Polyhedra in vector spaces without distinguished basis

[mkoeppe]

Currently, the ambient space of a polyhedron is always a vector space constructed by VectorSpace.

In this ticket, we define polyhedra in more general vector spaces (anything in the category VectorSpaces(K).FiniteDimensional() for some real field K). This includes:

• sage.combinat.free_module.CombinatorialFreeModule

• sage.tensor.modules.finite_rank_free_module.FiniteRankFreeModule (vector spaces without distinguished basis)

In particular, the latter has the notion of linear forms, which would be used in the H-description of the polyhedra.

The implementation reduces the problem to the existing polyhedral backends in the coordinates w.r.t. an arbitrary basis.

CC: @kliem @jplab @tscrim

Component: geometry

Issue created by migration from https://trac.sagemath.org/ticket/30198

[mkoeppe]

Dependencies: #30094

[mkoeppe]

Changed dependencies from #30094 to #30094, #30204

[mkoeppe]

Branch: u/mkoeppe/polyhedra_in_vector_spaces_without_distinguished_basis

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

20082d5	sage.geometry.polyhedron.parent.Polyhedra: Generalize the factory
2b672f5	Merge branch 't/30204/generalize_polyhedra_parent_factory_to_handle_more_general_ambient_spaces' into t/30198/polyhedra_in_vector_spaces_without_distinguished_basis

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Commit: 2b672f5

[mkoeppe]

comment:6

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

Changed dependencies from #30094, #30204 to none

[mkoeppe]

Changed commit from 2b672f5 to none

[mkoeppe]

Changed branch from u/mkoeppe/polyhedra_in_vector_spaces_without_distinguished_basis to none

[mkoeppe]

comment:9

There was no code on the branch; removed.

[mkoeppe]

comment:10

An alternative approach is #31660, which provides Polyhedron.as_manifold_subset