#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers:
Authors: Eric Gourgoulhon | Work issues:
Report Upstream: N/A | Commit:
Branch: | 252e616cc053a3b76ee563282222507cd78c9fb8
public/manifolds/top_manif_basics | Stopgaps:
Dependencies: #18175 |
-------------------------------------+-------------------------------------
Old description:
> This is the implementation of topological manifolds over a topological
> field ''K'' resulting from the [http://sagemanifolds.obspm.fr/
> SageManifolds project]. See the meta-ticket #18528 for an overview.
> By ''topological manifold over a topological field K'' it is meant a
> second countable Hausdorff space ''M'' such that every point in ''M'' has
> a neighborhood homeomorphic to ''K^n^'', with the same non-negative
> integer ''n'' for all points.
>
> This tickets implements the following Python classes:
>
> - `TopologicalManifold`: topological manifold over a topological field
> ''K''
> - `TopologicalManifoldPoint`: point in a topological manifold
> - `TopologicalManifoldSubset`: generic subset of a topological manifold
> - `Chart`: chart of a topological manifold
> - `RealChart`: chart of a topological manifold over the real field
> - `CoordChange`: transition map between two charts of a topological
> manifold
>
> `TopologicalManifold` is intended to serve as a base class for specific
> manifolds, like smooth manifolds (''K''='''R''') and complex manifolds
> (''K''='''C''').
>
> '''Documentation''':
> The reference manual is produced by
> `sage -docbuild reference/manifolds html`
> It can also be accessed online at
> http://sagemanifolds.obspm.fr/doc/18529/reference/manifolds/
> More documentation (e.g. example worksheets) can be found
> [http://sagemanifolds.obspm.fr/documentation.html here].
New description:
This is the implementation of topological manifolds over a topological
field ''K'' resulting from the [http://sagemanifolds.obspm.fr/
SageManifolds project]. See the meta-ticket #18528 for an overview.
By ''topological manifold over a topological field K'' it is meant a
second countable Hausdorff space ''M'' such that every point in ''M'' has
a neighborhood homeomorphic to ''K^n^'', with the same non-negative
integer ''n'' for all points.
This tickets implements the following Python classes:
- `TopologicalManifold`: topological manifold over a topological field
''K''
- `TopologicalManifoldPoint`: point in a topological manifold
- `TopologicalManifoldSubset`: generic subset of a topological manifold
- `Chart`: chart of a topological manifold
- `RealChart`: chart of a topological manifold over the real field
- `CoordChange`: transition map between two charts of a topological
manifold
`TopologicalManifold` is intended to serve as a base class for specific
manifolds, like smooth manifolds (''K''='''R''') and complex manifolds
(''K''='''C'''). The follow-up ticket, implementing continuous functions
to the base field, is #18640.
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at
http://sagemanifolds.obspm.fr/doc/18529/reference/manifolds/
More documentation (e.g. example worksheets) can be found
[http://sagemanifolds.obspm.fr/documentation.html here].
--
Comment (by egourgoulhon):
The above commit takes into account
[https://groups.google.com/forum/#!topic/sage-devel/Vzfj1haZHho this
discussion on sage-devel], as well as the first recommendation of Travis
in comment:41 : it removes `UniqueRepresentation` for manifolds and
charts, leaving only `WithEqualityById`. Some methods `_test_pickling`
have been introduced. They are weaker than `SageObject._test_pickling` in
the sense that they do not demand `loads(dumps(M)) == M` (which equality-
by-id forbids without any unique representation). However, these local
`_test_pickling` methods perform non trivial tests: they guarantee that
`loads(dumps(M))` proceeds without any error and they check the identity
of some characteristics between the unpickled object and the original one.
All the test suites are passed.
In addition the above commit takes into account the recommendation of
Jeroen in comment:49.
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:52>
Sage <http://www.sagemath.org>
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