Speedup of Poset characteristic polynomial

[trevorkarn]

📚 Description

Add special method for Moebius function computation with minimal element, add cached_method to HasseDiagram.bottom, change to sum over bottom_moebius_function

This drastically reduces the time required to compute characteristic polynomials. On commit fbb412787f, we see

sage: P = posets.SetPartitions(7)
sage: %time P.characteristic_polynomial()
CPU times: user 42.2 s, sys: 475 ms, total: 42.7 s
Wall time: 45.2 s
q^6 - 21*q^5 + 175*q^4 - 735*q^3 + 1624*q^2 - 1764*q + 720

With this commit we see:

sage: P = posets.SetPartitions(7)
sage: %time P.characteristic_polynomial()
CPU times: user 62.2 ms, sys: 1.83 ms, total: 64 ms
Wall time: 63.1 ms
q^6 - 21*q^5 + 175*q^4 - 735*q^3 + 1624*q^2 - 1764*q + 720

Fixes #34971

📝 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

None

@tscrim is a suggested reviewer.

[trevorkarn]

How do I add labels? This link https://docs.github.com/en/issues/using-labels-and-milestones-to-track-work/managing-labels seems to say I should see a gear next to "Labels" on the right sidebar, but I don't see that. Am I doing something wrong?

[mkoeppe]

I've sent you an invite to the Triage team, which has the necessary permissions

[trevorkarn]

@mkoeppe Thanks!

[tscrim]

Other than the small changes, LGTM. Yet there is a slightly bigger change that would get you some even more speed if you chose to do it.

In the depth_first_search() in the backend, there is an optional reverse parameter that is not exposed through the Sage Digraph.depth_first_search. I would expose that and use that instead of neighbors=self.neighbors_in as then it will be using the Cython code.

[codecov-commenter]

Codecov Report

Base: 88.59% // Head: 88.59% // Decreases project coverage by -0.01% ⚠️

Coverage data is based on head (2d99bd7) compared to base (fbb4127).
Patch coverage: 94.73% of modified lines in pull request are covered.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop   #35173      +/-   ##
===========================================
- Coverage    88.59%   88.59%   -0.01%     
===========================================
  Files         2140     2140              
  Lines       396961   397289     +328     
===========================================
+ Hits        351677   351965     +288     
- Misses       45284    45324      +40     

Impacted Files	Coverage Δ
src/sage/combinat/posets/posets.py	93.86% <50.00%> (-0.13%)	⬇️
src/sage/combinat/posets/hasse_diagram.py	98.81% <100.00%> (-0.08%)	⬇️
src/sage/plot/histogram.py	96.77% <0.00%> (-3.23%)	⬇️
src/sage/interfaces/qsieve.py	71.30% <0.00%> (-2.61%)	⬇️
...e/combinat/cluster_algebra_quiver/mutation_type.py	51.54% <0.00%> (-1.43%)	⬇️
src/sage/homology/matrix_utils.py	87.15% <0.00%> (-0.92%)	⬇️
src/sage/modular/quasimodform/element.py	99.14% <0.00%> (-0.86%)	⬇️
src/sage/schemes/elliptic_curves/hom_velusqrt.py	94.09% <0.00%> (-0.79%)	⬇️
src/sage/combinat/colored_permutations.py	95.46% <0.00%> (-0.60%)	⬇️
src/sage/sets/integer_range.py	91.41% <0.00%> (-0.51%)	⬇️
... and 45 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.

[trevorkarn]

In the depth_first_search() in the backend, there is an optional reverse parameter that is not exposed through the Sage Digraph.depth_first_search. I would expose that and use that instead of neighbors=self.neighbors_in as then it will be using the Cython code.

Doing this I get
sage: %time P.characteristic_polynomial()
CPU times: user 25.5 ms, sys: 817 µs, total: 26.3 ms
Wall time: 25.9 ms
q^6 - 21*q^5 + 175*q^4 - 735*q^3 + 1624*q^2 - 1764*q + 720

compared to
sage: %time P.characteristic_polynomial()
CPU times: user 63.5 ms, sys: 1.75 ms, total: 65.3 ms
Wall time: 64.8 ms
q^6 - 21*q^5 + 175*q^4 - 735*q^3 + 1624*q^2 - 1764*q + 720

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: 2d99bd7

[tscrim]

Thanks. LGTM.