Make open subsets of immersed/embedded submanifolds immersed/embedded submanifolds

[mkoeppe]

This would be convenient for example for #31660.

To implement this, we refactor the method open_subset, already now duplicated between TopologicalManifold and DifferentiableManifold through a new method _init_open_subset.

CC: @mjungmath @egourgoulhon @tscrim

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 58b43f7

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/31674

[mjungmath]

comment:1

Why not simply overwriting open_subset in TopologicalSubmanifold etc.?

[mkoeppe]

comment:2

It would lead to at least 3 more copies of the same code

[mkoeppe]

Branch: u/mkoeppe/make_open_subsets_of_immersed_embedded_submanifolds_immersed_embedded_submanifolds

[mkoeppe]

Commit: 1f6f295

[mkoeppe]

comment:4

Here's the first copy

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New commits:

1f6f295

TopologicalSubmanifold.open_subset: New

[sagetrac-git]

Changed commit from 1f6f295 to 58110f2

[sagetrac-git]

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

58110f2

TopologicalSubmanifold.open_subset: Fix docstring

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

Changed commit from 58110f2 to d815b63

[sagetrac-git]

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

d815b63

{DifferentiableSubmanifold,PseudoRiemannianSubmanifold}.open_subset: New

[sagetrac-git]

Changed commit from d815b63 to 004c23a

[sagetrac-git]

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

aac8835	{Topological,Differentiable,PseudoRiemannianSubmanifold}._repr_: Print subsets as subsets
004c23a	Add/update examples

[egourgoulhon]

Replying to @mkoeppe:

To implement this, perhaps the method open_subset, already now duplicated between TopologicalManifold and DifferentiableManifold could be refactored through a new method open_subset_class.

It sounds indeed a good idea to refactor the common code in the two (now three) open_subset methods!

Note that the comment

#!# update vector frames and change of frames

in DifferentiableManifold.open_subset means that vector frames that are not coordinate frames could be inherited from those on the ambient manifold. I've put the marker #!# to indicate that this is not implemented yet. For example:

sage: M = Manifold(2, 'M')                                                                                              
sage: X.<x,y> = M.chart()                                                                                               
sage: e0 = M.vector_field(1, 1)                                                                                          
sage: e1 = M.vector_field(1, -2)                                                                                         
sage: e = M.vector_frame('e', (e0, e1))                                                                                   
sage: M.frames()                                                                                                        
[Coordinate frame (M, (d/dx,d/dy)), Vector frame (M, (e_0,e_1))]
sage: U = M.open_subset('U', coord_def={X: x>0})                                                                        
sage: U.frames()                                                                                                        
[Coordinate frame (U, (d/dx,d/dy))]

The vector frame e is thus not transmitted to U. Of course, this can be achieved at any moment by the method restrict:

sage: e.restrict(U)                                                                                                     
Vector frame (U, (e_0,e_1))
sage: U.frames()                                                                                                        
[Coordinate frame (U, (d/dx,d/dy)), Vector frame (U, (e_0,e_1))]

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New commits:

aac8835	{Topological,Differentiable,PseudoRiemannianSubmanifold}._repr_: Print subsets as subsets
004c23a	Add/update examples

[mkoeppe]

comment:10

Replying to @egourgoulhon:

Replying to @mkoeppe:
Note that the comment

#!# update vector frames and change of frames

in DifferentiableManifold.open_subset means that vector frames that are not coordinate frames could be inherited from those on the ambient manifold. I've put the marker #!# to indicate that this is not implemented yet.

Yes, I have faithfully copied these TODO markers. Should this be implemented on this ticket?

[egourgoulhon]

comment:11

Replying to @mkoeppe:

Replying to @egourgoulhon:

Replying to @mkoeppe:
Note that the comment

#!# update vector frames and change of frames

in DifferentiableManifold.open_subset means that vector frames that are not coordinate frames could be inherited from those on the ambient manifold. I've put the marker #!# to indicate that this is not implemented yet.

Yes, I have faithfully copied these TODO markers. Should this be implemented on this ticket?

Maybe. I leave it to you. Actually, I don't remember why this was not implemented in the first version of the open_subset method.