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.

[git]

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

​52014ea

Improve the documentation of curves in manifolds

[git]

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

​4510196

Full doctest coverage for curves in manifolds

[git]

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

​2fff749

Small change in documentatin of DiffManifoldCurve

[git]

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

​fb139dc

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

[git]

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

​2673e58

Improve TensorField.__eq__ (case with no open cover known)

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​8ab80d8	Improvement in simplify_sqrt_real(); minor modif. in documentation
​2f231b6	Major improvements in the documentation of diff. manifolds (basic part)
​f0ca2de	Merge #18783 into #18725
​307e655	Major improvements in the documentation of diff. manifolds (tensor field part)
​dc7f7a1	Improve TensorField.__eq__ (case with no open cover known)
​4d6f21c	Merge #18843 into #18783
​04360b0	Major improvements in the documentation of diff. manifolds (tangent spaces part)
​513f5ba	Improve TensorField.__eq__ (case with no open cover known)
​e43e03b	Merge #19092 into #18843
​dc25947	Merge #19124 into #19092

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​bfa0cdf	One last doc tweak.
​d13c368	Fixing doc of metric spaces.
​2605c0b	Merge #18529 (Topological manifolds: basics) into #18175 (Implement categories for topological...)
​6dec6d5	Implement topological manifolds (basics, #18529) on the new categories for manifolds (#18175)
​3403978	Implement top. manifolds (scalar fields, #18640) on the new manifold categories (#18175)
​b0521ef	Implement top. manifolds (morphisms, #18725) on the new manifold categories (#18175)
​f643097	Implement diff. manifolds (basics, #18783) on the new manifold categories (#18175)
​a527726	Implement diff. manifolds (tensor fields, #18843) on the new manifold categories (#18175)
​22923ab	Implement diff. manifolds (tangent spaces, #19092) on the new manifold categories (#18175).
​666bbab	Implement diff. manifolds (curves, #19124) on the new manifold categories (#18175)

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​6518699	Introduce the attribute _field_type in class TopologicalManifold to check for real and complex manifolds.
​22383e6	Check for real/complex manifold performed on base_field_type() instead of RR/CC
​66f2c5a	Change function('f', x) to function('f')(x) to accomodate the deprecation warning introduced in #17447
​a28ed04	Morphisms of topological manifolds with the use of base_field_type()
​f31bed1	Remove UniqueRepresentation from differentiable manifolds
​0ee4c41	Tensor fields on differentiable manifolds without unique representation
​e8f11ff	Fix pickling test in tensor field modules.
​a967787	Suppress direct call to _element_constructor_ in tensor field parent classes
​1bf77fd	Tangent spaces on differentiable manifolds without unique representation
​dca7f9d	Curves on differentiable manifolds without unique representation

[git]

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

​d8397c1	Merge branch 'public/manifolds/top_manif_basics' of trac.sagemath.org:sage into public/manifolds/top_manif_basics
​0b08b11	Some small tweaks as part of the review.
​d3e5d4d	Revert to UniqueRepresentation for topological manifolds
​2481359	Revert to UniqueRepresentation for ScalarFieldAlgebra; better ScalarField constructor
​0cc06e8	Revert to UniqueRepresentation for topological manifold homsets
​322d5bd	Revert to UniqueRepresentation for differentiable manifolds
​45beae5	Revert to UniqueRepresentation for differentiable manifolds: tensor fields
​98c6036	Revert to UniqueRepresentation for differentiable manifolds: tangent spaces
​b836212	Revert to UniqueRepresentation for differentiable manifolds: curves

[git]

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

​85d03dc	Change the argument type to structure in Manifold
​5251ef0	Remove method _test_pickling from class TopologicalManifoldPoint
​f69c9ee	Fix doctest error in coord_func_symb.py due to #19312 (update to pynac-0.5.2)
​7889a5d	Change in simplify_sqrt_real to cope with the change of != operator induced by #19312 (Sage 6.10.beta7)
​e8d2ba6	Differentiable manifolds: basics with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)
​0d68f86	Diff. manifolds: tensor fields, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)
​347a9cc	Diff. manifolds: tangent spaces, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)
​6b51926	Diff. manifolds: curves, with the change in symbolic expression logic induced by #19312 (Sage 6.10.beta7)

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​db99641	Parallel plotting vectorfield: added example
​b07ffd9	Tangent spaces on refactored differentiable manifolds
​3cd03a4	Add methods lift() and retract() to ManifoldSubset; add method __eq__() in CoordChange
​984c3c2	Revert to simple hierarchy for manifold classes
​c01048f	Scalar fields with the simplified hierarchy for manifold classes
​c866d6c	Morphisms of topological manifolds with the simplified hierarchy for manifold classes
​0e04631	Basics of diff. manifolds with the simplified hierarchy for manifold classes
​1f226bd	Tensor fields with the simplified hierarchy for manifold classes
​9fa77c4	Tangent spaces with the simplified hierarchy for manifold classes
​db58a0c	Curves in diff. manifolds with the simplified hierarchy for manifold classes

