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18783 Differentiable manifolds: basics egourgoulhon egourgoulhon "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].
" enhancement closed major sage-7.2 geometry fixed differentiable manifolds mbejger bpillet Eric Gourgoulhon, Michal Bejger Volker Braun N/A 97172dde6f7b8a5f4002220f05554e351b48b4b1 97172dde6f7b8a5f4002220f05554e351b48b4b1 #18725, #18175