Since no one has emailed intelligent comments yet, I'll add my own
not-so-intelligent but hopefully encouraging ones below:-)
On Wed, Aug 27, 2008 at 3:18 PM, John Cremona <[EMAIL PROTECTED]> wrote:
>
> Currently in Sage, AbelianGroups are all multiplicative. There's a
> TODO in abelian_groups.py which asks to implement additive groups.
>
> As I got fed up with this sort of thing:
>
> sage: E=EllipticCurve('11a1')
> sage: T=E.torsion_subgroup()
> sage: list(T)
> [1, P, P^2, P^3, P^4]
>
> (where it should be something like [0,P,2*P,3*P,4*P] ), I started to
> try to adapt abelian_group.py to allow for multiplicative groups.
> I had some success (after changing just that file, all the original
> doctests still passed, since I had it take the group operation to be
> multiplication by default).
Agreed, this definitely needs fixing.
>
> But then I found that AbelianGroupElement was derived from
> MultiplicativeGroupElement which in turn is derived from
> MonoidElement, while AdditiveGroupElement is derived from
> ModuleElement. These two do have a common ancestor, plain Element.
> I think will make it hard to write common code for additive group
> elements and multiplicative group elements.
I don't see the problem here. It seems to me that the only
problem would arise if you are building a method which maps a
group (G,*) to a group (G,+) (in which case maybe you get something
circular), but I don't see why this is needed. I may be totally naive about this
though.
>
> I think it might work to use MultiplicativeGroupElement even when the
> operation is addition, but that would seem rather perverse. But it is
> perhaps notable that AdditiveGroupElement is hardly ever used in Sage:
> the only places are ine the definition of EllipticCurvePoint_field and
> JacobianMorphism_divisor_class_field.
>
> I would welcome some comments on what we might do about this. In the
> meantime I'll try to get AbelianGroupElements to behave additively
> even though they are derived from MultiplicativeGroupElements.
I'm not convinced this is the "right" procedure, but if it works and
is well-documented
then that is better than nothing!
>
> Relevant still-open tickets are:
>
> #1849: [with patch (part 1 of 2); not ready for review] rewrite abelian groups
> -- showing that William did a whole lot of work on this back in
> January/February (I remember, we were working in the same room at the
> time) which was not completed;
>
> and
>
> #3127: [duplicate] abelian groups (are lame?) -- bug in comparison of
> subgroups ...
> -- which is closed, but contains the comment from William:
> WARNINGS:
>
> 1. David Roe is recently rumored to be rewriting abelian groups.
> 2. I recently rewrote abelian groups but my patch rotted: #1849
> 3. There are other known problems with subgroups of abelian groups: #2272
>
>
> John
>
> >
>
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