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

[mkoeppe]

comment:12

It seems I need to make this a foliation so that I get access to a volume form

[sagetrac-git]

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

ab10ce2	correct base_rings for projection and section map and test suite method
69ceebc	base extend in test; only run defined tests
e409f37	Merge #27366

[sagetrac-git]

Changed commit from de50778 to e409f37

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Changed commit from e409f37 to cd15496

[sagetrac-git]

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

ba62e66	Polyhedron_base.affine_hull_projection: Fix for 0-dimensional case
934a33f	Polyhedron_base.affine_hull_projection: Error for the empty polyhedron
9629620	Polyhedron_base.affine_hull_projection: Fix up use of echelong form
cd15496	Merge #27366

[sagetrac-git]

Changed commit from cd15496 to 931b5ca

[sagetrac-git]

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

8c24c5c	Polyhedron_base.affine_hull_projection: Remove last occurrence of 'parametric_form'
9368947	Merge #27366
931b5ca	Polyhedron_base.affine_hull_manifold: Use a foliation

[sagetrac-git]

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

9f5560a	initialize empty matrix after trivial multiplication
f9faa02	minimal extension only avoid AA if the base ring is not already AA
397ae3a	src/sage/geometry/polyhedron/base.py: Update copyright according to git blame -w --date=format:%Y src/sage/geometry/polyhedron/base.py | sort -k2
2c1e2bd	Polyhedron_base.affine_hull_projection: Return a dataclass instance, not a dictionary
57fd3e1	Fixup doctest formatting
6e686a4	Merge #27366
643392c	Use new format of affine hull data
57dce72	Polyhedron.affine_hull_manifold: Update doctests

[sagetrac-git]

Changed commit from 931b5ca to 57dce72

[sagetrac-git]

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

a47ea80

Update doctest

[sagetrac-git]

Changed commit from 57dce72 to a47ea80

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Changed commit from a47ea80 to 915389d

[sagetrac-git]

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

b17aa8c	add another doctest
eee1aad	fix section map
915389d	Merge #27366

[sagetrac-git]

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

87a2bea	Polyhedron_base.affine_hull_manifold: In the full-dimensional case, do not create a submanifold
8af2c71	Polyhedron_base._affine_hull_name_latex_name: Add docstring

[sagetrac-git]

Changed commit from 915389d to 8af2c71

[sagetrac-git]

Changed commit from 8af2c71 to 8c6759a

[sagetrac-git]

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

8c6759a

Make docstrings raw

[sagetrac-git]

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

19a9ceb

Polyhedron_base.affine_hull_manifold: Add argument ambient_chart

[sagetrac-git]

Changed commit from 8c6759a to 19a9ceb

[sagetrac-git]

Changed commit from 19a9ceb to 62390c9

[sagetrac-git]

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

62390c9

src/sage/geometry/polyhedron/base.py: Fix typo

[mkoeppe]

Changed dependencies from #27366 to none

[mkoeppe]

comment:25

Ready for review; the failure on one of the patchbots is unrelated (#28559)

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:26

LGTM.

[mkoeppe]

comment:27

Thanks!

[vbraun]

Changed branch from u/mkoeppe/polyhedron_affine_hull_manifold to 62390c9