ABC for convex sets

[mkoeppe]

We create a base class ConvexSet_base with abstract methods to define an API for convex sets (convex subsets of a finite dimensional topological R-vector space such as R^n).

We use it to test/unify the API of Polyhedron, ConvexRationalPolyhedralCone, LatticePolytope, RelativeInterior (#31916)

See also:

• PolyhedronFace: Make it a subclass of ConvexSet_closed #31959 PolyhedronFace: Make it a subclass of ConvexSet_closed
• ConvexSet_base: Add methods an_element, some_elements #31990 ConvexSet_base: Add methods an_element, some_elements
• Meta-ticket: Connect Sage sets to sympy sets #31926 Connect Sage sets to sympy sets
• Set_base.contains, ConvexSet.contains: Handle symbolic argument #31947 ConvexSet.contains: Handle symbolic argument
• ABC for convex sets (follow up) #31955 ABC for convex sets (follow up)

Depends on #31916

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

Component: geometry

Author: Matthias Koeppe

Branch/Commit: 686d0af

Reviewer: Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/31919

[mkoeppe]

Branch: u/mkoeppe/abc_for_convex_sets

[sagetrac-git]

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

e67f753	ConvexRationalPolyhedralCone: Add method is_empty and aliases is_full_dimensional, is_universe
770fdcd	LatticePolytopeClass, IntegralRayCollection: Make ambient_dim an alias for lattice_dim
b2ac639	ConvexSet_base.dim: New
ccc8421	ConvexSet_base.is_compact, ConvexSet_compact: New

[sagetrac-git]

Commit: ccc8421

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Dependencies: #31916

[sagetrac-git]

Changed commit from ccc8421 to 4bac2fe

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

9df2104	sage.geometry.relative_interior: Move here from sage.geometry.polyhedron.relint
b8bfe20	ConvexRationalPolyhedralCone: Add methods interior, relative_interior
6869673	relative_interior: Fix for dimension 0
021d073	RelativeInterior: Add documentation, tests, comparison methods, method relative_interior
8f38e04	ConvexRationalPolyhedralCone.interior, relative_interior: Add doctests
5f9c852	RelativeInterior.interior: New
5c089ec	RelativeInterior.__eq__, __ne__: Handle comparisons with objects of other types
86ce301	Polyhedron_base.is_relatively_open: New; fix relative_interior for affine subspaces
42adced	Merge #31916
4bac2fe	RelativeInterior: Subclass ConvexSet_relatively_open, add missing methods

[sagetrac-git]

Changed commit from 4bac2fe to 1e8dd09

[sagetrac-git]

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

216cb81	ConvexRationalPolyhedralCone.is_relatively_open: New, fix ConvexRationalPolyhedralCone.relative_interior for linear subspaces
1e8dd09	Merge #31916

[mkoeppe]

Description changed:

--- 
+++ 
@@ -2,4 +2,4 @@
 
 We use it to test/unify the API of `Polyhedron`, `ConvexRationalPolyhedralCone`, `LatticePolytope`, `RelativeInterior` (#31916)
 
-
+See also: #31926 Connect Sage sets to sympy sets

[sagetrac-git]

Changed commit from 1e8dd09 to 3f4acb3

[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
fa4c2d2	Whitespace fixes
3f4acb3	Merge #31916

[sagetrac-git]

Changed commit from 3f4acb3 to dede9de

[sagetrac-git]

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

dede9de

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

[kliem]

comment:11

Missing doctest.

+    def is_empty(self):
+        """
+        Return whether ``self`` is the empty set.
+
+        Because a cone always contains the origin, this method returns ``False``.
+        """
+        return False