Differentiable manifolds: tangent spaces

[egourgoulhon]

This ticket implements tangent vectors and tangent spaces on differentiable manifolds. This is a follow-up of #18843 within the SageManifolds project (see the metaticket #18528 for an overview). As in #18843, the non-discrete topological field K over which the differentiable manifold is defined is generic, although in most applications, K=R or K=C.

This ticket implements the following Python classes:

• the parent class TangentSpace for tangent spaces to a differentiable manifold
• the element class TangentVector for tangent vectors to a differentiable manifold It also implements
• the method at() in tensor field classes (introduced in #18843) to take the value of a given tensor field (in particular a vector field) at a given point; the method at() is implemented for vector frames and coframes as well.
• the method plot() in class VectorField, to get some graphical representations of vector fields
• the methods differential(), differential_functions() and jacobian_matrix() to the class DiffMap introduced in #18783 (differential of a map between differentiable manifolds at a given point).

Documentation: The reference manual is produced by sage -docbuild reference/manifolds html It can also be accessed online at http://sagemanifolds.obspm.fr/doc/19092/reference/manifolds/ More documentation (e.g. example worksheets) can be found here.

Depends on #15916 Depends on #18843

CC: @sagetrac-mbejger

Component: geometry

Keywords: differentiable manifold, tangent vector, tangent space

Author: Eric Gourgoulhon, Michal Bejger, Marco Mancini

Branch/Commit: ff6eb09

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/19092

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 05f8cc7 to b4a4530

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

23eb9d8	Correct doctest and documentation in tangent spaces
b4a4530	Use sphinx_plot for 3D plots in the documentation of charts and vector fields

[egourgoulhon]

comment:33

Thank you so much for the review!

In the first commit above (23eb9d8), I've corrected a doctest error and fixed some documentation issue revealed by the patchbot.

In the second commit (b4a4530), I've added sphinx directives to render the 3D plots in the documentation of VectorField.plot (as well as in RealChart.plot), on the same footing as what is now done in the "3D Graphics" section of the reference manual.

Thanks for the addition of @options to VectorField.plot; I've added color to these options, to be consistent with what is done in RealChart.plot. I've also added some documentation about the use of v.plot.options.

A question: in the keyword arguments of VectorField.plot, you have changed nb_values to number_values, but it is still nb_values in RealChart.plot. For consistency, both plot methods should use the same name. It seems that nb is not a standard English abbreviation for number, is it? (I find number_values a little bit long, especially that we don't have the TAB completion to type the options).

[tscrim]

comment:34

Replying to @egourgoulhon:

Thank you so much for the review!

Not a problem; sorry it took so long.

A question: in the keyword arguments of VectorField.plot, you have changed nb_values to number_values, but it is still nb_values in RealChart.plot. For consistency, both plot methods should use the same name. It seems that nb is not a standard English abbreviation for number, is it? (I find number_values a little bit long, especially that we don't have the TAB completion to type the options).

Not to my knowledge. The standard abbreviation is "no." (with a period) but "num" has become standard (at least in the programming world), but IMO the verbosity is better. However, you can do tab completion for explicit arguments.

[egourgoulhon]

comment:35

Replying to @tscrim:

Not to my knowledge. The standard abbreviation is "no." (with a period) but "num" has become standard (at least in the programming world), but IMO the verbosity is better. However, you can do tab completion for explicit arguments.

OK, so let use number_values everywhere. I am going to change it in RealChart.plot.

[tscrim]

comment:36

Thanks.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

ff6eb09

Name of argument 'nb_values' in RealChart.plot changed to 'number_values'.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from b4a4530 to ff6eb09

[egourgoulhon]

comment:38

Change nb_values --> number_values done.

[tscrim]

comment:39

I'm sorry I missed that on the previous ticket. LGTM. Thank you.

[egourgoulhon]

comment:40

Thanks for the review!

[vbraun]

Changed branch from public/manifolds/diff_manif_tangent_spaces to ff6eb09