Chart: Implement pickling via __getstate__/__setstate__

[mkoeppe]

In this ticket, we implement the pickling protocol using __getstate__ and __setstate__

Depends on #31894

CC: @egourgoulhon @tscrim @mjungmath

Component: manifolds

Work Issues: redo on top of #31894

Branch/Commit: u/mkoeppe/chart__no_longer_use_uniquerepresentation__implement___getstate_____setstate__ @ 30a5d0b

Issue created by migration from https://trac.sagemath.org/ticket/31901

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,4 +1,7 @@
-Chart is missing `__classcall__` to normalize init arguments.
+Because of the method `add_restrictions` (which changes `self` by adding codomain restrictions), `Chart` needs to be considered as a mutable class. The current pickling based on `UniqueRepresentation` therefore cannot work correctly. 
 
-Perhaps all string parsing in `_init_coordinates` should already be done in `__classcall__`.
+In this ticket,
+- we make it possible to pass the codomain restrictions already when initializing the chart
+- we implement the pickling protocol using `__getstate__` and `__setstate__`
+- we implement the mutability protocol
 

[egourgoulhon]

Replying to @mkoeppe:

In this ticket,

• we make it possible to pass the codomain restrictions already when initializing the chart

This would be nice! In the early stages of the manifold project, I did not manage to do it simply, i.e. without changing Sage's preparser, since

sage: D = Manifold(2, 'D')                                                                          
sage: X.<x,y> = D.chart(restrictions=x^2 + y^2 < 1)                                                 

would generate NameError: name 'y' is not defined. Of course, one could replace x^2 + y^2 < 1 by the string "x^2 + y^2 < 1", but this is not very user-friendly. Do you already have some solution in mind?

[egourgoulhon]

comment:3

Some thought: if UniqueRepresentation is abandoned for charts, it may be desirable to maintain WithEqualityById (one of the two mother classes of UniqueRepresentation) to have a fast equality operator. Indeed charts are heavily used as dictionary keys: for coordinates of manifold points, for coordinate expressions of scalar fields (the latter being used, among other things, to store the components of tensor fields), for coordinate expressions of continuous maps between manifolds (the keys being pairs of charts in that case), etc. Certainly WithEqualityById is the fastest equality operator and thus provides a fast access to the above dictionaries.

[mkoeppe]

comment:4

Replying to @egourgoulhon:

Replying to @mkoeppe:

sage: D = Manifold(2, 'D')                                                                          
sage: X.<x,y> = D.chart(restrictions=x^2 + y^2 < 1)                                                 

would generate NameError: name 'y' is not defined. Of course, one could replace x^2 + y^2 < 1 by the string "x^2 + y^2 < 1", but this is not very user-friendly. Do you already have some solution in mind?

Ah! That's of course a problem, I didn't realize this

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,7 +1,6 @@
 Because of the method `add_restrictions` (which changes `self` by adding codomain restrictions), `Chart` needs to be considered as a mutable class. The current pickling based on `UniqueRepresentation` therefore cannot work correctly. 
 
 In this ticket,
-- we make it possible to pass the codomain restrictions already when initializing the chart
 - we implement the pickling protocol using `__getstate__` and `__setstate__`
 - we implement the mutability protocol
 

[mkoeppe]

comment:6

Maybe a chart should become immutable "upon first use"?

[mkoeppe]

Branch: u/mkoeppe/chart__no_longer_use_uniquerepresentation__implement___getstate_____setstate__

[mkoeppe]

New commits:

5215e93

Chart: WIP WithEqualityById instead of UniqueRepresentation; disambiguate _restrictions -> _coordinate_restrictions

[mkoeppe]

Description changed:

--- 
+++ 
@@ -4,3 +4,5 @@
 - we implement the pickling protocol using `__getstate__` and `__setstate__`
 - we implement the mutability protocol
 
+This is also preparation for #31894.
+

[mkoeppe]

Commit: 5215e93

[sagetrac-git]

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

facad97	ContinuousMap.preimage: Handle identity_map specially
c2ecf3e	ScalarField.preimage: Handle the case of the zero scalar field
3b1c428	ManifoldSubsetPullback: Make codomain_subset required 2nd init arg; fix pycodestyle/pyflakes warnings
d321b93	ContinuousMap: Return domain if the map's codomain is contained in the given subset
07aba9e	ManifoldSubsetPullback.is_closed: Preimage of finite sets is closed
653c651	src/sage/manifolds/subsets/pullback.py: Fix docstring markup
0f2e018	Merge #31688
e3e38ca	Chart.__init__: Move code that attaches self to the domain to TopologicalManifold.chart
3581c75	Chart.function_ring: Cache via @cached_method, not UniqueRepresentation
869599d	Chart: WIP equality/immutability/pickling

[sagetrac-git]

Changed commit from 5215e93 to 869599d

[mkoeppe]

Dependencies: #31688

[sagetrac-git]

Changed commit from 869599d to d071d56

[sagetrac-git]

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

d071d56

TopologicalSubmanifold: Adjust to renamed chart attribute _coord_restrictions