[git]

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

​8e17d54	Merge into the latest version of #18529; improve treatment of composite functions in ExpressionNice
​f00be00	Topological manifold morphisms: solved merge conflict with Sage 7.1.beta1
​21b3968	Basics of diff. manifolds: solve merge conflict with Sage 7.1.beta1
​8ba4b91	Tensor fields: solve merge conflict with Sage 7.1.beta1
​2fad9db	Correct doctest in class DiffFormParal
​b47f55f	Tangent spaces: solve merge conflict with Sage 7.1.beta1
​9a74549	Curves in diff. manifolds: solve merge conflict with Sage 7.1.beta1

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​f3f5470	Fixing a (essentially trivial) doctest failure.
​7b3dab3	Merge branch 'public/manifolds/top_manif_scalar_fields' of git://trac.sagemath.org/sage into Sage 7.2.rc0
​9ec7d3e	Python 3 format for print in manifolds
​d190b37	Morphisms of topological manifolds with coordinate functions as algebra elements
​2577fc5	Fixing a (essentially trivial) doctest failure.
​7125e29	Python3 format for print in morphims of topological manifolds
​bd2f35a	Diff. manifolds with coordinate functions as algebra elements
​73b4a03	Tensor fields with with coordinate functions as algebra elements
​37521ae	Tangent spaces with coordinate functions as algebra elements
​bdb91df	Curves in diff. manifolds with coordinate functions as algebra elements

[git]

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

​4fad094	Merge branch 'public/manifolds/top_manif_morphisms' of trac.sagemath.org:sage into public/manifolds/top_manif_morphisms
​cfecb18	Reviewer changes and tweaks for continuous maps ticket.
​efcb618	Modify authorship for continuous maps.
​84051b0	Merge branch 'public/manifolds/diff_manif_basics' of trac.sagemath.org:sage into public/manifolds/diff_manif_basics
​97172dd	Basics of differentiable manifolds with changes in morphisms of topological manifolds
​29832ec	Use @cached_method for VectorFieldModule.identity_map() and AutomorphismFieldGroup.one()
​159afb4	Tangent spaces upon latest version of tensor fields
​1b79561	Update of OpenInterval._Hom_

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 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
​3b1b794	Fix doctests in tangent spaces after the merge of #20770 in sage 7.3.beta3
​c70792e	Update tangent spaces to the latest version of #18843 (vector fields)
​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.
​72396dd	Merge with latest #19092 to fix doctests after the merge of #20770 in sage 7.3.beta3
​835b293	Update Lie algebroids to the latest version of #18843 (vector fields)
​edde604	Update curves to the latest version of #18843 (vector fields)

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​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
​cd27531	Update curves to the latest version of the dependency ticket #19092

[git]

Branch pushed to git repo; I updated commit sha1. 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
​cdb3f28	Bibliographic references for curves on manifolds moved to the master file created by #21454

[git]

Branch pushed to git repo; I updated commit sha1. 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.
​3a297f7	Merge branch 'public/manifolds/diff_manif_curves' of git://trac.sagemath.org/sage into public/manifolds/diff_manif_curves
​7a38c96	Doing some reviewer changes.

[tscrim]

Same things as on #19092. If you're happy with my changes, then you can set a positive review.

[git]

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

​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
​181d53a	Use sphinx_plot for 3D rendering of an example in DifferentiableCurve.plot documentation

[egourgoulhon]

Replying to tscrim:

Same things as on #19092. If you're happy with my changes, then you can set a positive review.

Thank you very much again for this review and the changes!

In the last commits, I've updated to the latest version of #19092 and have added the display of a 3D example in the documentation of DifferentiableCurve.plot. I am also changing the dependency to #20771, which itself depends on #19092.

[tscrim]

All LGTM. Thanks.

[egourgoulhon]

Thank you!

[git]

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

​d3f3798

Use \Bold{R} instead of \RR for the default LaTeX symbol of RealLine

[egourgoulhon]

I've just noticed that the LaTeX rendering of RealLine in Jupyter notebooks was not correct. It was using \RR, which worked fine in Sage legacy notebook, but is displayed as a red "\RR" in the Jupyter notebook (when using %display latex). The above commit changes the default LaTeX name to \Bold{R}, which is what is used by other Sage objects representing the real numbers: RR and RDF. It works fine with both the Jupyter notebook and the legacy notebook. Do you agree?

PS: an alternative would be to use \mathbb{R}, which is correctly rendered in both notebooks.

[tscrim]

I think we should be consistent with the rest of Sage, so I agree with \Bold{R}.