Curves in differentiable manifolds

[egourgoulhon]

This ticket implements differentiable curves in real differentiable manifolds. This is a follow-up of #19092 within the SageManifolds project (see the metaticket #18528 for an overview).

This ticket implements the following Python classes:

• the parent class OpenInterval for open intervals of R as 1-dimensional diff. manifolds
  with a canonical chart,
  • the subclass RealLine for R as a 1-dimensional diff. manifold
• the parent class DifferentiableCurveSet for homsets Hom(I,M), i.e. sets of differentiable maps
  I --> M, where I is an open interval of R and M a differentiable manifold over R
• the element class DifferentiableCurve for curves, i.e. differentiable maps I --> M

Documentation:
The reference manual is produced by
sage -docbuild reference/manifolds html
It can also be accessed online at http://sagemanifolds.obspm.fr/doc/19124/reference/manifolds/
More documentation (e.g. example worksheets) can be found here.

Depends on #20771

Component: geometry

Keywords: differentiable manifold, curve, interval, real line

Author: Eric Gourgoulhon

Branch/Commit: d3f3798

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/19124

[egourgoulhon]

Description changed:

--- 
+++ 
@@ -3,7 +3,7 @@
 This ticket implements the following Python classes:
 - the parent class `OpenInterval` for open intervals of **R** as 1-dimensional diff. manifolds
   with a canonical chart, 
-  - the subclass `RealLine` for **R** as a 1-dimensional diff. manifolds
+  - the subclass `RealLine` for **R** as a 1-dimensional diff. manifold
 - the parent class `DiffManifoldCurveSet` for homsets Hom(I,M), i.e. sets of differentiable maps
   I --> M, where I is an open interval of **R** and M a differentiable manifold over **R**
 - the element class `DiffManifoldCurve` for curves, i.e. differentiable maps I --> M

[sagetrac-git]

Changed commit from d38f3cf to 52014ea

[sagetrac-git]

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

52014ea

Improve the documentation of curves in manifolds

[sagetrac-git]

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

4510196

Full doctest coverage for curves in manifolds

[sagetrac-git]

Changed commit from 52014ea to 4510196

[sagetrac-git]

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

2fff749

Small change in documentatin of DiffManifoldCurve

[sagetrac-git]

Changed commit from 4510196 to 2fff749

[sagetrac-git]

Changed commit from 2fff749 to fb139dc

[sagetrac-git]

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

fb139dc

Major improvements in the documentation of diff. manifolds (curves part)

[sagetrac-git]

Changed commit from fb139dc to 2673e58