
\\ rnfdedekind
\\ rnfdet
rnfdisc(nf2,p)
\\ rnfeltabstorel
\\ rnfeltdown
\\ rnfeltreltoabs
\\ rnfeltup
rnfequation(nf2,p)
rnfequation(nf2,p,1)
rnfhnfbasis(bnf2,aa)
\\ rnfidealabstorel
\\ rnfidealdown
\\ rnfidealhnf
\\ rnfidealmul
\\ rnfidealnormabs
\\ rnfidealnormrel
\\ rnfidealreltoabs
\\ rnfidealtwoelt
\\ rnfidealup
rnfisfree(bnf2,aa)
\\ rnfisnorm
\\ rnflllgram
\\ rnfpolred
rnfsteinitz(nf2,aa)
\\
nfz=zetakinit(x^2-2);
zetak(nfz,-3)
zetak(nfz,1.5+3*I)
\\
setrand(1);quadclassunit(1-10^7,,[1,1])
setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
sizebyte(%)
getheap
print("Total time spent: ",gettime);
\q