RealSet: add methods closure, interior, boundary, is_open, is_closed

[mkoeppe]

The intervals in a RealSet already have these methods.

It would also be nice to be able to compute closure and interior relative to a given larger RealSet.

sage: RealSet((1, 2)).closure(relative_to=RealSet((0, 2))  # wishful thinking
[1, 2)

One could also imagine that these should be methods of the real fields (such as RR) considered as a members of the category TopologicalSpaces.

Depends on #31880

CC: @rwst @vbraun @pjbruin @tscrim @mjungmath @yuan-zhou

Component: basic arithmetic

Author: Matthias Koeppe

Branch/Commit: 9d41f0e

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/21243

[mkoeppe]

Dependencies: #31880

[mkoeppe]

Branch: u/mkoeppe/realset__add_methods_closure__interior__boundary__is_open__is_closed

[mkoeppe]

New commits:

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
a0e3bf5	Merge #31880
181b128	RealSet.is_open, is_closed, closure, interior, boundary: New

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Commit: 181b128

[sagetrac-git]

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

7f56338	PiecewiseFunction: Adjust doctests for changed RealSet repr
8cd74b5	Merge #31880

[sagetrac-git]

Changed commit from 181b128 to 8cd74b5

[tscrim]

comment:7

Could you also add a test:

RealSet((1, 2), (2, 3)).boundary()

Other than that, LGTM.

[sagetrac-git]

Changed commit from 8cd74b5 to 8fdb104

[sagetrac-git]

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

8fdb104

RealSet.boundary: Add another doctest

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:9

Thank you.

[mkoeppe]

comment:10

Thanks for reviewing!

[sagetrac-git]

Changed commit from 8fdb104 to 9d41f0e

[sagetrac-git]

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

9d41f0e

src/sage/sets/real_set.py: Remove unnecessary import

[mkoeppe]

comment:12

(as requested in #31927 comment:8)

[vbraun]

Changed branch from u/mkoeppe/realset__add_methods_closure__interior__boundary__is_open__is_closed to 9d41f0e