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. > 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. David --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
