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macsyma on Tue, 30 Jul 2019 03:44:52 +0200
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- To: "pari-users@pari.math.u-bordeaux.fr" <pari-users@pari.math.u-bordeaux.fr>
- Subject: Re: nfgaloisconj
- From: macsyma <macsyma@yahoo.co.jp>
- Date: Tue, 30 Jul 2019 10:44:45 +0900 (JST)
- Delivery-date: Tue, 30 Jul 2019 03:44:52 +0200
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- Reply-to: macsyma <macsyma@yahoo.co.jp>
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.
G12 can be applied even if G is not weakly super-solvable. However, for example, the processing time of https://www.math.u-bordeaux.fr/~ballombe/polynomials.gp takes 20 to 30 times that of galoisinit + nfgaloisconj, so I'm hoping that you make speed up nfisincl and nfsplitting.
macsyma