#18783: Differentiable manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: geometry | Resolution:
Keywords: differentiable | Merged in:
manifolds | Reviewers:
Authors: Eric Gourgoulhon, | Work issues:
Michal Bejger | Commit:
Report Upstream: N/A | e8d2ba6665db79c07866b1ccb4c3057224881f49
Branch: | Stopgaps:
public/manifolds/diff_manif_basics |
Dependencies: #18725, #18175 |
-------------------------------------+-------------------------------------
Description changed by egourgoulhon:
Old description:
> This is the first ticket about the implementation of differentiable
> manifolds resulting from the [http://sagemanifolds.obspm.fr/
> SageManifolds project]. See the metaticket #18528 for an overview.
>
> The base field K of the differentiable manifold is generic (only assumed
> to be some non-discrete topological field), so that the user may specify
> e.g. K='''R''' (real manifolds) or K='''C''' (complex manifolds). This
> ticket implements the following Python classes, all of them being
> subclasses of classes introduced for topological manifolds (tickets
> #18529, #18640, #18725):
>
> - `DiffManifold` (subclass of `TopManifold`, cf. #18529): differentiable
> manifold over
> a topological field K (Parent class)
> - `DiffChart` (subclass of `Chart`, cf. #18529): chart of a
> K-differentiable atlas
> - `RealDiffChart` (subclass of `RealChart`, cf. #18529): chart of a
> K-differentiable atlas
> for K='''R'''
> - `DiffCoordChange` (subclass of `CoordChange`, cf. #18529):
> differentiable transition map
> - `DiffScalarFieldAlgebra` (subclass of `ScalarFieldAlgebra`, cf.
> #18640): set C^k^(M) of
> k-times continuously K-differentiable functions M --> K, where M is a
> differentiable manifold
> over K, C^k^(M) being a commutative algebra over K (Parent class)
> - `DiffScalarField` (subclass of `ScalarField`, cf. #18640): k-times
> continuously
> K-differentiable function M --> K (Element class)
> - `DiffManifoldHomset` (subclass of `TopManifoldHomset`, cf. #18725): set
> Hom(M,N) of
> differentiable maps between the differentiable manifolds M and N over
> the same topological
> field K (Parent class)
> - `DiffMap` (subclass of `ContinuousMap`, cf. #18725): differentiable map
> M --> N (Element class)
>
> '''Documentation''':
> The reference manual is produced by
> `sage -docbuild reference/manifolds html`
> It can also be accessed online at
> http://sagemanifolds.obspm.fr/doc/18783/reference/manifolds/
> More documentation (e.g. example worksheets) can be found
> [http://sagemanifolds.obspm.fr/documentation.html here].
New description:
This is the first ticket about the implementation of differentiable
manifolds resulting from the [http://sagemanifolds.obspm.fr/ SageManifolds
project]. See the metaticket #18528 for an overview.
The base field K of the differentiable manifold is generic (only assumed
to be some non-discrete topological field), so that the user may specify
e.g. K='''R''' (real manifolds) or K='''C''' (complex manifolds). This
ticket implements the following Python classes, all of them being
subclasses of classes introduced for topological manifolds (tickets
#18529, #18640, #18725):
- `DifferentiableManifold` (subclass of `TopologicalManifold`, cf.
#18529): differentiable
manifold over a topological field K (Parent class)
- `DiffChart` (subclass of `Chart`, cf. #18529): chart of a
K-differentiable atlas
- `RealDiffChart` (subclass of `RealChart`, cf. #18529): chart of a
K-differentiable atlas
for K='''R'''
- `DiffCoordChange` (subclass of `CoordChange`, cf. #18529):
differentiable transition map
- `DiffScalarFieldAlgebra` (subclass of `ScalarFieldAlgebra`, cf. #18640):
set C^k^(M) of
k-times continuously K-differentiable functions M --> K, where M is a
differentiable manifold
over K, C^k^(M) being a commutative algebra over K (Parent class)
- `DiffScalarField` (subclass of `ScalarField`, cf. #18640): k-times
continuously
K-differentiable function M --> K (Element class)
- `DiffManifoldHomset` (subclass of `TopManifoldHomset`, cf. #18725): set
Hom(M,N) of
differentiable maps between the differentiable manifolds M and N over
the same topological
field K (Parent class)
- `DiffMap` (subclass of `ContinuousMap`, cf. #18725): differentiable map
M --> N (Element class)
The follow-up ticket is #18843.
'''Documentation''':
The reference manual is produced by
`sage -docbuild reference/manifolds html`
It can also be accessed online at
http://sagemanifolds.obspm.fr/doc/18783/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/18783#comment:16>
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