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 Differentiable manifolds: vector fields and tensor fields #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 Differentiable manifolds: basics #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