ManifoldSubset: Change some methods to generators

[Matthias Köppe]

This ticket proposes to change some methods that currently return lists to generators - like the method open_supersets added in #31677. This is in line with the changes in the Python standard library when we moved from Python 2 to 3.

ManifoldSubset:

• open_covers() currently returns a list of lists
  • change to generator of ManifoldSubsetFiniteFamily instances
  • add optional argument trivial to simplify the common use case that only needs the nontrivial open covers

• subsets() currently returns a frozenset
  • change to generator of ManifoldSubset instances

These API changes will probably make some updates to sage.manifolds worksheets that are maintained outside of the Sage tree necessary.

Follow-up for some methods of Manifold in #31720.

[Matthias Köppe]

New commits:

​186707b

ManifoldSubset.subsets: Change to generator

[git]

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

​42abda7	Adding __bool__ for other families.
​1f21a8f	Merge #31717
​f095988	FiniteManifoldObjectFamily.__bool__: Remove, inherited from superclass after #31717
​5d87cee	Manifold{Object,Subset}FiniteFamily: Rename from FiniteManifold{Object,Subset}Family
​2f2ace2	src/doc/en/reference/manifolds/manifold.rst: Add sage.manifolds.family
​1aff58a	Fix up docstring markup
​b922066	ManifoldSubsetFiniteFamily: If all subsets are open, include 'open' in repr
​30271af	Fixup doctest
​adac07a	Merge #31680
​78cc27a	ManifoldSubset.open_covers: Change to generator, add optional arg 'trivial'; update uses

[git]

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

​e026e7a

ManifoldSubset.subset_digraph: Use open_covers method

[Eric Gourgoulhon]

LGTM. Thanks!

[Matthias Köppe]

Thanks for reviewing!

[Michael Jung]

I assume it has a purpose, but just out of curiosity: why do you make a difference between families of manifold objects and families of manifold subsets? Do you have a further usage in mind other than just subsets? Because all the examples you provide are still with subsets.

[Michael Jung]

I can imagine this can be useful for frames whose domains cover the manifold? Perhaps this is a more suitable example for the non-subset case to show the difference?

Some time ago I provided a helper function _get_min_covering (can be found in manifolds/manifold.py) to obtain a minimal amount of manifold objects necessary to cover the manifold. It looks like this method is more suited within the family class you just provided.

Another example in the field I could imagine is for orientations. An orientation is given by a family of charts/frames, too, but yet not implemented as such.

[Matthias Köppe]

Replying to gh-mjungmath:

I assume it has a purpose, but just out of curiosity: why do you make a difference between families of manifold objects and families of manifold subsets? Do you have a further usage in mind other than just subsets?

Yes, in #31732 I use ManifoldObjectFiniteFamily directly for the family of open covers. Its elements are ManifoldSubsetFiniteFamily instances.

I agree that charts/frames are likely to benefit from becoming finite families too. This will also need a separate subclass because they are indexed not by names but by coordinate tuples.

[Michael Jung]

Replying to mkoeppe:

Replying to gh-mjungmath:

I assume it has a purpose, but just out of curiosity: why do you make a difference between families of manifold objects and families of manifold subsets? Do you have a further usage in mind other than just subsets?

Yes, in #31732 I use ManifoldObjectFiniteFamily directly for the family of open covers. Its elements are ManifoldSubsetFiniteFamily instances.

Alright, that makes sense. Just a personal taste: I think its better to add some distinct examples to ManifoldObjectFiniteFamily to clarify the difference to ManifoldSubsetFiniteFamily.

I agree that charts/frames are likely to benefit from becoming finite families too. This will also need a separate subclass because they are indexed not by names but by coordinate tuples.

Right. But don't you think it should rather be a new common parent class both inherit from?

In any case, this is something definitely need, indeed!

[Matthias Köppe]

Replying to gh-mjungmath:

I think its better to add some distinct examples to ManifoldObjectFiniteFamily to clarify the difference to ManifoldSubsetFiniteFamily.

Sure, let's do that when we introduce some more applications to families.

Replying to mkoeppe:

I agree that charts/frames are likely to benefit from becoming finite families too. This will also need a separate subclass because they are indexed not by names but by coordinate tuples.

Right. But don't you think it should rather be a new common parent class both inherit from?

Sure, that makes sense.

In any case, this is something definitely need, indeed!

Let's take this discussion to #31720 (Manifold: Change some methods to generators), which introduces generators for charts. Families could be introduced in the same ticket -- but I will need some guidance there what the keys should be.