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+1

If 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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