RealSet: Extend constructors so that they can build manifold objects

[mkoeppe]

From #30832:

We extend the RealSet constructors (default constructor and RealSet.open etc.) so that they can optionally build manifold objects; for example if structure or name is passed. This is done via chart pullbacks (#31688).

We deprecate the global bindings RealLine and OpenInterval (which will remain available through the manifolds catalog).

This will help make the functionality more discoverable. There are just too many global constructors: Reals, RealLine, RealSet, RealInterval, OpenInterval.

Depends on #31688
Depends on #32089
Depends on #30473

CC: @egourgoulhon @tscrim @mjungmath

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: f85db25

Reviewer: Michael Jung, Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31881

[mkoeppe]

Description changed:

--- 
+++ 
@@ -2,10 +2,17 @@
 
 We extend 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 (they are also available through the `manifolds` catalog).
+Overall, the `UniqueRepresentation` behavior of `RealLine` is inconsistent with the behavior of `Manifold`:
+
+```
+sage: RealLine(name='A') is RealLine(name='A')
+True
+sage: Manifold(1, name='A') is Manifold(1, name='A')
+False
+```
+but it is most disturbing for the invocation `RealLine()`, i.e., without an explicit `name` parameter. We deprecate this use of `RealLine` without `name` parameter - in preparation of using this as an alias for `RealSet(-oo, oo)` (the unique real line, without name or (mutable) manifold structure).
+
+We also deprecate the global binding `OpenInterval` (but it will remain available through the `manifolds` catalog).
 
 This will help make the functionality more discoverable. There are just too many global constructors: `Reals`, `RealLine`, `RealSet`, `RealInterval`, `OpenInterval`.
 
-
-
-

[egourgoulhon]

Replying to @mkoeppe:

Overall, the UniqueRepresentation behavior of RealLine is inconsistent with the behavior of Manifold:

sage: RealLine(name='A') is RealLine(name='A')
True
sage: Manifold(1, name='A') is Manifold(1, name='A')
False

This is intended because RealLine fully specifies the object (the set of real numbers endowed with the canonical manifold structure), while Manifold(1, name='A') does not (since there are two distinct manifolds of dimension 1: the real line and the circle). Hence RealLine has UniqueRepresentation behavior, while Manifold has not.

We also deprecate the global binding OpenInterval (but it will remain available through the manifolds catalog).

Agreed.

This will help make the functionality more discoverable. There are just too many global constructors: Reals, RealLine, RealSet, RealInterval, OpenInterval.

Indeed!

[mkoeppe]

comment:3

Replying to @egourgoulhon:

Replying to @mkoeppe:

Overall, the UniqueRepresentation behavior of RealLine is inconsistent with the behavior of Manifold:

sage: RealLine(name='A') is RealLine(name='A')
True
sage: Manifold(1, name='A') is Manifold(1, name='A')
False

This is intended because RealLine fully specifies the object [...]. Hence RealLine has UniqueRepresentation behavior, while Manifold has not.

I agree with this mathematical point, but on the implementation side you have additional mutable structure, namely the family of declared subsets, on every manifold. This makes the question of identity trickier.

[mkoeppe]

Dependencies: #31688

[mkoeppe]

Branch: u/mkoeppe/realset__extend_constructors_so_that_they_can_build_manifold_objects

[sagetrac-git]

Commit: 9db24e2

[sagetrac-git]

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

9db24e2

RealSet: Handle keywords arguments structure, name

[mkoeppe]

Changed dependencies from #31688 to #31688, #32089

[mkoeppe]

Changed dependencies from #31688, #32089 to #31688, #32089, #30473

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

2a23cb5	Unicode symbol 2202 (partial) for the text display of coordinate frames
5d096f1	f-string for unicode_symbol in TensorProductFunctor and SignedTensorProductFunctor
76c2fd5	Use Unicode symbol for the Riemann sphere example
5167e6c	Use Unicode symbol for default text display of RealLine
332410b	Use unicode_otimes in TensorProductFunctor and SignedTensorProductFunctor
f5d15d2	Merge branch 'public/manifolds/unicode_art' of git://trac.sagemath.org/sage into Sage 9.4.beta4.
d87d09b	#30473: fix doctest error in DiffMap.pullback
80321fe	Merge #30473
fe56446	RealSet: Update doctest output for manifold unicode changes
6f3a9cc	RealSet: Update new doctest output for manifold unicode changes

[sagetrac-git]

Changed commit from 9db24e2 to 6f3a9cc

[sagetrac-git]

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

cd83629	OpenInterval, RealLineDeprecate global bindings, replace all uses in doctests from manifolds catalog
ac561ae	Chart._restrict_set: Update doctest output
5a31e05	Merge #32089

[sagetrac-git]

Changed commit from 6f3a9cc to 5a31e05

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,18 +1,8 @@
 From #30832:
 
-We extend the `RealSet` constructors (default constructor and `RealSet.open` etc.) so that they can build manifold objects; for example if `structure` or `name` is passed
+We extend the `RealSet` constructors (default constructor and `RealSet.open` etc.) so that they can optionally build manifold objects; for example if `structure` or `name` is passed.
 
-Overall, the `UniqueRepresentation` behavior of `RealLine` is inconsistent with the behavior of `Manifold`:
-
-```
-sage: RealLine(name='A') is RealLine(name='A')
-True
-sage: Manifold(1, name='A') is Manifold(1, name='A')
-False
-```
-but it is most disturbing for the invocation `RealLine()`, i.e., without an explicit `name` parameter. We deprecate this use of `RealLine` without `name` parameter - in preparation of using this as an alias for `RealSet(-oo, oo)` (the unique real line, without name or (mutable) manifold structure).
-
-We also deprecate the global binding `OpenInterval` (but it will remain available through the `manifolds` catalog).
+We deprecate the global bindings `RealLine` and `OpenInterval` (which will remain available through the `manifolds` catalog).
 
 This will help make the functionality more discoverable. There are just too many global constructors: `Reals`, `RealLine`, `RealSet`, `RealInterval`, `OpenInterval`.