On Sat, Jun 6, 2009 at 1:18 AM, davidloeffler<dave.loeff...@gmail.com> wrote: > > On Jun 6, 3:47 am, William Stein <wst...@gmail.com> wrote: > >> * Galois theory and ramification groups for p-adic extensions (needs >> the previous features) > > I wrote a (very simplistic) implementation of Artin symbols and > decomposition and ramification groups a few months back for extensions > of *number fields*, so we have this via the canonical dumb algorithm: > find an extension of number fields whose local extension at some prime > is the p-adic extension you want.
Nice, thanks! > >> VII. Modules >> >> * Sage has nothing for modules over Dedekind domains (except over >> ZZ): this is an extremely important building block for certain >> algorithms (e.g., arithmetic in quaternion algebras over number >> fields), so needs to get implemented. I recently wrote code for >> general modules over ZZ, but it isn't in Sage yet. >> >> PROJECT: Finish modules over ZZ, optimize >> >> PROJECT: Extend modules over ZZ to modules over a PID > > Last week I wrote some code for Hermite form, which is the key linear- > algebra step for this; see trac #6178. So we have free modules over an > arbitrary PID (me) and arbitrary fg modules over ZZ (you), and > combining these probably won't be very hard. Actually, the code I wrote for "arbitrary fg modules over ZZ" should actually work for arbitrary fg modules over a PID. It was all written generically, assuming HNF and SNF algorithms. Of course, it's untested so I'm sure when we test it something will come up. William > > David > > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
