Hi Jonas,
On 2015-11-27, Jonas Jermann <jjerma...@gmail.com> wrote:
> It sometimes makes sense to view (homogeneous) elements of a graded
> ring as module elements (because operations might be specific to that
> module and not to the whole ring).
>
> On the other hand we still want to be able to multiply those *module*
> elements of possibly different homogeneous parts.
>
> So if we inherit from CommutativeAlgebraElement we get the __mul__
> operation but we can still treat elements as module elements...
That's what I recommend to do. See the thematic tutorial on coercion and
categories ("How to create new algebraic structures").
> Or what is the "modern" approach/solution for this?
It is possible to do everything based on
sage.combinat.free_module.CombinatorialFreeModule. It is a clean
mathematical approach (for defining something like a multiplication on
a module, it is enough to define what happens on a basis). But it is
pure python code and it uses an amazing amount of indirections. So, I
would recommend against using it for time-critical applications. And
that's part of the motivation for the two tickets that I mentioned before:
I want to make it possible to define a multiplication action in some
Cython file, and let the categoy framework (written in Python) put the
appropriate fast Cython methods into the parent's action cache.
Best regards,
Simon
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