Implement Milnor fiber and Coxeter complexes

[tscrim]

Implements Milnor fiber and Coxeter complexes and their associated posets. #34936

Dependencies: #34912

[codecov-commenter]

Codecov Report

Base: 88.59% // Head: 88.59% // Increases project coverage by +0.00% 🎉

Coverage data is based on head (b52defc) compared to base (84eebf0).
Patch coverage: 96.96% of modified lines in pull request are covered.

Additional details and impacted files

@@            Coverage Diff            @@
##           develop   #35038    +/-   ##
=========================================
  Coverage    88.59%   88.59%            
=========================================
  Files         2140     2140            
  Lines       396961   397093   +132     
=========================================
+ Hits        351671   351804   +133     
+ Misses       45290    45289     -1     

Impacted Files	Coverage Δ
src/sage/schemes/toric/sheaf/klyachko.py	92.43% <ø> (ø)
...age/categories/finite_complex_reflection_groups.py	83.84% <95.29%> (+4.72%)	⬆️
src/sage/categories/finite_coxeter_groups.py	95.85% <100.00%> (+1.00%)	⬆️
src/sage/groups/additive_abelian/qmodnz.py	91.48% <0.00%> (-2.13%)	⬇️
src/sage/combinat/combination.py	93.50% <0.00%> (-1.50%)	⬇️
src/sage/doctest/forker.py	80.24% <0.00%> (-1.48%)	⬇️
src/sage/groups/generic.py	88.34% <0.00%> (-0.68%)	⬇️
src/sage/graphs/graph_plot.py	84.33% <0.00%> (-0.57%)	⬇️
src/sage/combinat/constellation.py	91.18% <0.00%> (-0.41%)	⬇️
src/sage/groups/cactus_group.py	98.89% <0.00%> (-0.37%)	⬇️
... and 23 more

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[tscrim]

@fchapoton Would you be willing to review this?

[fchapoton]

I can try, but I cannot really check the code.

[tscrim]

Thank you. No problem if you can't. I can ask Vic Reiner to see if he would be willing to review the mathematical portion. I can also split off the Coxeter group portion too.

[fchapoton]

one linter is not green, about E305

[tscrim]

one linter is not green, about E305

Done, although the linter spec is not well-defined here as it is about blanklines before a class.

[fchapoton]

Looks good. Is there no way to avoid looping over all elements ?

Too bad that the posets gets huge very fast, so that one cannot even hope to reach H4 (62881 elts) or D5 (12483 elts). They seem to have nice Coxeter polynomials, by the way.

[tscrim]

The number of maximal elements is equal to the number of elements in the group, so we have to iterate over all elements in some fashion. I might be able to rework things so that we are building the group elements out, but this seems more technical and I am not convinced it will be faster in the end.

[github-actions]

Documentation preview for this PR (built with commit 6d9ee05; changes) is ready! 🎉

[fchapoton]

ok, let's get this in.

[tscrim]

Thank you!