Opened 16 months ago

Last modified 4 months ago

#30198 new enhancement

Polyhedra in vector spaces without distinguished basis

Reported by: mkoeppe Owned by:
Priority: major Milestone: sage-9.5
Component: geometry Keywords:
Cc: gh-kliem, jipilab, tscrim Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

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.

Change History (11)

comment:1 Changed 16 months ago by mkoeppe

  • Dependencies set to #30094

comment:2 Changed 16 months ago by mkoeppe

  • Dependencies changed from #30094 to #30094, #30204

comment:3 Changed 16 months ago by mkoeppe

  • Branch set to u/mkoeppe/polyhedra_in_vector_spaces_without_distinguished_basis

comment:4 Changed 16 months ago by git

  • Commit set to 2b672f5220c20613b32ab1ba6f87c51fbd723c0c

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

20082d5sage.geometry.polyhedron.parent.Polyhedra: Generalize the factory
2b672f5Merge branch 't/30204/generalize_polyhedra_parent_factory_to_handle_more_general_ambient_spaces' into t/30198/polyhedra_in_vector_spaces_without_distinguished_basis

comment:5 Changed 16 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:6 Changed 10 months ago by mkoeppe

  • Milestone changed from sage-9.3 to sage-9.4

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

comment:7 Changed 7 months ago by mkoeppe

  • Dependencies #30094, #30204 deleted

comment:8 Changed 7 months ago by mkoeppe

  • Branch u/mkoeppe/polyhedra_in_vector_spaces_without_distinguished_basis deleted
  • Commit 2b672f5220c20613b32ab1ba6f87c51fbd723c0c deleted

comment:9 Changed 7 months ago by mkoeppe

There was no code on the branch; removed.

comment:10 Changed 7 months ago by mkoeppe

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

comment:11 Changed 4 months ago by mkoeppe

  • Milestone changed from sage-9.4 to sage-9.5
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