Differentiable manifolds: basics

[egourgoulhon]

This is the first ticket about the implementation of differentiable manifolds resulting from the 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. Topological manifolds: basics #18529): differentiable
  manifold over a topological field K (Parent class)
• DiffChart (subclass of Chart, cf. Topological manifolds: basics #18529): chart of a K-differentiable atlas
  • RealDiffChart (subclass of RealChart, cf. Topological manifolds: basics #18529): chart of a K-differentiable atlas
    for K=R
• DiffCoordChange (subclass of CoordChange, cf. Topological manifolds: basics #18529): differentiable transition map
• DiffScalarFieldAlgebra (subclass of ScalarFieldAlgebra, cf. Topological manifolds: scalar fields #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. Topological manifolds: scalar fields #18640): k-times continuously
  K-differentiable function M --> K (Element class)
• DiffManifoldHomset (subclass of TopManifoldHomset, cf. Topological manifolds: morphisms #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. Topological manifolds: morphisms #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 here.

Depends on #18725
Depends on #18175

CC: @sagetrac-mbejger @sagetrac-bpillet

Component: geometry

Keywords: differentiable manifolds

Author: Eric Gourgoulhon, Michal Bejger

Branch/Commit: 97172dd

Reviewer: Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/18783

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f4c9f0f

Start to improve the documentation of differentiable manifolds

[sagetrac-git]

Changed commit from db4dd7d to f4c9f0f

[sagetrac-git]

Changed commit from f4c9f0f to 999cac5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

999cac5

Minor modifications in CoordFunctionSymb and ContinuousMap.__invert__

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8c8bfcd

Improve documentation of differentiable manifolds

[sagetrac-git]

Changed commit from 999cac5 to 8c8bfcd

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

127b1e0

Plot of coordinate charts and points

[sagetrac-git]

Changed commit from 8c8bfcd to 127b1e0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f2fef7b

Small improvements in the documentation of differentiable manifolds