{Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}

[mkoeppe]

We introduce new methods relative_interior and interior, which (in nontrivial cases) return a simple object with a __contains__ method.

Then one can write x in P.relative_interior() instead of P.relative_interior_contains(x).

This will also simplify #31660.

CC: @kliem @yuan-zhou @jplab @tscrim @novoselt @orlitzky

Component: geometry

Author: Matthias Koeppe

Branch/Commit: fa4c2d2

Reviewer: Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/31916

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Branch: u/mkoeppe/polyhedron_relative_interior

[mkoeppe]

Commit: e9c670c

[mkoeppe]

New commits:

e9c670c

sage.geometry.polyhedron.relint, Polyhedron_base.relative_interior, Polyhedron_base.interior: New

[sagetrac-git]

Changed commit from e9c670c to b8bfe20

[sagetrac-git]

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

9df2104	sage.geometry.relative_interior: Move here from sage.geometry.polyhedron.relint
b8bfe20	ConvexRationalPolyhedralCone: Add methods interior, relative_interior

[sagetrac-git]

Changed commit from b8bfe20 to 6869673

[sagetrac-git]

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

6869673

relative_interior: Fix for dimension 0

[sagetrac-git]

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

021d073

RelativeInterior: Add documentation, tests, comparison methods, method relative_interior

[sagetrac-git]

Changed commit from 6869673 to 021d073

[sagetrac-git]

Changed commit from 021d073 to 8f38e04

[sagetrac-git]

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

8f38e04

ConvexRationalPolyhedralCone.interior, relative_interior: Add doctests

[kliem]

Reviewer: Jonathan Kliem

[kliem]

comment:9

There are various small things:

The interior of a non-full-dimensional cone should be a cone, not a polyhedron.

Why do you implement relative_interior for relative interiors but not interior?

Why is closure defined for relative interiors, but not for polyhedra or cones? The problem is, that P.relative_interior().closure() will not always work.

Comparison will raise AttributeErrors, when other is the universe.

[kliem]

comment:10

#31919 solves the problem with closure.

[sagetrac-git]

Changed commit from 8f38e04 to 5c089ec

[sagetrac-git]

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

5f9c852	RelativeInterior.interior: New
5c089ec	RelativeInterior.__eq__, __ne__: Handle comparisons with objects of other types

[mkoeppe]

comment:12

Replying to @kliem:

The interior of a non-full-dimensional cone should be a cone, not a polyhedron.

Can't do - a ConvexRationalPolyhedralCone always contains 0

Why do you implement relative_interior for relative interiors but not interior?

Done

Why is closure defined for relative interiors, but not for polyhedra or cones? The problem is, that P.relative_interior().closure() will not always work.

For this ticket, it's just the accessor to the original polytope, not a more general API. See #31919 (ABC for convex sets), where I am adding such methods.

Comparison will raise AttributeErrors, when other is the universe.

Done

[kliem]

comment:14

LGTM.

[kliem]

comment:15

Replying to @mkoeppe:

Replying to @kliem:

The interior of a non-full-dimensional cone should be a cone, not a polyhedron.

Can't do - a ConvexRationalPolyhedralCone always contains 0

Right.

Why do you implement relative_interior for relative interiors but not interior?

Done

Why is closure defined for relative interiors, but not for polyhedra or cones? The problem is, that P.relative_interior().closure() will not always work.

For this ticket, it's just the accessor to the original polytope, not a more general API. See #31919 (ABC for convex sets), where I am adding such methods.

As noted above, I later discovered this on #31919 and it's fine to add it later on.

Comparison will raise AttributeErrors, when other is the universe.

Done

[mkoeppe]

comment:16

Thanks! But I think I need to revise relative_interior to handle polyhedra that are already relatively open

[sagetrac-git]

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

86ce301

Polyhedron_base.is_relatively_open: New; fix relative_interior for affine subspaces

[sagetrac-git]

Changed commit from 5c089ec to 86ce301

[kliem]

comment:19

I was locking for a boundary case, but yes, if a polyhedron is it's affine hull, then it either empty or the universe it it's affine hull.

[sagetrac-git]

Changed commit from 86ce301 to 216cb81

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

216cb81

ConvexRationalPolyhedralCone.is_relatively_open: New, fix ConvexRationalPolyhedralCone.relative_interior for linear subspaces

[mkoeppe]

comment:21

Sorry, here's the same fix for cones

[sagetrac-git]

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

44cde1e

src/doc/en/reference/discrete_geometry/index.rst: Add sage/geometry/relative_interior

[sagetrac-git]

Changed commit from 216cb81 to 44cde1e

[kliem]

comment:23

Is there a reason for the emptylines:

+    def is_relatively_open(self):
+
+        r"""
+        Return whether ``self`` is relatively open.

+class RelativeInterior(SageObject):
+
+    r"""

Surround top-level function and class definitions with two blank lines.

+# ****************************************************************************
+
+from sage.structure.sage_object import SageObject
+
+class RelativeInterior(SageObject):

I'm not sure, if it also applies to the import.

Really tiny: Does a docstring ending with an example contain an empty line in the end? (Doesn't need to be fixed, I just noticed.)

Maybe for another ticket: Replace the ppl imports in cone.py by explicity imports to help pyflakes.

Otherwise it's a positive review.

[sagetrac-git]

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

fa4c2d2

Whitespace fixes

[sagetrac-git]

Changed commit from 44cde1e to fa4c2d2

[kliem]

comment:25

LGTM.

[mkoeppe]

comment:26

Thanks!

[vbraun]

Changed branch from u/mkoeppe/polyhedron_relative_interior to fa4c2d2