Re: nfgaloisconj

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sat, Jul 27, 2019 at 11:24:06AM +0900, macsyma wrote:
> 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])};

This looks great. Could you tell me what it does ?

Cheers,
Bill.