On Wed, Sep 13, 2017 at 12:02:37PM +0000, johnathon simons wrote: > Dear all, > > Hope the the remainder of the Summer is treating you well. I've a brief > question: > > Once one has realized a finite group G (say the Mathieu group M12) as > a Galois group over Q, is there any method on how to extract a > polynomial whose Galois Group is M12? I've seen some papers where they > state the polynomials over Q whose Galois group is M12, but I've > never actually seen anything method of doing so. If so, is such an > implementation possible on GAP.
How do you give the realization ? In general, even when one has built a field with the right Galois group, obtaining a polynomial can be computationaly challenging, either due to its size of the polynomial or of intermediary computations. For example it is easy to find a field with Galois group 31:3. However computing a corresponding deg-31 polynomial is much harder, so you will have to add extra conditions on the field so that the computation is manageable. Cheers, Bill. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
