#19092: Differentiable manifolds: tangent spaces
-------------------------------------+-------------------------------------
Reporter: egourgoulhon | Owner: egourgoulhon
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-6.9
Component: geometry | Keywords: differentiable
Merged in: | manifold, tangent vector, tangent
Reviewers: | space
Work issues: | Authors: Eric Gourgoulhon,
Commit: | Michal Bejger
d5562a2bb8393824f5ec72b7e3a9c43990c8dbaf| Report Upstream: N/A
Stopgaps: | Branch:
|
public/manifolds/diff_manif_tangent_spaces
| Dependencies: #15916, #18100,
| #18843
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This ticket implements tangent vectors and tangent spaces on
differentiable manifolds. This is a follow-up of #18843 within the
[http://sagemanifolds.obspm.fr/ 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).
--
Ticket URL: <http://trac.sagemath.org/ticket/19092>
Sage <http://www.sagemath.org>
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