ConvexSet_base: Add affine_hull, affine_hull_projection, an_affine_basis

[mkoeppe]

We generalize an_affine_basis, affine_hull, affine_hull_projection, and AffineHullProjectionData (from #27366) from Polyhedron_base to ConvexSet_base.

To provide the default implementation of affine_hull_projection, this ticket also adds the Polyhedron_base methods linear_transformation and translation to the ConvexSet_base ABC, as well as dilation for completeness.

Depends on #31963
Depends on #32013

CC: @kliem

Component: geometry

Author: Matthias Koeppe

Branch/Commit: b909bdd

Reviewer: Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/31993

[mkoeppe]

Dependencies: #31963

[mkoeppe]

Branch: u/mkoeppe/convexset_base__add_affine_hull__affine_hull_projection__an_affine_basis

[sagetrac-git]

Commit: 0226965

[sagetrac-git]

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

2a96f18	sage.geometry: Import cached_method from a more specific module
0226965	WIP ConvexSet_base.affine_hull_projection

[mkoeppe]

comment:4

ConvexRationalPolyhedralCone.solid_restriction is similar to affine_hull_projection

[sagetrac-git]

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

23b08cd

RelativeInterior.an_affine_basis: New; relax _test_affine_basis to accept closure points

[sagetrac-git]

Changed commit from 0226965 to 23b08cd

[mkoeppe]

comment:6

Replying to @mkoeppe:

ConvexRationalPolyhedralCone.solid_restriction is similar to affine_hull_projection

... best taken care of in #30172, which adds a cone ABC

[sagetrac-git]

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

0e2965f

Polyhedron.affine_hull_projection: Refactor as ConvexSet_base.affine_hull_projection and Polyhedron._affine_hull_projection

[sagetrac-git]

Changed commit from 23b08cd to 0e2965f

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,5 +1,3 @@
-`affine_hull`, `affine_hull_projection` and `AffineHullProjectionData` (from #27366) should be generalized to `ConvexSet_base` via `an_affine_basis`.
-
-(A prototype for `an_affine_basis` is on the branch of #31955.)
+We generalize `an_affine_basis`, `affine_hull`, `affine_hull_projection`, and `AffineHullProjectionData` (from #27366) from `Polyhedron_base` to `ConvexSet_base`.
 
 

[sagetrac-git]

Changed commit from 0e2965f to 837b7f5

[sagetrac-git]

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

837b7f5

RelativeInterior.{dilation,linear_transformation,translation}: New

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,3 +1,4 @@
 We generalize `an_affine_basis`, `affine_hull`, `affine_hull_projection`, and `AffineHullProjectionData` (from #27366) from `Polyhedron_base` to `ConvexSet_base`.
 
+To provide the default implementation of `affine_hull_projection`, this ticket also adds the `Polyhedron_base` methods `linear_transformation` and `translation` to the `ConvexSet_base` ABC, as well as `dilation` for completeness.