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]

Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
-Instances of `RealSet` that are finite unions of open intervals should be connected in some way to `sage.manifolds`, in particular to `OpenInterval`.
+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)
 
 

[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