ManifoldSubset: New methods declare_empty, declare_nonempty, is_empty, has_defined_points, open_cover_family

[mkoeppe]

A subset is declared empty by giving it (or any superset) an open cover that is an empty family.

A subset is declared nonempty by defining a point on it (or on any subset).

Depends on #31718
Depends on #31727

CC: @egourgoulhon @mjungmath @tscrim

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 359dde1

Reviewer: Michael Jung

Issue created by migration from https://trac.sagemath.org/ticket/31732

[mkoeppe]

Changed dependencies from #31727 to #31718

[mkoeppe]

Branch: u/mkoeppe/manifoldsubset__new_methods_declare_empty__declare_nonempty__is_empty__has_defined_points__open_cover_family

[mkoeppe]

Commit: 1b5e5ac

[mkoeppe]

Last 10 new commits:

78cc27a	ManifoldSubset.open_covers: Change to generator, add optional arg 'trivial'; update uses
e026e7a	ManifoldSubset.subset_digraph: Use open_covers method
5a072cf	Merge #31718
83a9f47	ManifoldSubset.open_cover_family: New
a183575	ManifoldSubset.{declare_empty,declare_nonempty,is_empty,has_defined_points}: New
4ad562d	ManifoldSubset.{sub,super}set_{digraph,poset}: Add option 'points'
cec7fa2	ManifoldSubset.open_covers: Add option supersets; use it to fix is_empty
c40ec03	ManifoldSubset.open_cover_family: Add option supersets
a066387	Fix doctests
1b5e5ac	ManifoldSubset.declare_empty: Add plot

[mjungmath]

comment:4

I am not sure whether this is a good point to hook in, but long-term it would be nice to things like Cech cohomology. This construction needs "good covers" which are basically given by contractible intersections. Currently, we cannot determine a subset being contractible (or even connected). But perhaps this is something to consider at this point already?

[mkoeppe]

comment:5

An idea to do things like this would be to try to break complicated domains into "simple" subsets (for which we can algorithmically verify that they are simply connected) and to then use algebraic topology (e.g., simplicial complexes) on the subsets. At this point, I don't know what properties other than emptiness/nonemptiness really needs to be encoded on the level of a single subset.

[sagetrac-git]

Changed commit from 1b5e5ac to 48b2700

[sagetrac-git]

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

48b2700

src/sage/manifolds/subset.py: Remove unused import, make doctest stable by using 'sorted'

[mjungmath]

comment:7

Could you please open a new metaticket that collects the rough ideas and updates your progress regarding subsets? I think it would make it easier to keep track, at least for me.

[egourgoulhon]

comment:8

Replying to @mjungmath:

Could you please open a new metaticket that collects the rough ideas and updates your progress regarding subsets? I think it would make it easier to keep track, at least for me.

If you don't plan a lot of such tickets, maybe the metaticket #30525 is sufficient.

[mjungmath]

comment:9

Matthias already opened #31740 for that. It's a nice overview and as you can see, there are plenty of tickets concerning subsets already. Thanks Matthias!

[mjungmath]

comment:10

Mh, for some reason patchbot complains about coverage.

[mjungmath]

comment:11

Ah, is_empty, declare_nonempty and has_defined_points do not admit examples/tests.

[egourgoulhon]

comment:12

Replying to @mjungmath:

Matthias already opened #31740 for that.

Ah yes!

It's a nice overview and as you can see, there are plenty of tickets concerning subsets already.

Indeed!

Thanks Matthias!

+1

[sagetrac-git]

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

1e6a055

is_empty, declare_nonempty, has_defined_points: Add doc, examples