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.

[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]

Failing test suite will be handled by improvements #19092.

[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.

[tscrim]

This is not a Lie algebra over the scalar field (only over the base field).

[tscrim]

We will change this to be a ​Lie algebroid.

[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]

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

[git]

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

​2150a43	Correct doctests in vector fields after the merge of #20770 in sage 7.3.beta3
​3b1b794	Fix doctests in tangent spaces after the merge of #20770 in sage 7.3.beta3
​72396dd	Merge with latest #19092 to fix doctests after the merge of #20770 in sage 7.3.beta3

[egourgoulhon]

Looks good to me, thanks (the above commits are just to fix doctests in dependency tickets).

[git]

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

​3ab0af0	Initial reviewer changes.
​d7ad8e1	Merge branch 'public/manifolds/diff_manif_tensor_fields' of git://trac.sagemath.org/sage into sage 7.3.beta5
​dcb08fc	Decrease doctest times in tensor fields; remove xder from the global namespace
​c70792e	Update tangent spaces to the latest version of #18843 (vector fields)
​835b293	Update Lie algebroids to the latest version of #18843 (vector fields)

[egourgoulhon]

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

[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]

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

[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

[egourgoulhon]

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

[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

[egourgoulhon]

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