Modules of vector fields as Lie algebroids

[tscrim]

This ticket adds Lie bracket to vector fields, giving the structure of Lie algebroid to the set X(M) of all vector fields over the manifold M.

Depends on #19092
Depends on #20770

CC: @egourgoulhon

Component: geometry

Keywords: lie algebras, days74

Author: Travis Scrimshaw

Branch/Commit: 2f1d037

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/20771

[tscrim]

Last 10 new commits:

60f743a	Parsing the input so that it uses the indexing set.
a02380f	Merge branch 'public/lie_algebras/fd_structure_coeff-16820' in 7.0.rc1
50f4441	trac #16820 correct the spelling of Cartesian
f1514bd	Merge branch 'public/lie_algebras/fd_structure_coeff-16820' into 7.3.b2
7d155ec	Fixing trivial doctest failures.
a016182	Implementing a better way to compare indices.
127d348	Merge branch 'public/lie_algebras/fd_structure_coeff-16820' into public/manifolds/lie_algebras-TBA
e8b6105	Added list of basis and finite-dimensionality to finite rank free modules.
b849e47	Merge branch 'public/modules/add_category_support_finite_rank_free_modules-20770' into public/manifolds/lie_algebras-TBA
bb95148	Adding vector field module to the category of Lie algebras.

[tscrim]

Commit: bb95148

[tscrim]

Branch: public/manifolds/lie_algebras-20771

[tscrim]

comment:2

Failing test suite will be handled by improvements #19092.

[tscrim]

Changed dependencies from #16820, #20770 to #16820, #19092, #20770

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

6b71b13

Removing finite-dimensionality for generic vectorfield module.

[sagetrac-git]

Changed commit from bb95148 to 6b71b13

[tscrim]

comment:5

This is not a Lie algebra over the scalar field (only over the base field); it fails to be bilinear.

[tscrim]

comment:6

We will change this to be a Lie algebroid.

[sagetrac-git]

Changed commit from 6b71b13 to 96f09ab

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

0d6f47e	Merge branch 'public/manifolds/diff_manif_tangent_spaces' of trac.sagemath.org:sage into public/manifolds/lie_algebras-20771
96f09ab	Added information about the vector field module being a Lie algebroid.

[tscrim]

comment:8

I've changed this as per our discussions and the forced push is to remove the dependency of #16820.

[tscrim]

Changed dependencies from #16820, #19092, #20770 to #19092, #20770

[sagetrac-git]

Changed commit from 96f09ab to 72396dd

[sagetrac-git]

Changed commit from 835b293 to a5ab39a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. Last 10 new commits:

58f7fb9	Merge branch 'develop' into public/manifolds/diff_manif_tensor_fields
3e73095	Merge branch 'develop' into public/manifolds/diff_manif_tensor_fields
4955c3c	Final review of everything.
7cf4ff4	Merge branch 'public/manifolds/diff_manif_tensor_fields' of trac.sagemath.org:sage into public/manifolds/diff_manif_tensor_fields
58ae506	Merge branch 'public/manifolds/diff_manif_tensor_fields' of git://trac.sagemath.org/sage into Sage 7.4.beta6
8219403	Fix documentation error; change in TensorField comparison to zero
a841f79	Python 3 compatible syntax in tensor fields
5a5f400	Slight change in TensorField.__eq__ (comparison to zero)
98efa66	Update tangent spaces to the final version of the dependency ticket #18843
a5ab39a	Update Lie algebroids to the latest version of the dependency ticket #19092

[egourgoulhon]

comment:15

Setting back to positive review, since the latest commit simply propagates changes in the dependency ticket #19092

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

8860387	Add missing reference Lee13
fb7f4dd	Bibliographic references for tensor fields moved to the master file
8205dca	Update tangent spaces to the last change (adding a missing reference) in the dependency ticket #18843
785300b	Bibliographic references for tangent spaces moved to the master file created by #21454
6af8ad2	Bibliographic references for vector field modules as Lie algebroids moved to the master file created by #21454

[sagetrac-git]

Changed commit from a5ab39a to 6af8ad2

[egourgoulhon]

comment:17

Setting back to positive review, since the latest commit simply solves a merge conflict with #21454.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

4ce1118	Merge branch 'public/manifolds/diff_manif_tangent_spaces' of git://trac.sagemath.org/sage into public/manifolds/diff_manif_tangent_spaces
567b892	Doing some reviewer changes for #19092.
05f8cc7	A little bit of extra cleanup.
23eb9d8	Correct doctest and documentation in tangent spaces
b4a4530	Use sphinx_plot for 3D plots in the documentation of charts and vector fields
ff6eb09	Name of argument 'nb_values' in RealChart.plot changed to 'number_values'.
2f1d037	Update Lie algebroids to the latest version of tangent spaces

[sagetrac-git]

Changed commit from 6af8ad2 to 2f1d037

[egourgoulhon]

comment:19

Setting back to positive review, since the latest commit simply propagates changes in the dependency ticket #19092

[vbraun]

Changed branch from public/manifolds/lie_algebras-20771 to 2f1d037