In view of the previous thread, I thought I'd mention that I wrote up some code a while ago to be able to use pari to compute arithmetic invariants (ramification, etc) while viewing the Galois group of a possibly non-Galois field as a group of permutations of the roots of the original non-Galois polynomial. The code is available at https://github.com/rharron/ArtinGalois .
One must communicate between pari and gap, which is currently done with a clunky collection of dictionaries. I also fixed a few other problems. Currently, the code is written as a GaloisGroups_v3 object that inherits from v2 so as to only behave slightly differently. The goal of the project is to be able to compute with Artin representations in Sage. That part of the code is quite prelminary (though it can already compute conductors, Euler factors, some root numbers, and has an interface to the Dokchitser L-function calculator). The galois group code is functional, though some work would be required to make it nice enough to incorporate into Sage. Part of what was holding me up regarding the Galois group code was to ask people how they felt the code should be incorporated. For instance, is a class inheriting from GaloisGroup_v2 the best option? (Also note that the code is currently based off of version 5.12 of Sage) Anyway, if you have any opinions, I'd be happy to hear them. Best, Rob -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
