Re: nfgaloisconj

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

On Sat, Aug 03, 2019 at 12:44:25AM +0200, Bill Allombert wrote:
> On Thu, Aug 01, 2019 at 11:40:20AM +0900, macsyma wrote:
> > > Bill Allombert on Wed, 31 Jul 2019 11:06:53 +0200
> > > 2) if the order of the Galois group is not given and the group is not
> > > the symmetric group, then nfsplitting already computes a large part of
> > > nfisincl to check that the tower stops, so we could arrange for
> > > nfsplitting to return also the embeddings.
> > 
> > That is good news.
> 
> I created a git branch 'bill-nfsplitting' that implement this.
> This adds a flag to nfpslitting to also get the embedding:
> 
> ? P=x^3-2;[Q,S]=nfsplitting(P,,1)
> %4 = [x^6+108,[-1/36*x^4-1/2*x,-1/36*x^4+1/2*x,1/18*x^4]]
> ? liftpol(subst(P,x,S*Mod(1,Q)))
> %5 = [0,0,0]

I have updated the branch bill-nfsplitting 
so that nfsplitting(P,,2) returns also the automorphisms.

? nfsplitting(x^3-2,,2)
%1 =
[x^6+108,[-x,x,-1/12*x^4-1/2*x,-1/12*x^4+1/2*x,1/12*x^4-1/2*x,1/12*x^4+1/2*x]~]

There are some minor interface issues due to the fact that nfsplitting
accept reducible and non-monic polynomials.

Cheers,
Bill