Transition of combinatorial computations of Polyhedron to Combinatorial Type

[kliem]

In #26887 we created a new class, that handles the calculations depending only on the combinatorial type more quickly.

The goal of this ticket is to make use of this class throughout Polyhedron_base.

Add methods:

• Add CombinatorialPolyhedron method to Polyhedron objects #28621: Add method combinatorial_polyhedron,
• Use CombinatorialPolyhedron to obtain faces of polyhedra #28646: face_generator,
• Use CombinatorialPolyhedron to obtain faces lattice of polyhedra #28982: hasse_diagram,
• Add simplicity and simpliciality to polyhedra #29186: simpliciality, simplicity

Replace the existing computation:

• Let CombinatorialPolyhedron handle f_vector of polyhedra #28625: f_vector,
• Use CombinatorialPolyhedron to obtain faces of polyhedra #28646 faces,
• Compute graph of polyhedron with CombinatorialPolyhedron #28626: graph/vertex_graph,
• graph/vertex_graph with incidences instead of Vrepresentation/expose the names=False option
• Polyhedron_base.vertex_adjacency_matrix: Do not use face_lattice #32666: vertex_adjacency_matrix
• vertex_digraph
• Polyhedron_base.facet_adjacency_matrix: Do not use face_lattice #33008: facet_adjacency_matrix,
• Use CombinatorialPolyhedron to obtain faces lattice of polyhedra #28982 face_lattice.

Migrate code to CombinatorialPolyhedron:

• Move is_prism and is_bipyramid to combinatorial polyhedron #33009: is_prism
• is_combinatorially_isomorphic
• Migrate neighborly to combinatorial polyhedron #29565: is_neighborly, neighborliness
• Move is_simple and is_simplicial to CombinatorialPolyhedron #29078: is_simple,is_simplicial
• Migrate is_lawrence_polytope and is_pyramid to combinatorial polyhedron #29189: is_lawrence_polytope
• is_self_dual
• Migrate is_lawrence_polytope and is_pyramid to combinatorial polyhedron #29189: is_pyramid
• Move is_prism and is_bipyramid to combinatorial polyhedron #33009: is_bipyramid
• combinatorial_automorphism_group
• Move vertex facet graph to combinatorial polyhedron #29188: vertex_facet_graph

NOTE: The remaining bulletins are taken care of by exposing the adjacency matrices.

Depends on #28621
Depends on #28625
Depends on #28626

CC: @jplab @mkoeppe

Component: geometry

Keywords: polyhedron, face lattice

Author: Jonathan Kliem

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/27063

[embray]

comment:1

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.

[kliem]

Changed dependencies from #26887 to #26887, #27987

[kliem]

Branch: public/27063

[kliem]

Commit: 25407f8

[kliem]

Description changed:

--- 
+++ 
@@ -1,10 +1,10 @@
-In #26887 we create a new class, that handles the calculations depending only on the combinatorial type much more quickly. This includes the following methods of the class Polyhedron:
+In #26887 we create a new class, that handles the calculations depending only on the combinatorial type much more quickly. The following methods now make use of this:
 
 - face_lattice
 - faces
 - f_vector
 - vertex_graph
-- vertex_digraph (?)
+- vertex_digraph
 - neighborliness
 
 Maybe adding new methods concerning flag-vector, h-Vector k-simplicial, k-neighborly etc.

[kliem]

Last 10 new commits:

9b69f50	added documentation and examples to each module
4e8fd8c	correct hyperlinks
72ac3b0	documentation fix
611099f	Do not iterate twice for CombinatorialPolyhedron.facets()
d38e130	added combinatorial face
ca60665	improved docstring in list_of_all_faces
abe00b6	fixed small issues
8765313	A number of small edits.
d419d72	Merge branch 'public/26887' of git://trac.sagemath.org/sage into public/27063
25407f8	faces, f_vector, vertex_graph, vertex_digraph, neighborliness now use CombinatorialPolyhedron

[kliem]

Author: Jonathan Kliem