CombinatorialPolyhedron: ridge_graph -> facet_graph

[kliem]

In order to make CombinatorialPolyhedron more consistent with Polyhedron, we replace ridge_graph by facet_graph.

In case of of the half space this makes a difference, as there is a facet, but no ridges.

For now we keep ridge_graph and add a deprecation warning.

While we are at it, we fix some bugs:

• CombinatorialPolyhedron.ridges(names=False, add_equalities=True) ignores add_equalities=True now.

  Equalities do not carry indices and can only be added with names=True.

• facet_graph is now aware of the following:
  a ridge in ridges is a tuple of indices with names=False and a tuple of tuples with names=True and add_equalities=True,

  e.g. (1,2) vs. (('my_vertex_1',), ('my_vertex_2',)).

• ridges now appends equations at the end. This is consistent with FaceIterator.Hrepresentation.

Depends on #28603

CC: @jplab @LaisRast

Component: geometry

Keywords: polytopes, combinatorial polyhedron

Author: Jonathan Kliem

Branch/Commit: 9d93a14

Reviewer: Laith Rastanawi

Issue created by migration from https://trac.sagemath.org/ticket/28604

[kliem]

Author: Jonathan Kliem

[kliem]

Branch: public/28604

[kliem]

New commits:

a005e47	added vertex_graph, deprecated edge_graph
8654f9f	ridge_graph -> facet_graph; fixed bug in ridges with arguments

[kliem]

Commit: 8654f9f

[kliem]

Description changed:

--- 
+++ 
@@ -3,3 +3,5 @@
 In case of of the half space this makes a difference, as there is a facet, but no ridges.
 
 For now we keep `ridge_graph` and add a deprecation warning.
+
+While we at it, we fix a bug, where `CombinatorialPolyhedron.ridges(names=False, add_equalities=True)` lead to nonsense output (the equalities do not carry indices and hence can only be added with `names=True`).

[LaisRast]

comment:2

facet_graph does not work for non-full-dimensional polyhedra:

    sage: C = CombinatorialPolyhedron(polytopes.hypersimplex(5,2)); C
    A 4-dimensional combinatorial polyhedron with 10 facets
    sage: C.facet_graph()
    Graph on 20 vertices

The problem arises since each facet in C.ridges(names=True, add_equalities=True) is represented as (equation, inequality), while in C.face_iter(C.dimension() - 1, dual=False)), each facet is represented as (inequality, equation).

facet_graph does not work when names=False:

    sage: C = CombinatorialPolyhedron(polytopes.cube()); C
    A 3-dimensional combinatorial polyhedron with 6 facets
    sage: C.facet_graph(names=False)
    Graph on 12 vertices

The problem arises sincefacet.Hrepr(names=False) returns a tuple, for example (5,). While in C.ridges(names=False), each facet is represented by a number.

[sagetrac-git]

Changed commit from 8654f9f to 597afd8

[sagetrac-git]

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

c54886b	bux fix regarding elements and 1-element tuples
597afd8	ridges append eualities at the end