Poset of manifold subsets

[mkoeppe]

The declared subsets or supersets of a ManifoldSubset form finite posets. We add methods to expose them as instances of FinitePoset.

Depends on #31681
Depends on #31717

CC: @mjungmath @egourgoulhon @tscrim

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 84896c4

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31680

[mjungmath]

comment:1

Possibly related: #30263.

[mkoeppe]

comment:2

Yes, hopefully this new feature can be used as a debugging tool

[mkoeppe]

Branch: u/mkoeppe/poset_of_manifold_subsets

[mkoeppe]

comment:4

Here's a first step: Building a digraph from the defined subsets.

(Plotting needs dot2tex and looks bad because of the long labels. I don't know if it is possible to replace the labels by the latex names)

---

New commits:

1b5c153

ManifoldSubset.subset_digraph: New

[mkoeppe]

Commit: 1b5c153

[sagetrac-git]

Changed commit from 1b5c153 to 91bbc3e

[sagetrac-git]

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

91bbc3e

ManifoldSubset.subset_poset: New

[sagetrac-git]

Changed commit from 91bbc3e to 858c82d

[sagetrac-git]

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

858c82d

Fixup

[mkoeppe]

Dependencies: #31681

[sagetrac-git]

Changed commit from 858c82d to a1e21b0

[sagetrac-git]

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

280a82d	trac #31681: fix sorting in layout_acyclic_dummy
a1e21b0	Merge #31681

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

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

2e2d91e

ManifoldSubset.{sub,super}set_{digraph,poset}: More options

[sagetrac-git]

Changed commit from a1e21b0 to 2e2d91e

[egourgoulhon]

comment:11

Replying to @mkoeppe:

Here's a first step: Building a digraph from the defined subsets.

I'm happy to see this happening! At the beginning of the SageManifolds project, it was pretty clear that graphs would be the proper way to deal with subsets, but I was not familiar with this part of Sage and wanted to move fast...

(Plotting needs dot2tex and looks bad because of the long labels. I don't know if it is possible to replace the labels by the latex names)

This would be nice, indeed. Playing with the doctest examples,

sage: view(latex(D))                                                                                
sage: view(latex(P))                                                                                

yields nice figures, with the latex names.

[mjungmath]

comment:12

This digraph approach might also be useful to improve restrictions of tensor fields and make them even faster, no?

[mkoeppe]

comment:13

Replying to @mjungmath:

This digraph approach might also be useful to improve restrictions of tensor fields and make them even faster, no?

Yes, I think there are many more digraph / poset structures in sage.manifolds that could be exposed by similar methods in follow-up tickets.

On this ticket I am not making an attempt to actually change any of the internal representations of these structures. Just providing some tools that give a high-level view on the existing structures.

[mjungmath]

comment:14

Replying to @mkoeppe:

Replying to @mjungmath:

This digraph approach might also be useful to improve restrictions of tensor fields and make them even faster, no?

Yes, I think there are many more digraph / poset structures in sage.manifolds that could be exposed by similar methods in follow-up tickets.

On this ticket I am not making an attempt to actually change any of the internal representations of these structures. Just providing some tools that give a high-level view on the existing structures.

+1

Besides, I really like the way you write code. It's clear and neat!

[sagetrac-git]

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

02a82f9

Fix up handling of {lower,upper}_bound, add examples

[sagetrac-git]

Changed commit from 2e2d91e to 02a82f9

[sagetrac-git]

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

44c8d8c

Include example for open_covers=True

[sagetrac-git]

Changed commit from 02a82f9 to 44c8d8c

[sagetrac-git]

Changed commit from 44c8d8c to 0571aaa

[sagetrac-git]

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

0571aaa

src/sage/manifolds/subset.py: Fix docstring markup

[sagetrac-git]

Changed commit from 120fe97 to 97ec61d

[mkoeppe]

comment:29

Ready for review.

