Polyhedron constructors: minimal vs. non-minimal input representations; input both Vrep and Hrep

[mkoeppe]

Follow-up from #17339 - Polyhedron class mistreats empty inputs.

As suggested in ​https://trac.sagemath.org/ticket/17339#comment:5, we complement the Polyhedron constructor with several new constructors with simpler semantics.

• Polyhedron.from_Vrep
• Polyhedron.from_Hrep
• Polyhedron.empty

We also add a constructor Polyhedron.from_Vrep_and_Hrep that accepts both Vrep and Hrep (backend work for this appears on #22701, #26368).

But there are open questions regarding the possible design. All Polyhedron methods currently guarantee minimal representations. This is reflected also in the names of methods for accessing the V-represenation, such as vertex_generator; but not in those for the H-representation (inequality_generator). (Note the minimize argument is unused in the whole Polyhedron code.) Compare with polymake, which has a clear distinction between minimal and non-minimal presentations (VERTICES vs. POINTS).

Follow-up / related:

• make this used in as_polyhedron method in face.py
• "lazy" backend for Polyhedron

[jipilab]

Here is just a note about constructing from both V- and H- representation:

The method as_polyhedron of PolyhedronFaces would benefit greatly from this, so perhaps as a follow-up or on this ticket.

[mkoeppe]

This is an early draft, with the purpose of supporting #31799. Comments and improvements to the design are very welcome.

One thing needed for #31799 is finding the parent early - then, for parents that implement init from both representations, one could efficiently compute the double description before calling the element constructor.

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New commits:

​05fef94

src/sage/geometry/polyhedron/constructor.py: Add more constructors