sage.sets.family: Cythonize; change MIPVariable to a subclass of FiniteFamily

[mkoeppe]

📚 Description

Fixes #31750

📝 Checklist

• I have made sure that the title is self-explanatory and the description concisely explains the PR.
• I have linked an issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[codecov-commenter]

Codecov Report

Base: 88.60% // Head: 88.58% // Decreases project coverage by -0.03% ⚠️

Coverage data is based on head (0858a2d) compared to base (8f5bbd2).
Patch coverage: 100.00% of modified lines in pull request are covered.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop   #35121      +/-   ##
===========================================
- Coverage    88.60%   88.58%   -0.03%     
===========================================
  Files         2140     2139       -1     
  Lines       397273   397017     -256     
===========================================
- Hits        352004   351678     -326     
- Misses       45269    45339      +70     

Impacted Files	Coverage Δ
src/sage/combinat/root_system/type_relabel.py	99.11% <100.00%> (ø)
...e/combinat/cluster_algebra_quiver/mutation_type.py	50.23% <0.00%> (-2.74%)	⬇️
src/sage/interfaces/qsieve.py	71.30% <0.00%> (-2.61%)	⬇️
src/sage/modular/local_comp/liftings.py	98.33% <0.00%> (-1.67%)	⬇️
src/sage/cpython/_py2_random.py	75.20% <0.00%> (-1.24%)	⬇️
src/sage/combinat/posets/poset_examples.py	87.53% <0.00%> (-1.15%)	⬇️
src/sage/schemes/elliptic_curves/hom_velusqrt.py	94.48% <0.00%> (-0.79%)	⬇️
src/sage/quadratic_forms/binary_qf.py	92.03% <0.00%> (-0.75%)	⬇️
src/sage/coding/channel.py	97.10% <0.00%> (-0.73%)	⬇️
src/sage/modular/modform/numerical.py	94.19% <0.00%> (-0.65%)	⬇️
... and 22 more

Help us with your feedback. Take ten seconds to tell us how you rate us. Have a feature suggestion? Share it here.

☔ View full report at Codecov.
📢 Do you have feedback about the report comment? Let us know in this issue.

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: 0858a2d

[tscrim]

LGTM overall except one of the tests is failing. My guess is that this is due to a circular import that was somehow being resolved beforehand. My guess for a simple fix would be to bring the Family import in sage.rings.semirings.non_negative_integer_semiring to the one method where it is called. I doubt this is being used in any tight loops that the extra import check will have an impact.

[mkoeppe]

Do you mean the failing "Build documentation" job?

[tscrim]

Yes. I don't know exactly why that isn't failing in the usual tests, but it seems like an import issue.

[mkoeppe]

It's just a funny malfunction that happens only here on this PR. The docbuild tries to import sage_docbuild after the Python file family.py has been removed but before family.pyx has been compiled.

[tscrim]

Okay, then let it be so.

Families are used so often in lower-level things they probably should have been cythonized awhile ago.

[mkoeppe]

Thanks!