Connect RealSet to sage.manifolds

[mkoeppe]

Instances of RealSet that are finite unions of open intervals should be connected in some way to sage.manifolds, in particular to OpenInterval and RealLine (which are both in the global namespace).

In this ticket, we add functionality to initialize a RealSet from instances of OpenInterval and RealLine, as well as from their topological closures (#31644)

Depends on #31644
Depends on #31877

CC: @mjungmath @egourgoulhon @tscrim

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 81b43f4

Reviewer: Michael Jung

Issue created by migration from https://trac.sagemath.org/ticket/30832

[mkoeppe]

comment:2

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

Dependencies: #31644

[mkoeppe]

Branch: u/mkoeppe/connect_realset_to_sage_manifolds

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Last 10 new commits:

e7f7a7d	Merge #31764
9259a2c	Merge #31798
ac53984	src/sage/manifolds/subsets/__init__.py: New
21739de	src/sage/manifolds/subset.py: Simplify code, make pyflakes happy
6bbd4ae	src/sage/manifolds/subset.py: Add coding header
2d7fda7	src/sage/manifolds/subset.py: Simplify code more to make pyflakes happy
8d3ad85	Merge #31764
60505b0	Merge #31798
9dd9f90	Merge #31644
fb33c0f	RealSet: Allow initialization from RealLine and OpenInterval instances and OpenInterval closures

[mkoeppe]

Commit: fb33c0f

[mjungmath]

comment:6

Restricted to open intervals (not closures), this is nothing but the forgetful functor from manifolds into sets. Perhaps it is a good idea to add this functor somehow?

Other than that it looks good! Let's wait for the patchbot.

[mkoeppe]

comment:7

... or rather from manifolds to topological spaces (see #31877).

Do we have forgetful functors anywhere already?

[mkoeppe]

comment:8

We may also want to consider

• adding a method RealSet.as_manifold_subset
• extending the RealSet constructors (default constructor and RealSet.open etc.) so that they can build manifold objects; for example if structure or name is passed; then perhaps the global bindings RealLine and OpenInterval can be deprecated.

[mjungmath]

comment:9

Notice that RealSet supports unions of intervals whereas OpenInterval does not.

[mjungmath]

comment:10

Moreover, you represented closed or clopen intervals by a topological closure, which is fine for now. But as soon as we have manifolds with boundary, we probably want them to be represented by those objects/instances instead (or as well).

[mjungmath]

comment:11

LGTM

[mjungmath]

Reviewer: Michael Jung

[mkoeppe]

comment:12

Replying to @mjungmath:

Notice that RealSet supports unions of intervals whereas OpenInterval does not.

Yes, it does. You can initialize a RealSet using several OpenInterval instances, and it will take the union.

[mkoeppe]

comment:13

Thanks for the review!

[mjungmath]

comment:14

Replying to @mkoeppe:

Replying to @mjungmath:

Notice that RealSet supports unions of intervals whereas OpenInterval does not.

Yes, it does. You can initialize a RealSet using several OpenInterval instances, and it will take the union.

That is not what I mean. There are no unions of OpenInterval on the manifold level yet. This is, for example, important for a potential RealSet.as_manifold_subset.

[mkoeppe]

comment:15

Replying to @mjungmath:

There are no unions of OpenInterval on the manifold level yet. This is, for example, important for a potential RealSet.as_manifold_subset.

If you create OpenInterval instances with the same ambient_interval set, then you can take unions.

sage: I02 = OpenInterval(0, 2, ambient_interval=RealLine())
sage: I13 = OpenInterval(1, 3, ambient_interval=RealLine())
sage: I02.union(I13)
Open subset (0, 2)_union_(1, 3) of the Real number line R

[mjungmath]

comment:16

Right, but

sage: I02 = OpenInterval(0, 2, ambient_interval=RealLine())
sage: I13 = OpenInterval(1, 3, ambient_interval=RealLine())
sage: U = I02.union(I13)
sage: RealSet(U)

won't work, no?

[mkoeppe]

comment:17

Good catch...

[mkoeppe]

comment:18

Folllow up in #31878.

[tscrim]

comment:19

Replying to @mkoeppe:

... or rather from manifolds to topological spaces (see #31877).

Do we have forgetful functors anywhere already?

categories.functor.ForgetfulFunctor

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. Last 10 new commits:

fd4506a	Merge #31732
7fed9ef	Merge #31736
c4acd09	Merge tag '9.4.beta2' into t/31763/manifoldsubset__new_methods_declare_subset__declare_superset
2ba18ab	Merge #31763
0e9e5cd	Merge #31732
a96f736	Merge #31736
582b58d	Merge #31763
2113f78	Merge #31764
9abc617	Merge #31798
785aed0	Merge #31644

[sagetrac-git]

Changed commit from fb33c0f to 785aed0

[mkoeppe]

comment:21

Trivial merge with updated dependency

[mkoeppe]

Changed dependencies from #31644 to #31644, #31877

[sagetrac-git]

Changed commit from 785aed0 to 81b43f4

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

4b09685	RealSet: Put it in a suitable subcategory of TopologicalSpaces()
46eed0e	RealSet.ambient: Change to a normal method
5b8ceca	InternalRealInterval, RealSet: Add `_latex_` methods
69ca854	RealSet._repr_: Use unicode cup sign instead of +
dbdfc06	InternalRealInterval, RealSet: Remove extra whitespace in latex, add documentation
7f56338	PiecewiseFunction: Adjust doctests for changed RealSet repr
8abdc8b	src/sage/functions/piecewise.py: Add coding header
5b0f85d	Merge #31880
81b43f4	Merge branch 't/31877/refine_category_of_realset' into t/30832/connect_realset_to_sage_manifolds

[mkoeppe]

comment:24

Another trivial merge to remove a merge conflict

[vbraun]

Changed branch from u/mkoeppe/connect_realset_to_sage_manifolds to 81b43f4