forvec(v=[[0,1],[0,2]],print1(v," ")) [0,0] [0,1] [0,2] [1,0] [1,1] [1,2] forvec(v=[2,3],print1(v," ")) [0,0] [0,1] [0,2] [1,0] [1,1] [1,2] nf=nfinit(a^2-2); nfeltissquare(nf,-70*a+99,&z) z nfbasistoalg(nf,nfeltpow(nf,z,2)) nfeltispower(nf,-70*a+99,3,&z) z Q = bnfinit(y); bnr1 = bnrinit(Q, [7, [1]]); bnr1.cyc bnr2 = bnrinit(Q, [13, [1]]); bnr2.cyc H1 = Mat(2); bnrclassfield(bnr1, H1) H2 = Mat(2); bnrclassfield(bnr2, H2) [bnr,H] = bnrcompositum([bnr1, H1], [bnr2,H2]); bnrclassfield(bnr,H) bnf = bnfinit(a^2 - a - 9); bnr = bnrinit(bnf, [2, [0,0]]); subg = Mat(3); L = lfuncreate([bnr, subg]); P = bnrclassfield(bnr,subg,2) lfunan(P,100) == lfunan(L,100) E = ellinit([-13^2, 0]); P = Mod([2,5], a^2-2); \\ defined over Q, seen over a quadratic extension elltrace(E,P) == ellmul(E,P,2) P = Mod([-10*x^3+10*x-13, -16*x^3+16*x-34], x^4-x^3+2*x-1); ellisoncurve(E,P) Q = elltrace(E,P) ellisoncurve(E,Q) hyperelldisc([x^5,1]) W = [x^6+216*x^3+324,0]; D = hyperelldisc(W) Wn = hyperellminimalmodel(W) hyperelldisc(Wn) hyperellminimaldisc(W) Wn = hyperellminimalmodel(W,&M) M hyperellchangecurve(W, M) L = hyperellratpoints(Wn,10) hyperellisoncurve(Wn, [2,13]) my([x,y]=[2,13]);y^2+x^3*y-(2*x^6+18*x^3+1) genus2igusa(W) genus2igusa(Wn) genus2igusa(Wn,2) genus2igusa(Wn,4) lift(factormodcyclo(15, 11)) factormodcyclo(15, 11, 1) \\ single z1 = lift(factormod(polcyclo(12345),11311)[,1]); z2 = factormodcyclo(12345,11311); z1 == z2 G = matdiagonal([650, -104329, -104329]); [H,U]=qfminimize(G); H U U~*G*U lerchphi(I,2,1) -( Catalan + I * Pi^2/48 ) lerchzeta(2,1,1/4) -( Catalan + I * Pi^2/48 ) intnum(x = 0, [oo,Pi*I],besselj(0,x)) intnumosc(x = 0, besselj(0,x),Pi) setdelta(Set([2,3,5,7,11]),Set([1,2,3,4,5]))