sum(i=1,5*10^5,primepi(i))
##

for(i=1,100,factor(3^1000-1,5*10^5))
##

maplistput(~M, k, v) =
{
  mapapply(~M, k,
      (~y)->listput(~y,v),
      ()->List(v));
}

M = Map();
maplistput(~M, "a", 1); M
maplistput(~M, "a", 2); M
maplistput(~M, "b", 3); M
maplistput(~M, "a", 4); M

Q = nfinit(x); Qi = nfinit(x^2 + 1);
nfweilheight(Q, [1, 2, -3, 101])
nfweilheight(Qi, [1, 2, -3, 101])
nfweilheight(Q, [1, x+2, x+3])

bnf = bnfinit(y^2 - 2);
bnr = bnrinit(bnf, [15, [1,0]]);
P = lift(bnrstarkunit(bnr))
rnfisabelian(bnf,P)
rnfconductor(bnf, P)[1]

E  = ellinit("11a1");
E2 = ellinit("11a2");
E3 = ellinit("11a3");
Et = elltwist(E,-7);
E2t = elltwist(E2,-7);
E3t = elltwist(E3,-7);
F = intformal(Polrev(ellan(E,1000)));
h = (-13+sqrt(-7))/22;
z = 2*real(subst(F,x,exp(2*I*Pi*h))/sqrt(-7))

ellztopoint(Et,z)
ellztopoint(E2t,z)
ellztopoint(E3t,z)
ellztopoint(E3t,z*5)
ellmaninconstant(E)
ellmaninconstant(E2)
ellmaninconstant(E3)

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

P = x^6+3*x+2;
hyperellordinate(P,1/2)
hyperellisoncurve(P,[1/2,15/8])
W = [x^6+5, x];
hyperellordinate(W,1)
hyperellisoncurve(W,[1,2])

(psi(21,10)-psi(1,10))/10!
harmonic(20,11)*1.
(psi(21+O(101^10),10)-psi(1+O(101^10),10))/10!
harmonic(20,11)+O(101^10)

zetahurwitz(3+O(11^7),0,0)
zeta(3+O(11^7))
zetahurwitz(3+O(11^7),0,-2)
-psi(O(11^7),2)/2!

quadclassunit(1-2^128)
##