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).

[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

[gh-mjungmath]

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]

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.

[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'

[gh-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.

[egourgoulhon]

Replying to gh-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.

[gh-mjungmath]

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!

[gh-mjungmath]

Mh, for some reason patchbot complains about coverage.

[gh-mjungmath]

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

[egourgoulhon]

Replying to gh-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

[git]

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

​1e6a055

is_empty, declare_nonempty, has_defined_points: Add doc, examples

[mkoeppe]

No more coverage warnings.

[gh-mjungmath]

Thanks! Patchbot is also green.

How exactly is this ticket related to #31743? What exactly are the dependencies you have in mind?

Other than that, looks good to me. Eric, what do you say?

[mkoeppe]

Replying to gh-mjungmath:

How exactly is this ticket related to #31743? What exactly are the dependencies you have in mind?

#31743 will certainly depend on the present ticket.

[gh-mjungmath]

A nice and important addition to the current code. Thank you! LGTM.

[mkoeppe]

Thanks for the review!

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​3c5555a	Merge #31718
​52a93f9	ManifoldSubset.subset_family: New; deprecate .list_of_subsets
​7a22bb0	ManifoldSubset.superset_family: New, use it in doctests
​bdc07ff	Merge #31677
​2b47b1b	ManifoldSubset.open_superset_family: New
​359dde1	Merge branch 't/31727/manifoldsubset__add_methods_subset_family__superset_family__equal_subset_family__deprecate_method_list_of_subsets' into t/31732/manifoldsubset__new_methods_declare_empty__declare_nonempty__is_empty__has_defined_points__open_cover_family

[mkoeppe]

Merged #31727 to resolve a merge conflict