Speed improvements for categories with axioms

[simon-king-jena]

With the "axiomatic" approach towards categories introduced in #10963, we are now using join categories far more frequently than in the past. This involves many little operations (sorting, computation of index, ...) that should be made as fast as possible.

Hence, this ticket is about using Cython and optimizing basic algorithms in sage.categories.category and friends.

Depends on #10963
Depends on #15801
Depends on #16309

CC: @nthiery @mezzarobba

Component: categories

Keywords: cython performance categories

Author: Simon King

Branch/Commit: 5bad2ff

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/16296

[nathanncohen]

comment:2

(curious)

[simon-king-jena]

comment:3

First observation: Moving sage.categories.category to Cython is not trivial, since it relies on abstract_method, which currently only accepts Python functions. Hence, abstract_method needs to be cythoned, too, or at least needs to be more permissive in the assertion that the input is types.FunctionType.

[simon-king-jena]

comment:4

Good: If one removes the assertion from abstract_method, then Sage starts.

[simon-king-jena]

Branch: u/SimonKing/ticket/16296

[simon-king-jena]

comment:7

I have pushed an initial branch (starting with #10963, of course), changing the assertion so that both types.FunctionType and cython_function_or_method are permitted (no idea how to test the latter more elegantly than by the name of the type...), and I changing AbstractMethod.__repr__ so that it gives comparable output for both Python and Cython methods.

Note: I don't think we should Cython AbstractMethod. After all, they are just placeholders for "real" methods and are thus not time-critical.

With the branch, Sage starts.

---

Last 10 new commits:

f262faa	trac #16269: Merged with 6.2.rc1
338cc5b	trac #16269: Reviewer's remarks
8ac32c2	#16280: Fix call for FiniteEnumeratedSet's of plain Python objects
4e27454	#16280: Trivial doctest fixes
f67d82e	trac #16269: Merged with #16280
0a54b68	Trac 16269: little improvements + line folding in the doctest output
b5ad803	Trac 16269 (or follow up): optimize CartesianProduct._cartesian_product_of_elements
d2bc8b2	Merge cartesian product functionalities from '#16269 and #16288' into categories/axioms-10963
e9c3586	Some fixes to the docs and to comments in the code (review patch)
2cc9090	Start with transitioning basic category code to Cython

[simon-king-jena]

Commit: 2cc9090