Polyhedron_normaliz: Initialize new cone from both Vrep and Hrep

[gh-kliem]

This ticket implements a method to initialize a cone from vertices, rays, inequations and equalities.

More precisely

• we outsource a new method _cone_from_normaliz_data from the existing method _init_from_normaliz_data.
• Then we add a method _cone_from_Vrepresentation_and_Hrepresentation, which returns a cone form vertices, rays, ieqs and eqns.

Note that lines must be recomputed, hence the cone might reorder them.

The trivial cases of neither rays nor lines or without inequalities are not covered by this method. In either case None is returned.

As a follow up we

• fix Polyhedron_normaliz.save in #26363,
• we allow converting to 'normaliz' backend with both Vrep and Hrep in the spirit of #22701.

[gh-kliem]

New commits:

​c42c907

method to obtain cone from Vrep and Hrep

[gh-kliem]

I have set up doctests to test whether the cone is correct. Are there critical/important examples missing there?

[gh-kliem]

I'm also a bit puzzled that it states that the equations are not precomputed from the data (see EXAMPLE block in the code). However, not giving the equations will lead to errors.

[git]

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

​cc17f07

added documentation to cone from normaliz data

[tscrim]

Minor detail:

         - ``vertices`` -- list of point; each point can be specified
-           as any iterable container of
-           :meth:`~sage.geometry.polyhedron.base.base_ring` elements
+          as any iterable container of
+          :meth:`~sage.geometry.polyhedron.base.base_ring` elements

Also, shouldn't _cone_from_Vrepresentation_and_Hrepresentation be called from somewhere in the code? Or is this done indirectly through the more general framework?

[gh-kliem]

New commits:

​a54cfd9	Merge branch 'public/28639' of git://trac.sagemath.org/sage into public/28639-reb
​fc4c596	alignment fix in docs

[gh-kliem]

I fixed the alignment error and also at the place, where I copied it from.

The method is not being used yet. I added a branch to #26363, which uses it in order to fix pickling/unpickling. Initializing from both Vrep and Hrep does not work yet. Eventually, we should open a new ticket and allow it at least when converting to backend normaliz.

Replying to tscrim:

Minor detail:

         - ``vertices`` -- list of point; each point can be specified
-           as any iterable container of
-           :meth:`~sage.geometry.polyhedron.base.base_ring` elements
+          as any iterable container of
+          :meth:`~sage.geometry.polyhedron.base.base_ring` elements

Also, shouldn't _cone_from_Vrepresentation_and_Hrepresentation be called from somewhere in the code? Or is this done indirectly through the more general framework?

[tscrim]

Okay. Thanks. Then LGTM.