It does rather depend on what sort of field you mean! When K is a number field, of course K*/K*^2 is obviously infinte, but Magma's function pSelmerGroup() (with p=2) allows you to define finite subgroups of it unramified outside finite sets of primes. This is heavily used in descent on elliptic curves. It returns the abstract abelian group (an elementary abelian 2-group when p=2) together with maps to and from K^*.
Sage could implement this since the required funtionality is in pari which Sage already uses for number field stuff. It would be good to get someone with expereince (more than me) of pari's number fields to enhance what Sage has in this direction. [This is the second response to a Magme query I have made recently. Perhaps we should keep the questions and responses somewhere separate and donate them to our friends in Sydney!] John 2008/5/28 William Stein <[EMAIL PROTECTED]>: > > On Wed, May 28, 2008 at 12:35 PM, [EMAIL PROTECTED] > <[EMAIL PROTECTED]> wrote: >> >> Hello, I'm stuck trying to do something in MAGMA (sorry but the >> support on that front seems to be lacking). Having a field K, i'm >> trying to set up K^*/(K^*)^2 with some sort of structure. >> >> Thanks and apologies if this is slightly irrelevant to the group. >> > > When you asked on irc that you had a magma question, I didn't > realize it would be this incredibly vague. Seriously, that question > is way way way too vague. > > -- William > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
