Add .boundary_complex() method for simplicial polytopes

[jplab]

The boundary of polytopes are nice and relatively well-behaved cell complexes.

When the polytope is simplicial, its boundary is a simplicial complex. This ticket implements a method to return that simplicial complex.

Depends on #27974

CC: @LaisRast @kliem @tscrim @jhpalmieri

Component: geometry

Keywords: polytopes, simplicial complex, days100

Author: Jean-Philippe Labbé

Branch: 7432567

Reviewer: Laith Rastanawi

Issue created by migration from https://trac.sagemath.org/ticket/28248

[jplab]

Dependencies: #27974

[jplab]

Branch: u/jipilab/28248

[jplab]

Commit: 21ae478

[sagetrac-git]

Changed commit from 21ae478 to 890c350

[sagetrac-git]

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

890c350

Added to quickref

[sagetrac-coulbois]

Author: Jean-Philippe Labbé

[LaisRast]

comment:5

Since you only need the combinatorial data of the polytope, it would be much faster to use the .incidence_matrix() instead of the .faces() (or facets() here).
(You can see the difference, for instance, clearly if you take the dual of the 7-permutahedron)

[kliem]

comment:6

Replying to @LaisRast:

Since you only need the combinatorial data of the polytope, it would be much faster to use the .incidence_matrix() instead of the .faces() (or facets() here).
(You can see the difference, for instance, clearly if you take the dual of the 7-

The difference will only be minor, once #27063 is done.
It's still going to be faster to just take the incidence matrix, but not by much.

Try it out tuple(CombinatorialPolyhedron(P).face_iter(P.dimension()-1)) vs P.incidence_matrix().

Be aware that the incidence matrix is cashed.