declare_union yields wrong results

[mjungmath]

(for the visualization of the posets, use #31680 and install the dot2tex package - without that package, the layout is quite misleading)

sage: M = Manifold(3, 'M')
sage: U = M.open_subset('U'); V = M.open_subset('V'); W = M.open_subset('W')
sage: M.declare_union(U, V, W)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-3-c7f527dcc1ea> in <module>()
----> 1 M.declare_union(U, V, W)

TypeError: declare_union() takes 3 positional arguments but 4 were given

sage: def label(element): 
....:     try: 
....:         return element._name 
....:     except AttributeError: 
....:         return '[' + ', '.join(sorted(x._name for x in element)) + ']' 

sage: P = M.subset_poset(open_covers=True); P.plot(element_labels={element: label(element) for element in P})

sage: M.declare_union(U, V.union(W))
sage: P = M.subset_poset(open_covers=True); P.plot(element_labels={element: label(element) for element in P})

sage: U.union(V).union(W)
Open subset U_union_V_union_W of the 3-dimensional differentiable manifold M
sage: P = M.subset_poset(open_covers=True); P.plot(element_labels={element: label(element) for element in P})

sage: U.union(V.union(W))
3-dimensional differentiable manifold M
sage: P = M.subset_poset(open_covers=True); P.plot(element_labels={element: label(element) for element in P})  # same

sage: M.is_subset(U.union(V).union(W))                                                         
False

#31764 adds support for arbitrary unions. But the main issue here is the failing associativity of the union.

We fix it as follows.

When creating a union, we update the open covers of the supersets of the members, replacing the union members by the union.

Depends on #31764

CC: @egourgoulhon @tscrim

Component: manifolds

Keywords: sets, union

Author: Matthias Koeppe

Branch/Commit: u/mkoeppe/declare_union_yields_wrong_results @ 743f114

Issue created by migration from https://trac.sagemath.org/ticket/30263

[mkoeppe]

comment:2

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review.

[mkoeppe]

comment:3

Unions of several subsets also appear in another form - as open covers (which are merely lists of subsets and not manifold subsets in their own right). One might ask whether this could be unified as well.

[mkoeppe]

Dependencies: #31680

[mkoeppe]

comment:5

An issue with the existing code is that through a sequence of declare_union calls, it is possible to obtain a situation in which two subsets must be the same, although declare_union makes a (not very effective) attempt to stop the user from doing so (by checking whether the two arguments are the same).

In terms of the poset of subsets that is defined by the _subsets (and _supersets) attributes (which is visualized by the code from #31680), this is quite problematic.

This could be solved by introducing equivalence classes of subsets - for example by keeping the _subsets relation acyclic and introducing an _equal_sets attribute; loops that update subsets will have to be modified.
The elements of the poset introduced in #31680 then would be equivalence classes of subsets rather than subsets.

[mkoeppe]

Changed dependencies from #31680 to #31680, #31718

[mkoeppe]

Branch: u/mkoeppe/declare_union_yields_wrong_results

[mkoeppe]

Last 10 new commits:

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
e026e7a	ManifoldSubset.subset_digraph: Use open_covers method
fca7e89	ManifoldSubset.declare_empty etc.

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Commit: fca7e89

[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
3364468	Merge #31680
6c8374e	ManifoldSubset.open_covers: Add option supersets; use it to fix is_empty
28650bc	Fix doctests
26401dd	ManifoldSubset.declare_empty: Add plot

[sagetrac-git]

Changed commit from fca7e89 to 26401dd

[sagetrac-git]

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

fee8b99	ManifoldSubsetFiniteFamily.from_subsets_or_families: New constructor
ba51202	ManifoldSubset.declare_union: Add option 'disjoint'

[sagetrac-git]

Changed commit from 26401dd to ba51202

[sagetrac-git]

Changed commit from ba51202 to 4cf4a52

[sagetrac-git]

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

9ca80d2	ManifoldSubset.{equal_subsets,supersets,superset_family}: New
55d2aa8	ManifoldSubset.{subset,superset}_digraph: New option quotient; use it for {subset,superset}_poset
4cf4a52	ManifoldSubset.declare_equal: New; use it for 1-arg ManifoldSubset.declare_union

[sagetrac-git]

Changed commit from 4cf4a52 to 55a28ce

[sagetrac-git]

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

0f037ff	ManifoldSubset.intersection: Handle arbitrary intersections
9c75d18	intersection: Refactor
8d63c32	ManifoldSubset.intersection: Only pass name, latex_name to the final intersection
0867b0c	ManifoldSubset.intersection: Go through ManifoldSubsetFiniteFamily to make the order of operations canonical
de5f928	ManifoldSubset._union_subset: Factor out from ManifoldSubset.union
4698da1	ManifoldSubset.union: Handle arbitrary unions
51a89d0	ManifoldSubset.union: Add example and plots
55a28ce	ManifoldSubset.declare_union: Handle arbitrary unions

[mkoeppe]

Work Issues: rebase on #31732, #31727

[mkoeppe]

Changed work issues from rebase on #31732, #31727 to rebase on #31732, #31727, #31736

[mkoeppe]

Changed branch from u/mkoeppe/declare_union_yields_wrong_results to none

[mkoeppe]

Changed commit from 55a28ce to none

[mkoeppe]

Changed dependencies from #31680, #31718 to #31764

[mkoeppe]

Changed author from Matthias Koeppe to none

[mkoeppe]

Changed work issues from rebase on #31732, #31727, #31736 to none

[mkoeppe]

Branch: u/mkoeppe/declare_union_yields_wrong_results

[mkoeppe]

Commit: 743f114

[mkoeppe]

Last 10 new commits:

0032bf9	ManifoldSubset.intersection: Go through ManifoldSubsetFiniteFamily to make the order of operations canonical
282010b	ManifoldSubset._union_subset: Factor out from ManifoldSubset.union
6772570	ManifoldSubset.union: Handle arbitrary unions
edfea33	ManifoldSubset.union: Add example and plots
fdd0aba	ManifoldSubset.declare_union: Handle arbitrary unions
c2f484c	src/sage/manifolds/subset.py: import itertools
a083569	ManifoldSubset._intersection_subset, _union_subset: Use declare_subset, declare_superset; fix doctest
5d41b46	Merge #31764
aceb0e8	ManifoldSubset._union_subset: Do cache store the union here
743f114	ManifoldSubset._union_subset: Update open covers

[mkoeppe]

Author: Matthias Koeppe