P = polfromroots([1,2,3,4,5])
nfroots(,%)

forvec(v=[[0,1],[0,2]],print1(v," "))
forvec(v=[2,3],print1(v," "))

f(p)=vecmin(abs(qfbsolve(Qfb(1,0,1),p)));
export(f);
S=0;n=0; parforprimestep(p=2,100000,Mod(1,4),\
    f(p), v, S+=v/sqrt(p); n++);
S/n-(4-2*sqrt(2))/Pi

C = quadclassunit(5*13)
C.normfu
C = quadclassunit(13*17)
C.normfu

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([1,2,3,4,5]);
F=ellinit([61/16,127/32]);
urst=ellisisom(E,F)
ellchangecurve(E,urst)[1..5]

E = ellinit([-13^2, 0]);
P = Mod([2,5], a^2-2);

elltrace(E,P) == ellmul(E,P,2)

P = [-10*x^3+10*x-13, -16*x^3+16*x-34];
P = Mod(P, x^4-x^3+2*x-1);
ellisoncurve(E,P)
Q = elltrace(E,P)
ellisoncurve(E,Q)

E = ellinit([0,1,0,-3,1]); elliscm(E)
ellisomat(E)[2]
Enf = ellinit(E,nfinit(a^2+2));
elliscm(Enf)
ellisomat(Enf)
F=ellinit([a],nfinit(polclass(-23,,a)));
elliscm(F)
polisclass(minpoly(F.j))

j = ellsupersingularj(1009)
ellissupersingular(j)
a = ffgen([1009,2],'a);
j = ellsupersingularj(a)
ellissupersingular(j)

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

M=matdiagonal([1,1,1,-(53!+1)]);
qfsolve(M)
##
F=factor(matdet(M));
##
qfsolve([M,F])
##

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]))

plotinit(1);plotmove(1,0,0); 
plotell(1,50,50); plotdraw([1,100,100]);

7#
2*3*5*7
Qfb(2*x^2+3*x+4)
Qfb([2,3,4])
Qfb([2,3/2;3/2,4])
M=matrix(3,4);[#M, #M~]
digits(11,-2)