#18529: Topological manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: geometry | Resolution:
Keywords: topological | Merged in:
manifolds | Reviewers: Travis Scrimshaw
Authors: Eric Gourgoulhon, | Work issues:
Travis Scrimshaw | Commit:
Report Upstream: N/A | 984c3c26bf827f44eee26fc6afd321e11dca8f2e
Branch: | Stopgaps:
public/manifolds/top_manif_basics |
Dependencies: #18175 |
-------------------------------------+-------------------------------------
Description changed by egourgoulhon:
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''
> - `OpenTopologicalSubmanifold`: open subset of a topological manifold
> - `ManifoldSubset`: generic subset of a topological manifold
> - `ManifoldPoint`: point in 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
>
> as well as some technical classes: `AbstractNamedObject`, `AbstractSet`,
> `TopologicalStructure` and
> `RealTopologicalStructure`.
>
> `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].
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:
- `ManifoldSubset`: generic subset of a topological manifold (the open
subsets being implemented by the subsclass `TopologicalManifold`)
- `TopologicalManifold`: topological manifold over a topological field
''K''
- `ManifoldPoint`: point in 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
as well as the singleton classes`TopologicalStructure` and
`RealTopologicalStructure`.
`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].
--
--
Ticket URL: <http://trac.sagemath.org/ticket/18529#comment:116>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
