Bill Allombert on Sat, 03 Aug 2019 23:06:23 +0200

 Re: nfgaloisconj

• To: pari-users@pari.math.u-bordeaux.fr
• Subject: Re: nfgaloisconj
• From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
• Date: Sat, 3 Aug 2019 23:06:17 +0200
• Delivery-date: Sat, 03 Aug 2019 23:06:23 +0200
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```On Sat, Aug 03, 2019 at 07:38:26PM +0200, Bill Allombert wrote:
> On Tue, Jul 30, 2019 at 10:44:45AM +0900, macsyma wrote:
> > Thank you, Bill.
> >
> > > what it does
> >
> > In my code, G1 is a permutation representation, G2 is a polynomial
> > representation of G the Galois group of f over Q. The principle is
> > directly linked to Q-automorphism, that for each m_j in G, the
> > permutation of the roots of f is obtained by replacing alpha the
> > primitive element in the root representation of f with m_j(alpha) the
> > image of alpha that is a root of g. One can consider alpha =
> > polroots(g)[1], m_j(alpha) = polroots(g)[i] in G12 code.
>
> Could you tell me why you replaced
>
> K=lindep(concat(x,R)); K = K[2..-1]/-K[1];
>
> by
>
> K=matinverseimage(matconcat(vector(d,i,subst(R,v,i))~),[1..d]~);

Ah I see, sometimes lindep() return a solution with K[1]==0.

This is an alternative that avoid this problem:

K=matinverseimage(matconcat([Colrev(r,d)|r<-R]),Colrev(x,d));

this should be faster than your solution.

Cheers,
Bill.

```

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