Schouten, Cotton, and Cotton-York tensors of a riemannian metric

[sagetrac-pang]

Add three methods to class PseudoRiemannianMetric in order to compute Schouten, Cotton, and Cotton-York tensors. This is a follow-up of #19209 within the SageManifolds project (see the metaticket #18528 for an overview).

Depends on #19209

CC: @egourgoulhon @sagetrac-mbejger @man74cio

Component: geometry

Keywords: differentiable manifold, Riemannian metric, Cotton tensor, Cotton-York tensor, Schouten tensor

Author: Pablo Angulo

Branch/Commit: fdd9051

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/19823

[sagetrac-pang]

First draft

[sagetrac-pang]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
+Add three methods to class `PseudoRiemannianMetric` in order to compute Schouten, Cotton, and Cotton-York tensors.
 
+Work is already advanced, git branch will follow soon.

[sagetrac-pang]

comment:1

Attachment: cotton.patch.gz

[sagetrac-pang]

Last 10 new commits:

8be9a45	Merge branch 'public/manifolds/diff_manif_metrics' of git://trac.sagemath.org/sage into #19147 (affine connections on manifolds with unique representation).
8f0659a	Pseudo-Riemannian metrics on smooth manifolds without unique representation
cb47399	Merge branch 'diff_manif_connections' into diff_manif_metrics to propagate minor changes in affine connections.
58723e9	Revert to UniqueRepresentation for differentiable manifolds: metric
2918953	Diff. manifolds: metrics, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)
aae566d	Improve parallelization in Components and derived classes
98810df	Diff. manifolds: metrics, with improvements in parallelization of Components
bd5d69f	Merge branch 'public/manifolds/sm-0.9' of git://trac.sagemath.org/sage into sagemanifolds
14b7b6c	Merge branch 'develop' of git://github.com/sagemath/sage into sagemanifolds
5fa71f7	Add three methods schouten, cotton, cotton_york, toghether with internal variables self._schouten, self._cotton, self._cotton_york that work analogously to the method self.ricci or self.ricci_scalar

[sagetrac-pang]

Commit: 5fa71f7

[sagetrac-pang]

Branch: public/manifolds/Schouten_Cotton_York

[sagetrac-pang]

Dependencies: #19209

[sagetrac-pang]

Description changed:

--- 
+++ 
@@ -1,3 +1 @@
 Add three methods to class `PseudoRiemannianMetric` in order to compute Schouten, Cotton, and Cotton-York tensors.
-
-Work is already advanced, git branch will follow soon.

[sagetrac-git]

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

8d3ba19

Modifies doctest that threw a deprecation warning

[sagetrac-git]

Changed commit from 5fa71f7 to 8d3ba19

[sagetrac-pang]

comment:6

The tests take really long to run on my (rather old) laptop. I can't come up with examples that are meaningful and take less than 5 seconds to compute. How should I proceed?