I cannot post to sage-devel so am sending this to a couple of other groups.
---------- Forwarded message ----------
From: John Cremona <john.c...@gmail.com
Date: 3 May 2012 22:47
Subject: Re: [sage-edu] Abelian Groups: comments and suggestions
To: Rob Beezer <goo...@beezer.cotse.net
, David Joyner <wdjo...@gmail.com
Don't forget that we do have things like
sage: E = EllipticCurve('11a1')
sage: T = E.torsion_subgroup()
Torsion Subgroup isomorphic to Z/5 associated to the Elliptic Curve
defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field
sage: O = T(0)
using the abelian group wrapper for the PID modules code. It's
already used in quite a few places.
On 3 May 2012 21:52, Rob Beezer <goo...@beezer.cotse.net
> On Thursday, March 15, 2012 1:50:08 PM UTC-7, William Stein wrote:
>> It would be good if somebody rewrote abelian groups from scratch
>> taking into account your comments above. Personally, I would probably
>> make the user interface be similar to Magma's abelian groups, which is
>> pretty well thought out, and will make it easier for people (like me)
>> to use both Sage and Magma:
> (Been away for a while and missed this thread.)
> Agreed. I might be the 7th attempt. I started this once, and then when I
> came back to it a year later, the category code had changed so much that it
> needed a severe rewrite (which I may have lost). But I have support this
> summer for exactly this task and a good idea of how to attack it.
> Mike O'S - I'll take your comments into account and would love further
> feedback. First attempt is at:
> General strategy: extend a good idea of Cremona and others (iirc) to build
> on William's code for finitely generated modules over PID's. A lot of
> things (like forming a subgroup, nee submodule) then come for free.
> I wanted to build one abstract class, then extend it into additive and
> multiplicative flavors. These would then be suitable for building generic
> cyclic groups, the group of units mod n, the multiplicative subgroup of a
> finite field, etc, etc.