Construct lattice polytope faces as polytopes

[novoselt]

As opposed to a separate class with different methods. Advantages:

• uniform behaviour with cones
• all polytope methods are available to their faces as well
• less dependence on a particular backend

Since there is now lattice_polytope.ambient() returning "the canonical" containing polytope, amibient_dim was renamed to lattice_dim to avoid confusion. Unfortunately, there is now less consistency in names with generic polyhedra (for which lattice_dim makes no sense), but they are very different anyway.

There is some performance penalty associated with the new way of constructing faces (#19077 improves things somewhat), but it is mostly due to constructing face lattice as a poset. So less speed, but more features. Plus "more speed" was available only through the use of batch methods that few people use/are aware of.

Depends on #19070

CC: @vbraun

Component: geometry

Keywords: toric

Author: Andrey Novoseltsev

Branch/Commit: 6547b5b

Reviewer: Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/19071

[novoselt]

Branch: u/novoselt/19071

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

9cee82b

WIP

[sagetrac-git]

Commit: 9cee82b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

6547b5b

Stop using deprecated methods in other modules.

[sagetrac-git]

Changed commit from 9cee82b to 6547b5b

[novoselt]

Changed keywords from none to toric

[novoselt]

Description changed:

--- 
+++ 
@@ -1 +1,8 @@
-As opposed to a separate class with different methods.
+As opposed to a separate class with different methods. Advantages:
+- uniform behaviour with cones
+- all polytope methods are available to their faces as well
+- less dependence on a particular backend
+
+Since there is now `lattice_polytope.ambient()` returning "the canonical" containing polytope, `amibient_dim` was renamed to `lattice_dim` to avoid confusion. Unfortunately, there is now less consistency in names with generic polyhedra (for which `lattice_dim` makes no sense), but they are very different anyway.
+
+There is some performance penalty associated with the new way of constructing faces (#19077 improves things somewhat), but it is mostly due to constructing face lattice as a poset. So less speed, but more features. Plus "more speed" was available only through the use of batch methods that few people use/are aware of.

[vbraun]

Reviewer: Volker Braun