Polyhedron.relative_interior_manifold, as_manifold_subset

[mkoeppe]

We extend the ManifoldSubsetPullback constructor to handle relatively open convex sets.

In this case, we

• set up the affine hull as an embedded submanifold via ConvexSet_base.affine_hull_projection (ConvexSet_base: Add affine_hull, affine_hull_projection, an_affine_basis #31993), generalized from Polyhedron.affine_hull_manifold (Polyhedron.affine_hull_manifold #31659)
• make the relatively open set an open subset; the pullback is the image of the open subset

We add ConvexSet_base methods

• as_manifold_subset.
• relative_interior_manifold

Next step: Polyhedron.face_manifold_poset, top element of which is the polyhedron as a union of its relative interior and its facets. Using #31732, the intersection of the relative interior and each facet is declared empty.

Depends on #31688
Depends on #31963
Depends on #31993

CC: @mjungmath @kliem @yuan-zhou @jplab @tscrim @egourgoulhon

Component: manifolds

Work Issues: Refactor through #31688, #31916, #31963, #31993

Author: Matthias Koeppe

Branch/Commit: u/mkoeppe/polyhedron_relative_interior_manifold @ 1f4bd68

Issue created by migration from https://trac.sagemath.org/ticket/31660

[mkoeppe]

Branch: u/mkoeppe/polyhedron_relative_interior_manifold

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Last 10 new commits:

8414039	Polyhedron_base.affine_hull_projection: Document a weaker guarantee of parametric_form
dba2763	Polyhedron_base.affine_hull_projection: Replace 'affine_map' by 'projection_map', 'parametric_form'/'coordinate_images' by 'section_map'
d49c313	Polyhedron_base.affine_hull_projection: section map for non-orthogonal case
d77181b	Add doctest
6f30843	Polyhedron_base.affine_hull_manifold: New
0538280	Polyhedron_base.affine_hull_manifold: Finish
f2bdbf2	Add example
eb88cfe	also plot the polyhedron
10136e9	Put '# not tested' in the right place
cead8ce	Polyhedron_base.relative_interior_manifold: New

[mkoeppe]

Commit: cead8ce

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
-This returns the relative interior of the polyhedron as a differentiable submanifold of its `affine_hull_manifold` (#31659).
+This returns the relative interior of the polyhedron as an open subset of its `affine_hull_manifold` (#31659).
 
 

[mkoeppe]

Changed dependencies from #31659 to #31659, #31674

[sagetrac-git]

Changed commit from cead8ce to 1c2b1bb

[sagetrac-git]

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

d815b63	{DifferentiableSubmanifold,PseudoRiemannianSubmanifold}.open_subset: New
3fc1922	Merge #31674
006fd02	{Topological,Differentiable,PseudoRiemannianSubmanifold}._repr_: Print subsets as subsets
ed1a2ea	Update doctest output: Riemannian
aac8835	{Topological,Differentiable,PseudoRiemannianSubmanifold}._repr_: Print subsets as subsets
004c23a	Add/update examples
ef1614a	Refactor Manifold.open_subset methods through new method _init_open_subset
b2ccbba	Merge #31674
3fdb300	Polyhedron_base.affine_hull_manifold: Small edit to the doctest
1c2b1bb	Polyhedron_base.relative_interior_manifold: Use open_subset method

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,3 +1,4 @@
 This returns the relative interior of the polyhedron as an open subset of its `affine_hull_manifold` (#31659).
 
+Next step: `Polyhedron.manifold_subset_poset`, top element of which is the polyhedron as a union of its relative interior and its facets.
 

[sagetrac-git]

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

643392c	Use new format of affine hull data
57dce72	Polyhedron.affine_hull_manifold: Update doctests
a4d3d5c	Merge #31659
265b0e2	TopologicalManifold._init_open_subset: Add docstring
a93f7ed	TopologicalSubmanifold._init_open_subset: Add docstring
58b43f7	DifferentiableManifold._init_open_subset: Add docstring
dee6cef	Merge #31674
730f5e6	Update doctest
a47ea80	Update doctest
7a6a10c	Merge #31659

[sagetrac-git]

Changed commit from 1c2b1bb to 7a6a10c

[sagetrac-git]

Changed commit from 7a6a10c to 9734f98

[sagetrac-git]

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

9734f98

Polyhedron_base.relative_interior_manifold: Substitute the values of the foliation parameters

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
 This returns the relative interior of the polyhedron as an open subset of its `affine_hull_manifold` (#31659).
 
-Next step: `Polyhedron.manifold_subset_poset`, top element of which is the polyhedron as a union of its relative interior and its facets.
+Next step: `Polyhedron.face_manifold_poset`, top element of which is the polyhedron as a union of its relative interior and its facets. Using #30263, the intersection of the relative interior and each facet is declared empty.
 

[sagetrac-git]

Changed commit from 9734f98 to 9e8eb27