Add simplicity and simpliciality to polyhedra

[kliem]

In #27086 we have implemented simplicity and simpliciality for combinatorial polyhedra. We expose this methods in Polyhedron_base.

The methods return the largest k such that the polytope is k-simple/simplicial. In case of unbounded polyhedra a NotImplementedError is raised.

A polytope is k-simplicial if every k-face is a simplex. It is k-simple if its dual/polar is k-simplicial.

CC: @jplab @LaisRast

Component: geometry

Keywords: simplicity, simpliciality, polytopes

Author: Jonathan Kliem

Branch/Commit: 573dbfc

Reviewer: Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/29186

[kliem]

Commit: 3406851

[kliem]

Branch: public/29186

[kliem]

New commits:

3406851

added simplicity and simpliciality to polyhedra

[jplab]

Reviewer: Jean-Philippe Labbé

[jplab]

comment:2

Some comments:

-        Return the largest `k` such that the polytope is `k`-simple.
-
-        Return the dimension in case of a simplex.
-
-        A polytope `P` is `k`-simple, if every `(d-1-k)`-face
-        is contained in exactly `k+1` facets of `P` for `1 <= k <= d-1`.
-
-        Equivalently it is `k`-simple if the polar/dual polytope is `k`-simplicial.
+        Return the largest integer `k` such that the polytope is `k`-simple.
+
+        A polytope `P` is `k`-simple, if every `(d-1-k)`-face
+        is contained in exactly `k+1` facets of `P` for `1 <= k <= d-1`.
+        Equivalently it is `k`-simple if the polar/dual polytope is `k`-simplicial.
+        If `self` is a simplex, it returns its dimension.

similarly:

-        Return the largest `k` such that the polytope is `k`-simplicial.
-
-        Return the dimension in case of a simplex.
-
-        A polytope is `k`-simplicial, if every `k`-face is a simplex.
+        Return the largest interger `k` such that the polytope is `k`-simplicial.
+
+        A polytope is `k`-simplicial, if every `k`-face is a simplex.
+        If `self` is a simplex, returns its dimension.

Once this is fixed and the bots gives a green light, you can set this on positive review on my behalf.

[kliem]

Changed commit from 3406851 to 297c686

[kliem]

Changed branch from public/29186 to public/29186-reb

[kliem]

New commits:

c9ff832	added simplicity and simpliciality to polyhedra
297c686	improved documentation

[mkoeppe]

comment:4

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[jplab]

comment:5

Small things:

+        is contained in exactly `k+1` facets of `P` for `1 <= k <= d-1`.

You can use \leq there.

Otherwise, looks good, once this is done you can put this on positive review on my behalf.

[kliem]

Changed branch from public/29186-reb to public/29186-reb2

[kliem]

Changed commit from 297c686 to 573dbfc

[kliem]

New commits:

d6e1bf6	added simplicity and simpliciality to polyhedra
f4689d3	improved documentation
573dbfc	latex \lex

[vbraun]

Changed branch from public/29186-reb2 to 573dbfc