Make Hrepresentation of `CombinatorialPolyhedron` bit more consistent

[kliem]

From #29683.

We change name equalities to equations, which is mostly used for internals and documentation.

We have the equation always last.

We make CombinatorialFace.ambient_H_indices, CombinatorialFace.ambient_Hrepresentation and CombinatorialFace.n_ambient_Hrepresentation consistent.

CC: @yuan-zhou

Component: geometry

Keywords: Hrepresentation, combinatorial polyhedron

Author: Jonathan Kliem

Branch/Commit: 3e0229f

Reviewer: Yuan Zhou, Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/31834

[kliem]

New commits:

b49a061

equalities -> equations

[kliem]

Commit: b49a061

[kliem]

Branch: public/31834

[sagetrac-git]

Changed commit from b49a061 to a7d13f5

[sagetrac-git]

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

9dc75c2	have equations always last
a7d13f5	make Hrep methods of combinatorial face more consistent

[kliem]

Changed keywords from none to Hrepresentation, combinatorial polyhedron

[yuan-zhou]

comment:4

Looks great to me!

Some small suggestions:

• Doctests of def ambient_H_indices(self, add_equations=True): It would be good to test with add_equations=False and add_equations=True on a polyhedron that has equation (e.g. on the first P = polytopes.permutahedron(5)). The second P =polytopes.cyclic_polytope(4,6) has no equation, so it doesn't show a difference. I'm also curious if add_equations always appends larger indices no matter the backend is field or ppl.
• if add_equations and self._ambient_facets: probably should be two if's, so that not self._ambient_facets and add_equations and self._equations does not result in equations = ()?
• Docstring of Hrepr: the description is unclear, but since it's deprecated, maybe it doesn't matter.

[sagetrac-git]

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

d2ee51e	meaningful doctest for ambient_H_indices
0111d1f	make add_equalities more stable

[sagetrac-git]

Changed commit from a7d13f5 to 0111d1f

[kliem]

comment:6

Replying to @yuan-zhou:

Looks great to me!

Some small suggestions:

• Doctests of def ambient_H_indices(self, add_equations=True): It would be good to test with add_equations=False and add_equations=True on a polyhedron that has equation (e.g. on the first P = polytopes.permutahedron(5)). The second P =polytopes.cyclic_polytope(4,6) has no equation, so it doesn't show a difference.

Fixed.

I'm also curious if add_equations always appends larger indices no matter the backend is field or ppl.

Yes, why wouldn't it. It counts the number of facets and then appends indices. The equations are taken out of the Hrepresentation in base.pyx.

• if add_equations and self._ambient_facets: probably should be two if's, so that not self._ambient_facets and add_equations and self._equations does not result in equations = ()?

Fixed.

• Docstring of Hrepr: the description is unclear, but since it's deprecated, maybe it doesn't matter.

I really don't think it matters. It's deprecated for one hear already and has only been with us for one release total. Only there in case someone used it at some point.