Polyhedron.affine_hull_manifold

[mkoeppe]

This new method will return the affine hull of the polyhedron as an embedded submanifold of the ambient space, with a default chart defining coordinates that are the same as those that affine_hull_projection gives.

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

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 62390c9

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/31659

[mkoeppe]

Branch: u/mkoeppe/polyhedron_affine_hull_manifold

[mkoeppe]

Commit: c2e6c55

[mkoeppe]

comment:2

Here's a beginning.

Unfortunately affine_hull_projection(as_affine_map=True) is a bit strange - it does not return everything what we need: The inverse affine map, from the projection back to the polyhedron. Maybe we should add more output options to this function (see also #27366)

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New commits:

c2e6c55

Polyhedron_base.affine_hull_manifold: New

[mkoeppe]

Author: Matthias Koeppe, ...

[mkoeppe]

Dependencies: #27366

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

b407987	Merge tag '9.3.rc2' into t/27366/affine-hull-more
d25f7f3	Fixup merge
7e0f31d	affine_hull -> affine_hull_projection in doctests
58e6dcc	Merge tag '9.3.rc3' into t/27366/affine-hull-more
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

[sagetrac-git]

Changed commit from c2e6c55 to 0538280

[mkoeppe]

Changed author from Matthias Koeppe, ... to Matthias Koeppe

[sagetrac-git]

Changed commit from 0538280 to f2bdbf2

[sagetrac-git]

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

f2bdbf2

Add example

[sagetrac-git]

Changed commit from f2bdbf2 to eb88cfe

[sagetrac-git]

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

eb88cfe

also plot the polyhedron

[mkoeppe]

comment:10

The plotting is best tested with #31600

[sagetrac-git]

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

3d5f3c4	Put '# not tested' in the right place
de50778	Polyhedron_base.affine_hull_manifold: Make it Riemannian

[sagetrac-git]

Changed commit from eb88cfe to de50778