Opened 8 months ago

Last modified 4 months ago

#31740 new task

Meta-ticket: Families, posets, complexes of manifold subsets — at Version 23

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:

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Description (last modified by mkoeppe)

New subsets:

  • #31674 Make open subsets of immersed/embedded submanifolds immersed/embedded submanifolds (merged in Sage 9.4.beta1)
  • #31677 Open subsets of arbitrary subsets of manifolds (merged in Sage 9.4.beta1)
  • #31653 Images of continuous maps and embedded submanifolds as manifold subsets (merged in Sage 9.4.beta1)
  • #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 and domain_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 to sage.manifolds
  • #31878 Replace OpenInterval, RealLine instances by instances of a subclass of DifferentiableManifold+RealSet
  • #21243 RealSet: add closure and interior 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 methods declare_empty, declare_nonempty, is_empty, has_defined_points, open_cover_family
  • #31727 ManifoldSubset: Add methods subset_family, superset_family, open_superset_family; deprecate method list_of_subsets
  • #31736 ManifoldSubset: New methods declare_equal, equal_subsets, equal_subset_family
  • #31763 ManifoldSubset: New methods declare_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

Set_base and ConvexSet_base:

  • #31916 {Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}
  • #31919 ABC for convex sets
  • #31959 PolyhedronFace: Make it a subclass of ConvexSet_closed
  • #31990 ConvexSet_base: Add methods an_element, some_elements
  • #32013 Initialize a Set from a `ConvexSet_base instance

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 (23)

comment:1 Changed 8 months ago by mkoeppe

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comment:2 Changed 8 months ago by mkoeppe

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comment:3 Changed 8 months ago by mkoeppe

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comment:4 Changed 8 months ago by mkoeppe

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comment:5 Changed 8 months ago by mkoeppe

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comment:6 Changed 8 months ago by mkoeppe

  • Cc yzh added

comment:7 Changed 7 months ago by mkoeppe

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comment:8 Changed 7 months ago by mkoeppe

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comment:9 Changed 7 months ago by mkoeppe

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comment:10 Changed 7 months ago by mkoeppe

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comment:11 Changed 7 months ago by mkoeppe

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comment:12 Changed 7 months ago by mkoeppe

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comment:13 Changed 7 months ago by gh-mjungmath

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?

comment:14 Changed 7 months ago by mkoeppe

git log --first-parent goes a long way

comment:15 Changed 7 months ago by mkoeppe

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comment:16 Changed 7 months ago by gh-mjungmath

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 gh-mjungmath

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 gh-mjungmath

This is also good for subset topologies in case of e.g. embedded manifolds.

comment:19 Changed 7 months ago by mkoeppe

See also #31785 "Category of open subsets of a topological space".

comment:20 Changed 6 months ago by mkoeppe

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comment:21 Changed 6 months ago by mkoeppe

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comment:22 Changed 6 months ago by egourgoulhon

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comment:23 Changed 6 months ago by mkoeppe

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