On 11/1/07, Utpal Sarkar <[EMAIL PROTECTED]> wrote:
> 1) Does anyone know if sage has functions that compute the fixed field
> for a given subgroup of the Galois group?

Short answer -- no, not yet.
Just out of curiosity, do you want to do this in a setting where the
computation is very difficult?  Or just sort of routine small computations?
E.g., could you give an example of the field, etc.?

> 2) Is there a function to obtain the Artin map of an Abelian
> extension, or at least for the Hilbert class field of a quadratic
> field?

Maybe PARI (included in SAge) can do some of this.  I don't think
Sage itself has an easy interface to this functionality yet.

William

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