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Computing Galois groups


From: Fabio Stumbo
Subject: Computing Galois groups
Date: Sat, 7 May 2022 16:13:09 +0200
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:91.0) Gecko/20100101 Thunderbird/91.8.1

Hi,

I am trying to compute some Galois groups with Axiom.

A way is to go after the example given in section 8.13 of the manual which follows closely and implements the original definition by Galois of the Galois group.

I am trying a different way: I would like to exploit a theorem by Kronecker which provides an easy algorithm to compute the Galois group of a given polynomial.

I wrote the function which implements the algorithm and it works... sometimes. :(

Which means that I have some problems.

My question is: is there anybody that is willing to help me to fix it if I post the code?

The code is not very long (about 40-50 lines) but it needs to be explained, so I am asking before to make the effort.

TIA

Fabio




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