What if it is inconvenient to define multiplication in terms of the
basis (e.g. what if we don't want to work with a basis unless it is
really necessary)?
What if we have infinite dimensional spaces but multiplication can
still be defined (without using a basis)?
Best
Jonas
On 28.11.2015 20:49, Travis Scrimshaw wrote:
> 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.
A lot of the functionality has also been abstracted up to the category
ModulesWithBasis. However, I agree that there are a large number of
indirections that we might want to simplify, and CombinatorialFreeModule
would likely benefit from more cythonization (and common abstraction
with sparse free modules).
Best,
Travis
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