Topological manifolds: morphisms

[egourgoulhon]

This ticket implements morphisms of topological manifolds, i.e. continuous maps between topological manifolds. This is a follow-up of #18640 within the ​SageManifolds project. See the metaticket #18528 for an overview.

Two new Python classes are introduced in this ticket:

• the parent class TopologicalManifoldHomset for sets Hom(M,N) of morphisms between two topological manifolds M and N over the same topological field K
• the element class ContinuousMap for elements of Hom(M,N), i.e. continuous maps M --> N

Moreover, this ticket introduces plotting capabilities for charts (method RealChart.plot()) and for points (method ManifoldPoint.plot()), which require continuous maps and thus could not have been introduced in #18529.

Documentation: The reference manual is produced by sage -docbuild reference/manifolds html It can also be accessed online at ​http://sagemanifolds.obspm.fr/doc/18725/reference/manifolds/ More documentation (e.g. example worksheets) can be found ​here.

[git]

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

​bab7bb4

Add doctests to TopManifoldHomset and ContinuousMap

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

​6289514

Remove unnecessary import in chart.py

[git]

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

​a4b414c

Modifications in CoordChange and TopManifold.__init__ to allow for subclasses.

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

​0880811

Changes in ContinuousMap, in particular in __invert__

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

​30e812a

Minor modifications in CoordFunctionSymb and ContinuousMap.__invert__

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

​c0b3284

Improve documentation of classes Chart and ContinuousMap

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

​4c72118

Add method plot() to RealChart and TopManifoldPoint

[git]

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

​055bf3e

Improve documentation of RealChart.plot() and TopManifoldPoint.plot()

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

​57b21df

Add doctest to set_axes_labels

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

​e558c06

Improvement in simplify_sqrt_real(); TestSuite run non-verbose

[git]

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

​d65f654

Introduce open covers on top manifolds + many improvements in the documentation

[git]

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

​00c327d

Slight reorganization of the reference manual of topological manifolds (morphisms part)

[git]

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

​4de19a7	Merge branch 'public/manifolds/top_manif_basics' of git://trac.sagemath.org/sage into sage 6.9
​ccc2f81	Remove unnecessary import in chart.py
​aad7c58	Modifications in CoordChange and TopManifold.__init__ to allow for subclasses.
​3f22784	Minor modifications in CoordFunctionSymb
​ba5d142	Improvement in simplify_sqrt_real() and in the documentation.
​9977194	Minor improvements in the doc of top manifolds (scalar fields part)
​63357e4	Introduce open covers on top manifolds and improve documentation
​92da04b	Slight reorganization of the reference manual for topological manifolds (scalar field part)
​31d3fa5	Merge #18640 into #18529
​f8d3f27	Merge #18725 into #18640

[git]

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

​375ff46	Fixing doctest failures and letting a few other rings know they are metric spaces.
​8b851a0	Merge branch 'develop' into public/categories/topological_metric_spaces-18175
​f8f5b93	Fixing last remaining doctests.
​041a5d1	Adding p-adics to metric spaces and some cleanup.
​bfa0cdf	One last doc tweak.
​d13c368	Fixing doc of metric spaces.
​2605c0b	Merge #18529 (Topological manifolds: basics) into #18175 (Implement categories for topological...)
​6dec6d5	Implement topological manifolds (basics, #18529) on the new categories for manifolds (#18175)
​3403978	Implement top. manifolds (scalar fields, #18640) on the new manifold categories (#18175)
​b0521ef	Implement top. manifolds (morphisms, #18725) on the new manifold categories (#18175)

[git]

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

​f582241	Introduce function Manifold() as the global entry point to construct any type of manifold.
​f342e03	Remove UniqueRepresentation from topological manifolds, subsets and charts.
​902908b	Revert to UniqueRepresentation for topological manifolds and charts, with the possibility to reuse manifold names.
​252e616	Remove UniqueRepresentation, leaving only WithEqualityById, for topological manifolds and charts.
​e7139ab	Merge branch top_manif_basics without UniqueRepresentation into top_manif_scalar_fields.
​e2f192f	Remove UniqueRepresentation, leaving only WithEqualityById, for scalar fields on topological manifolds
​668bc26	Remove UniqueRepresentation, leaving only WithEqualityById, for topological manifold homsets

[egourgoulhon]

The above commit takes into account ​this discussion on sage-devel and on ticket #18529: it removes UniqueRepresentation for the class TopologicalManifoldHomset, leaving only WithEqualityById.

