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Dear GAP-Forum,

David Burggraf asked:

I'm just wondering if anyone know if it's possible for GAP4 to compute the

galois groups of the following polynomials over the rationals:x^12-12*x+1 x^12-12/11*x^11+1If so, an explanation of how it is done would be greatly appreciated.

GAP4 unfortunately does not yet have the functionality to recognize Galois

groups. (The functionality exists in GAP3 via the `Galois' command. This

will be ported to GAP4 at a later point.)

However in this particular case one can prove that both polynomials have

Galois group S12 also in GAP4 by factoring modulo different primes, which

don't divide the discriminant.

I can give you more details if you want (I'm not sure from your question

whether you need a command to do it or whether you want an explanation of

the mathematics involved).

I hope this helps,

Alexander Hulpke

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