a = ffgen(2^127,'a); g = ffprimroot(a); b = random(a); my(t=getwalltime());fflog(b, g);getwalltime()-t my(t=getwalltime());polmodular(101);getwalltime()-t default(nbthreads,1) my(t=getwalltime());fflog(b, g);getwalltime()-t my(t=getwalltime());polmodular(101);getwalltime()-t derivnum(x=0,zeta(x),5) lfun(1,0,5) derivnum(x=0,exp(2*x),[1,3,5]) nf=nfinit(a^2-67); bnf=bnfinit(nf); pr=idealprimedec(nf,11)[1]; modpr=nfmodprinit(nf, pr); u=bnf.fu[1] u11=nfmodpr(nf,u,modpr) o=fforder(u11) nfmodprlift(nf,u11^2,modpr) u^2 nf=nfinit(a^2-2); nf.roots u=Mod(1-a,a^2-2)^1000; subst(lift(u),a,-sqrt(2)) subst(lift(u),a,sqrt(2)) nfeltsign(nf,u) K = nfinit(y^2+1); P = idealprimedec(K,2)[1]; \\ the ramified prime above 2 nfislocalpower(K,P,-1, 2) \\ -1 is a square nfislocalpower(K,P,-1, 4) \\ ... but not a 4-th power nfislocalpower(K,P,2, 2) \\ 2 is not a square bnf=bnfinit(a^2-101329); bnr=bnrinit(bnf,1); setrand(1); lift(rnfkummer(bnr)) +(11351819629750*a-3613535788129902) N = nfinit(a^2+23); R = rnfinit(N, x^3-x-1); pr= idealprimedec(N,11); [[id.e,id.f]| id<-pr] Pr=rnfidealprimedec(R, pr[1]); [[id.e,id.f]| id<-Pr] polclass(-23) polclass(-23,5) polclass(-23,1) polmodular(5) polmodular(5,5) polmodular(5,1) G=galoisinit(x^6+108); A=alggroup(G); algissemisimple(A) apply(algdim,algsimpledec(A)) \p100 realprecision = 115 significant digits (100 digits displayed) Z=zetamultall(10); ## V=vector(#Z,i,zetamult(zetamultconvert(i,0))); ## zmult(evec) = Z[zetamultconvert(evec,2)]; zmult([2,3,5]) zetamult([2,3,5]) L=lfungenus2([x^2+x, x^3+x^2+1]); lfunan(L,10) localprec(19); lfun(L,1) E=ellinit([0,0,1,-1,0],O(37^8)); P=[0,0]; ellisoncurve(E,P) z=ellpointtoz(E,P) Q=liftall(bestappr(ellztopoint(E,z^5))) ellisoncurve(E,Q) getcurve(p)= { parfor(a=1,oo, my(E=ellinit([1,a],p)); isprime(ellsea(E,1)) ,r ,if(r,return(a))); } p=randomprime(2^128); a=getcurve(p); ## E=ellinit([1,a],p); isprime(ellcard(E)) serprec(x^2+O(x^9),x) qfeval(matid(24),[1..24]) qfeval(matid(24),[1..24],vector(24,i,1)) sumnumap(i=1,i^-(2+1/i)) matpermanent([a,b;c,d])