[mkoeppe]

Changed dependencies from #31681 to #31681, #31717

[sagetrac-git]

Changed commit from 97ec61d to f095988

[sagetrac-git]

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

cbbef90	Adding a `__bool__` to trivial family.
42abda7	Adding `__bool__` for other families.
1f21a8f	Merge #31717
f095988	FiniteManifoldObjectFamily.__bool__: Remove, inherited from superclass after #31717

[egourgoulhon]

comment:32

Thanks for the update. Looks good. I've got two remarks:

1. Is there any reason for the names FiniteManifoldObjectFamily and FiniteManifoldSubsetFamily instead of ManifoldObjectFiniteFamily and ManifoldSubsetFiniteFamily? The latter ones sound more natural to me, making clear that we are dealing with finite families.

2. To generate the documentation about these classes in the reference manual, the new entry sage/manifolds/family must be added to src/doc/en/reference/manifolds/manifolds.rst

[sagetrac-git]

Changed commit from f095988 to 2f2ace2

[sagetrac-git]

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

5d87cee	Manifold{Object,Subset}FiniteFamily: Rename from FiniteManifold{Object,Subset}Family
2f2ace2	src/doc/en/reference/manifolds/manifold.rst: Add sage.manifolds.family

[sagetrac-git]

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

1aff58a

Fix up docstring markup

[sagetrac-git]

Changed commit from 2f2ace2 to 1aff58a

[mkoeppe]

comment:35

Replying to @egourgoulhon:

1. Is there any reason for the names FiniteManifoldObjectFamily and FiniteManifoldSubsetFamily instead of ManifoldObjectFiniteFamily and ManifoldSubsetFiniteFamily? The latter ones sound more natural to me, making clear that we are dealing with finite families.

Good idea, done.

2. To generate the documentation about these classes in the reference manual, the new entry sage/manifolds/family must be added to src/doc/en/reference/manifolds/manifolds.rst

Thanks, done - I always forget to do this.

[sagetrac-git]

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

b922066

ManifoldSubsetFiniteFamily: If all subsets are open, include 'open' in repr

[sagetrac-git]

Changed commit from 1aff58a to b922066

[mkoeppe]

comment:37

Did one final improvement for more informative printing

[sagetrac-git]

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

30271af

Fixup doctest

[sagetrac-git]

Changed commit from b922066 to 30271af

[egourgoulhon]

comment:39

Thanks for the changes. One minor remark: shouldn't

TypeError: all... subsets must have the same manifold

be replaced by

TypeError: all open subsets must have the same manifold

in the output of the doctest

sage: ManifoldSubsetFiniteFamily([M, N])

in ManifoldSubsetFiniteFamily ? Both doctests passed, but the latter is identical to the actual message get by the user.

Besides, do you think it is worth to add PLOT directives like

        .. PLOT::

            M = Manifold(3, 'M')
            U = M.open_subset('U'); V = M.open_subset('V'); W = M.open_subset('W')
            VW = V.union(W)
            P = M.subset_poset()
            g = P.plot(element_labels={element: element._name for element in P})
            sphinx_plot(g)

immediately after the doctest

            sage: P.plot(element_labels={element: element._name for element in P})

to generate plots of posets and digraphs in the reference manual?

In any case, I would suggest that the doctest markers # not tested are removed from the plot examples:

- sage: P.plot(element_labels={element: element._name for element in P})  # not tested
+ sage: P.plot(element_labels={element: element._name for element in P})                              
+ Graphics object consisting of 10 graphics primitives

[sagetrac-git]

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

215c378	ManifoldSubset.subset_{digraph,poset}: Add plots in documentation, remove # not tested
84896c4	ManifoldSubsetFiniteFamily: Use full error message in doctest

[sagetrac-git]

Changed commit from 30271af to 84896c4

[mkoeppe]

comment:41

How's this look?

[egourgoulhon]

comment:42

Replying to @mkoeppe:

How's this look?

That's perfect, thanks!

[mkoeppe]

comment:43

Thanks for the review!

[vbraun]

Changed branch from u/mkoeppe/poset_of_manifold_subsets to 84896c4