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

[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

[sagetrac-git]

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

5571025	RealSet: Use ambient.manifold().canonical_chart(), add nested example
766b141	RealSet: Add another example

[sagetrac-git]

Changed commit from 5a31e05 to 766b141

[mjungmath]

comment:15

This looks nice. Makes the access of these objects more natural. Good work!

Two things:

1. For some reason, there is no documentation of the class RealSet. That's a pity. It would be nice to add at least an INPUT block and explain the optional keyword(s). We should also shift the preexisting examples in __init__ to the RealSet class documentation, where they can be seen from the official documentation.
2. Similarly it would be good to extend the INPUT block for each method with those new optional keywords accordingly (perhaps it is enough to refer to RealSet, once this is documented). A short example per method would be preferable, too.

[sagetrac-git]

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

4558e26	Polyhedron_base.incidence_matrix: Remove accidental change to doctest
b537f1b	Merge #31688
63c2cfe	ConvexSet_base._test_convex_set: Do not test _test_as_set_object here
4844cd6	Merge #32013
d6055c4	Merge #32089

[sagetrac-git]

Changed commit from 766b141 to d6055c4

[sagetrac-git]

Changed commit from d6055c4 to ffe18b0

[sagetrac-git]

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

f2ae50e	#30473: fix doctests outside sage/manifolds and sage/tensor/modules
55240bb	Merge #30473
82f12e2	Merge #32013
0f60232	ConditionSet: Do not sort the conditions, just use _stable_uniq
69d045a	ConditionSet: In doctests, do not rename ZZ^2 etc.
ffe18b0	Merge #32089

[mkoeppe]

comment:18

Thanks for taking a look, I'll work on the documentation.

[mjungmath]

comment:52

It's good to maintain some consistency. Besides, the patchbot doesn't like it. So it must be of some importance.

I am just afraid: if we don't fix it here, we probably will never...

[tscrim]

comment:53

You can push a review commit or do a general cleanup ticket later on. It is there in the patchbot as advice to the reviewer. You have some discretion about these things.

[mjungmath]

comment:54

As proposed by Travis, here is a clean-up follow-up ticket: #32192.

LGTM.

[mjungmath]

Reviewer: Michael Jung, Eric Gourgoulhon

[mkoeppe]

comment:56

Thanks!

[vbraun]

comment:57

PDF docs don't build

[sagetrac-git]

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

80f6195	Chart, RealChart: In class docstring, order arguments as they appear in __classcall__/__init__
a39e6fc	DiffChart, RealDiffChart: In class docstring, order arguments as they appear in __classcall__/__init__; add description of argument coord_restrictions
cdf20b0	TopologicalManifold.chart: Add description of argument coord_restrictions
741fd2e	TopologicalManifold.chart: Add an example of using coord_restrictions
bf62543	Merge branch 't/32089/conditionset__conditionset_callable_symbolic_expression' into t/32009/eliminate_direct_use_of_the_chart__domain_attribute
141ccb5	Merge #32009
c89c697	Merge #32102
451f5cf	Sets.ParentMethods: Update doctest
f135a05	Merge #32015
8093a4d	Merge #32089

[sagetrac-git]

Changed commit from cb307e1 to 8093a4d

[mkoeppe]

comment:59

Works for me after merging the lastest versions of the dependencies

[vbraun]

comment:60

Still borked. Make sure you merge in the next beta before changing the state again.

[sagetrac-git]

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

3ce89e8	Merge tag '9.4.beta6' into t/31881/realset__extend_constructors_so_that_they_can_build_manifold_objects
f85db25	src/sage/docs/conf.py: Add more \DeclareUnicodeCharacter

[sagetrac-git]

Changed commit from 8093a4d to f85db25

[mkoeppe]

comment:62

OK, found it, fixed it

[vbraun]

Changed branch from u/mkoeppe/realset__extend_constructors_so_that_they_can_build_manifold_objects to f85db25