#18783: Differentiable manifolds: basics
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: geometry | Keywords: differentiable
Merged in: | manifolds
Reviewers: | Authors: Eric Gourgoulhon,
Work issues: | Michal Bejger
Commit: | Report Upstream: N/A
db4dd7da31b0135806dc4be42842d8bfc5ed9d94| Branch:
Stopgaps: | public/manifolds/diff_manif_basics
| Dependencies: #18725, #18175
-------------------------------------+-------------------------------------
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 manifolds is generic, so that the
user may specify 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)
--
Ticket URL: <http://trac.sagemath.org/ticket/18783>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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