Re: nfgaloisconj

[macsyma <macsyma@yahoo.co.jp>]

Thank you, Bill.

> require knowing the Galois group

Yes. So I devised a numerical method as following.


G12(f) =
{
  my(g = nfsplitting(f), d = poldegree(g),
     R = nfisincl(f, g), v = variable(f), N, M, G1, K, G2);
  localprec(max(200, floor(1.5*d)));
  N = round(10^5*[subst(R, v, s)|s <- polroots(g)]);
         /* These parameters are only heuristics. */
  M = Map(Mat([N[1]~, [1..poldegree(f)]~]));
  G1 = [Vecsmall([mapget(M, s)|s <- t])|t <- N];
  K = matinverseimage(matconcat(vector(d, i, subst(R, v, i))~), [1..d]~);
  G2 = [R*[K[s]|s <- Vec(t^(-1))]~|t <- G1];
  return([G1, G2])};