V = binomial(10) foreach(V,n,print1(sigma(n)," ")) 1 18 78 360 576 728 576 360 78 18 1 my(s=0);parforeach(V,n,sigma(n),S,s+=S);s gcdext(135,95) [,v,d]=gcdext(135,95); [v,d] my([u,,d]=gcdext(135,95)); [u,d] setdebug() setdebug("qflll",5); nfinit(x^8+1); setdebug("qflll") default(debug,0) permcycles(Vecsmall([2,7,1,8,4,5,9,10,3,6])) permcycles(Vecsmall([3,1,4,5,9,2,6,8,7])) [M,C] = halfgcd(23,59) M*[23,59]~ P = truncate(sqrt(1+x+O(x^4))); Q = x^4; [M,C] = halfgcd(P, Q) M*[P,Q]~ bnf = bnfinit(a^2+47); bnr = bnrinit(bnf,77); bnr.cyc bnr3 = bnrinit(bnf,77,,3); bnr3.cyc bnrclassfield(bnr3) p = nextprime(2^64); \\ bnr = bnrinit(bnf,p); very very slow bnr = bnrinit(bnf,p,, (2*3*5*7)^10); \\ fast bnr.cyc F=bnrclassfield(bnr,3) \\ R = rnfconductor(bnf,F[1]); \\very slow R = rnfconductor(bnf,F[1],1); \\fast [cnd,bnr2,subg] = R; cnd bnr2.cyc [cnd,cndf] = rnfconductor(bnf,F[1],2); cnd cndf P = x^5+20*x+16; polgalois(P) G = galoissplittinginit(P); G.pol == nfsplitting(P) galoisidentify(G) galoisfixedfield(G,[G.group[2],G.group[6]],1) E = ellinit([2,3]); [N,k,vga] = lfunparams(E) L = lfunqf(matdiagonal([1,2,3,4])); Ld = lfundual(L); eps = lfunrootres(L)[3] lfunlambda(L,Pi)/lfunlambda(Ld,2-Pi) polylogmult([2,2,2],[1,-1,1]) v = [3,5,2,2]; vd = zetamultdual(v) zetamultdual(vd) zetamult(v) zetamult(vd) bz=besseljzero(Pi,1) besselj(Pi,bz) bz=besselyzero(2,10) bessely(2,bz) hypergeom([1,1,1],[5/3,5/3],z+O(z^5)) hypergeom([1,1,1],[5/3,5/3],1/2) hypergeom([1,1,1],[5/3,5/3],1/2+z+O(z^5)) mf=mfinit([1,16,1],1); S=mfeigenbasis(mf)[1]; mfcoef(S,101) ramanujantau(101,16) mfcoef(S,10001) ramanujantau(10001,16) l=lambertw(-1/4) l*exp(l) l=lambertw(-1) l*exp(l) l=lambertw(-1,1) l*exp(l) eulerreal(100) eulerfrac(100) Qfb(1,2,3).disc