[git]

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

​6518699	Introduce the attribute _field_type in class TopologicalManifold to check for real and complex manifolds.
​22383e6	Check for real/complex manifold performed on base_field_type() instead of RR/CC
​66f2c5a	Change function('f', x) to function('f')(x) to accomodate the deprecation warning introduced in #17447
​a28ed04	Morphisms of topological manifolds with the use of base_field_type()

[git]

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

​d8397c1	Merge branch 'public/manifolds/top_manif_basics' of trac.sagemath.org:sage into public/manifolds/top_manif_basics
​0b08b11	Some small tweaks as part of the review.
​d3e5d4d	Revert to UniqueRepresentation for topological manifolds
​2481359	Revert to UniqueRepresentation for ScalarFieldAlgebra; better ScalarField constructor
​0cc06e8	Revert to UniqueRepresentation for topological manifold homsets

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

​85d03dc	Change the argument type to structure in Manifold
​5251ef0	Remove method _test_pickling from class TopologicalManifoldPoint
​f69c9ee	Fix doctest error in coord_func_symb.py due to #19312 (update to pynac-0.5.2)
​7889a5d	Change in simplify_sqrt_real to cope with the change of != operator induced by #19312 (Sage 6.10.beta7)

[git]

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

​2ca24ff	Merge branch 'public/manifolds/top_manif_basics' of git://trac.sagemath.org/sage into Sage 6.10.rc1
​0fb39df	Refactoring the code to separate out the structural part of the manifold.
​cdfa817	Merge branch u/tscrim/top_manifolds_refactor into Sage 6.10.rc1 + public/manifolds/top_manif_basics
​c5f35af	Make AbstractSet inherit from UniqueRepresentation; correct doctests; start to change documentation.
​3a52500	Some class renaming; add more examples and doctests (full coverage)
​a1ba52a	Replace a!=b by not(a==b) in simplify_sqrt_real to cope with the change of logic induced by #19312 (Sage 6.10.beta7)
​e2c7ab3	Scalar fields on the refactored topoological manifolds
​cb53417	Add argument full_name to AbstractNamedObject; remove _repr_() from all parent classes; improve documentation
​ce03503	Scalar fields on topological manifolds: slight improvements in the documentation
​bc77059	Morphisms on the refactored topoological manifolds

[git]

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

​c38ae80	Suppress the (unused) argument category in OpenTopologicalSubmanifold; minor doc improvements
​069baf4	Merge branch 'public/manifolds/top_manif_basics' into Sage 7.0.beta2.
​19caedb	Revert to AbstractNamedObject without argument full_name; restore _repr_() in manifold classes
​9d25aa0	Scalar field algebras with AbstractNamedObject without argument full_name
​ed4aa58	ScalarFieldAlgebra does not longer inherit from AbstractNamedObject
​f6c6a34	Topological manifold morphisms with AbstractNamedObject without full_name

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

​3cd03a4	Add methods lift() and retract() to ManifoldSubset; add method __eq__() in CoordChange
​984c3c2	Revert to simple hierarchy for manifold classes
​c01048f	Scalar fields with the simplified hierarchy for manifold classes
​c866d6c	Morphisms of topological manifolds with the simplified hierarchy for manifold classes

[git]

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

​8e17d54	Merge into the latest version of #18529; improve treatment of composite functions in ExpressionNice
​f00be00	Topological manifold morphisms: solved merge conflict with Sage 7.1.beta1

[git]

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

​c767696	Merge branch 'public/manifolds/top_manif_scalar_fields' of trac.sagemath.org:sage into public/manifolds/top_manif_scalar_fields
​3b92a85	Some formatting and small reviewer changes.
​e44f7d9	Merge branch 'develop' into public/manifolds/top_manif_scalar_fields
​0fd44d6	Some cleanup and creating a parent for coordinate functions.
​33abe9e	Marking known bugs in utilities.py.
​57b7b7b	Implementing global_options for display formatting.
​f11df50	Set CoordFunctionSymbRing in the category of commutative algebras over SR; minor documentation changes
​d190b37	Morphisms of topological manifolds with coordinate functions as algebra elements

[git]

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

​2577fc5

Fixing a (essentially trivial) doctest failure.

[tscrim]

​2577fc5 was meant to go on #18640. However, #18640 will merge in with this cleanly (at the very minor cost of a merge commit). The other option would be to start a "new" branch here rebased on #18640.

[git]

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

​f3f5470	Fixing a (essentially trivial) doctest failure.
​7b3dab3	Merge branch 'public/manifolds/top_manif_scalar_fields' of git://trac.sagemath.org/sage into Sage 7.2.rc0
​9ec7d3e	Python 3 format for print in manifolds
​7125e29	Python3 format for print in morphims of topological manifolds

[git]

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

​4fad094	Merge branch 'public/manifolds/top_manif_morphisms' of trac.sagemath.org:sage into public/manifolds/top_manif_morphisms
​cfecb18	Reviewer changes and tweaks for continuous maps ticket.

[tscrim]

Okay, I made it through this ticket. I made a number of formatting changes and little tweaks that I think improves the doc (including a few I missed on the previous ticket). I also made aliases *expression of *expr because it is good to be verbose, made some things @cached_method rather than doing attribute caching, and used the @options decorator for some plot() options. If you agree with my changes, you can set a positive review.

[git]

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

​efcb618

Modify authorship for continuous maps.

[egourgoulhon]

Replying to tscrim:

Okay, I made it through this ticket. I made a number of formatting changes and little tweaks that I think improves the doc (including a few I missed on the previous ticket). I also made aliases *expression of *expr because it is good to be verbose, made some things @cached_method rather than doing attribute caching, and used the @options decorator for some plot() options. If you agree with my changes, you can set a positive review.

Thank you very much for all the improvements. I've made a few checks on the impact on the subsequent tickets in #18528 (especially regarding the changes in TopologicalManifoldHomset.__call__); they all passed. So I am setting the ticket to positive review.