Opened 8 months ago
Last modified 4 months ago
#31740 new task
Meta-ticket: Families, posets, complexes of manifold subsets — at Version 21
Reported by: | mkoeppe | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-9.5 |
Component: | manifolds | Keywords: | |
Cc: | gh-mjungmath, egourgoulhon, tscrim, yzh | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
New subsets:
- #31674 Make open subsets of immersed/embedded submanifolds immersed/embedded submanifolds
- #31677 Open subsets of arbitrary subsets of manifolds
- #31653 Images of continuous maps and embedded submanifolds as manifold subsets
- #31765
DegenerateManifold
: update subsets code - #31644 Topological closure of manifold subsets, methods
ManifoldSubset.closure
,is_closed
,declare_closed
- #31757 Topological interior of manifold subsets
- #31745 Images of differentiable maps
- #31688 Pullbacks of manifold subsets under continuous maps
- #31724
ManifoldFiniteSubset
- #31685
ContinuousMap.image
: if map is an isomorphism anddomain_subset
is open, create a submanifold - #31743 Charts, transitions, subsets with restrictions defined using
NNC_Polyhedron
RealSet
(see also Meta-ticket #20877):
- #30832 Connect
RealSet
tosage.manifolds
- #31878 Replace
OpenInterval
,RealLine
instances by instances of a subclass ofDifferentiableManifold
+RealSet
- #21243
RealSet
: addclosure
andinterior
methods - #31881
RealSet
: Extend constructors so that they can build manifold objects
Families and posets of manifold subsets:
- #31680 Poset of manifold subsets
- #31718
ManifoldSubset
: Change some methods to generators - #31732
ManifoldSubset
: New methodsdeclare_empty
,declare_nonempty
,is_empty
,has_defined_points
,open_cover_family
- #31727
ManifoldSubset
: Add methodssubset_family
,superset_family
,open_superset_family
; deprecate methodlist_of_subsets
- #31736
ManifoldSubset
: New methodsdeclare_equal
,equal_subsets
,equal_subset_family
- #31763
ManifoldSubset
: New methodsdeclare_subset
,declare_superset
- #31764
ManifoldSubset
:union
,intersection
,declare_{union,intersection}
with arbitrary number of arguments - #31798
ManifoldSubset.difference
,complement
- #31766
ManifoldSubset
: Replace use of_top_subsets
by a generator - #31738
ManifoldSubset.intersection
: Compute more supersets - #31682 manifolds: Add
_test_...
methods that check invariants of subset relations - #30263
declare_union
yields wrong results
Topological tools:
- #31741
ManifoldSubset.separating_open_supersets
- #31744
ManifoldSubset
: Propagate emptiness/nonemptiness using LP
Application to polyhedra and optimization:
- #31659
Polyhedron.affine_hull_manifold
- #31660
Polyhedron.relative_interior_manifold
- #31728
manifolds.Sphere
: Make relation to simplicial spheres more concrete - #31742
MixedIntegerLinearProgram.ambient_manifold
,feasible_subset
,objective_scalar_field
,optimal_subset
- #31376 Complex of differentiable manifolds associated with active sets of nonlinear optimization problems
- #31751 Reformulations of optimization problems as continuous maps on manifolds
Change History (21)
comment:1 Changed 8 months ago by
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- Cc yzh added
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comment:14 Changed 7 months ago by
git log --first-parent
goes a long way
comment:15 Changed 7 months ago by
- Description modified (diff)
comment:16 Changed 7 months ago by
I think it would be nice to have something like powerset
and topology
that dynamically keep track of whether a (open) subset is contained in it.
This might also be a good opportunity to shift all this open_covers
and subsets
business to those classes and decouple it more from the manifold code. We can consider doing a similar thing for atlases, too. I can imagine that these changes could make pickling of manifolds easier.
This comes handy especially for sheaves, since it would allow to see them as (lazy) families indexed by topology
.
Opinions?
comment:17 Changed 7 months ago by
In principle, this could also lead to the more general notion of topological spaces. Manifolds are then nothing but topological spaces equipped with an atlas (roughly).
But to get there eventually, we need a lot of refactoring, i.e. something for the further future.
comment:18 Changed 7 months ago by
This is also good for subset topologies in case of e.g. embedded manifolds.
comment:19 Changed 7 months ago by
See also #31785 "Category of open subsets of a topological space".
comment:20 Changed 6 months ago by
- Description modified (diff)
comment:21 Changed 6 months ago by
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For me, it gets harder and harder to keep track of the actual changes taking place in a particular ticket since there are a lot of cross-dependencies and no positively reviewed tickets have been merged lately, meaning the changes swiftly accumulate.
It might be helpful to state the ticket number in the commits which would make it easier to track the differences down, at least for me.
Or perhaps there is a nice git feature I am not aware of?