Changing brick polytopes of subword complexes to brick polyhedra

[DennisJahn]

generalize the method brick_polytope() of sage.combinat.subword_complex.py to brick_polyhedron() as done in

https://arxiv.org/abs/2103.03715

Depends on #32669

CC: @stumpc5 @jplab @kliem

Component: combinatorics

Keywords: subword complex, brick vector, brick polyhedron, brick polytope

Author: Dennis Jahn

Branch/Commit: u/gh-DennisJahn/changing_brick_polytopes_of_subword_complexes_to_brick_polyhedra @ b3abcc9

Issue created by migration from https://trac.sagemath.org/ticket/32681

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

436a8ba

fixing gap3 doctests

[stumpc5]

comment:36

The code looks good to me! @tscrim, @fchapoton: I am sure you have some comments, at least concerning the formatting and/or the doctests. Could you maybe have a quick look? -- Thanks!

[fchapoton]

comment:37

doc does not build

 /home/sagemath/sage/src/sage/combinat/subword_complex.py:docstring of sage.combinat.subword_complex.SubwordComplex.brick_polyhedron:50: WARNING: citation not found: JS2021

[fchapoton]

comment:38

the new deprecation must be doctested, for exemple in the module documentation near the top of the file

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 436a8ba to b3abcc9

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

b3abcc9

one more function, new doctest for new deprecation

[DennisJahn]

comment:40

Replying to Frédéric Chapoton:

doc does not build

 /home/sagemath/sage/src/sage/combinat/subword_complex.py:docstring of sage.combinat.subword_complex.SubwordComplex.brick_polyhedron:50: WARNING: citation not found: JS2021

The reference [JS2021] was added in #32669 I added the doctest for the new deprecation

[fchapoton]

comment:41

I disagree with the replacement of non-gap3-optional doctests with gap3 optional doctests.

[DennisJahn]

comment:42

Replying to Frédéric Chapoton:

I disagree with the replacement of non-gap3-optional doctests with gap3 optional doctests.

The replacement of brick_polytope() by brick_polyhedron() requires the computation of the associated Bruhat cone which is implemented for finite real reflection groups and needs gap3.

[tscrim]

comment:43

Sorry it took me a while to get to this.

It shouldn't be hard to implement the bruhat_cone for Weyl groups. However, you still are removing functionality. This needs to be justified, and, if deemed to be reasonable, deprecated. At least in the short term, you can just have a isinstance(G, RealReflectionGroup): to do the new implementation while keeping the old since they are both fairly short.

Also, I think it would be easier to replace the string sign with a boolean positive[_roots].

[stumpc5]

comment:44

I think using isinstance(G, RealReflectionGroup) is a reasonable workaround.