Opened 6 years ago

Last modified 7 weeks ago

#18528 new task

SageManifolds metaticket — at Version 156

Reported by: egourgoulhon Owned by: egourgoulhon
Priority: major Milestone:
Component: geometry Keywords: manifold, tensor, differential geometry
Cc: mbejger, mmancini, tscrim, bpillet, gh-LBrunswic, gh-mjungmath Merged in:
Authors: see ticket description Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #18175 Stopgaps:

Description (last modified by egourgoulhon)

This is the implementation of manifolds resulting from the SageManifolds project, developed by the following authors.

Algebraic part

  • Tensors on free modules of finite rank: #15916 (merged in Sage 6.6)
  • Parallelization of tensor computations on free modules of finite rank: #18100 (merged in Sage 6.10)
  • Improve category for finite rank free modules and provide list functionality for basis: #20770 (merged in Sage 7.3.beta3)
  • Exterior powers of free modules of finite rank: #23207 (merged in Sage 8.1.beta0)
  • More functionalities for bases of free modules of finite rank: #24792 (merged in Sage 8.2.beta8)
  • Better treatment of the zero element: #28562 (merged in Sage 9.0.beta3)
  • Multiple symmetries and multiple contractions with index notation: #28784 (merged in Sage 9.0.beta8)
  • Tensor addition with index notation: #28787 (merged in Sage 9.1.beta2)
  • Enhance symmetry handling for tensors: #28813
  • Extension of admissible indices conventions for tensors with indices: #29099
  • Index notation for tensors should allow for unicode characters: #29248

Topological and differential part

  • Topological manifolds (over R, C or a topological field K):
    • basics (charts, subsets): #18529 (merged in Sage 7.1.beta1)
    • scalar fields (continuous functions to the base field): #18640 (merged in Sage 7.3.beta0)
    • morphisms (continuous maps between manifolds): #18725 (merged in Sage 7.3.beta0)
    • SymPy as an alternative to SR for symbolic calculus on manifolds: #22801 (merged in Sage 8.2.beta0)
    • improve simplifications in calculus on manifolds: #24151
    • periodic coordinates on manifods: #27548 (merged in Sage 8.8.beta0)
    • customizing simplifications in coordinate calculus: #27601 (merged in Sage 8.8.beta1)
    • scalar field restrictions: #28554 (merged in Sage 9.0.beta4)
  • Differentiable manifolds (over R, C or a non-discrete topological field K):
    • basics (charts, transition maps, scalar fields, morphisms): #18783 (merged in Sage 7.3.beta2)
    • vector fields, tensor fields and p-forms: #18843 (merged in Sage 7.5.beta1)
    • tangent spaces: #19092 (merged in Sage 7.5.beta3)
    • sets of vector fields as Lie algebroid: #20771 (merged in Sage 7.5.beta3)
    • curves: #19124 (merged in Sage 7.5.beta3)
    • affine connections: #19147 (merged in Sage 7.5.beta4)
    • parallelization of Lie derivative computations: #22200 (merged in Sage 7.6.beta3)
    • Multivector fields and the Schouten-Nijenhuis bracket: #23429 (merged in Sage 8.1.beta8)
    • Deprecate CoordinatePatch and DifferentialForm classes: #24444 (merged in Sage 8.2.beta3)
    • Embedded submanifolds: #25164 (merged in Sage 8.3.beta4)
    • Tensor fields along a submanifold: #25254 (merged in Sage 8.3.beta2)
    • Tensor series expansion: #25866 (merged in Sage 8.8.beta0)
    • Add manifold catalog: #25869 (merged in Sage 8.5.beta0)
    • Initializing the components of a tensor field while declaring it: #27581 (merged in Sage 8.8.beta1)
    • Mixed differential forms: #27584 (merged in Sage 8.8.beta3)
    • Ease the display of tensor fields in a coordinate frame: #27655 (merged in Sage 8.8.beta3)
    • Mixed forms improvements: #28578 (merged in Sage 9.0.beta5)
    • Vector bundles: #28159 (merged in Sage 9.0.beta3)
    • Characteristic classes on vector bundles: #27784 (merged in Sage 9.0.beta8)
    • Tensor fields: consistent naming: #28564 (merged in Sage 9.0.beta7)
    • Immutability of tensor fields and mixed forms: #28519 (metaticket)
    • Automorphism fields: remove SR enforcement when computing the inverse: #28629
    • Vector-valued forms: #28640
    • Constructing a vector frame from a family of vector fields: #28716 (merged in Sage 9.0.beta8)
    • Inheritance structure: tensor fields as sections of vector bundles: #29234
    • Apply a function to all components of a tensor field: #29244
  • Complex and almost complex manifolds:
    • almost complex structures through Hodge structures: #18786
  • Pseudo-Riemannian manifolds:
    • pseudo-Riemannian metrics: #19209 (merged in Sage 7.5.beta4)
    • Schouten, Cotton, and Cotton-York tensors: #19823 (merged in Sage 7.5.beta4)
    • integrated curves and geodesics: #22951 (merged in Sage 8.1.beta2)
    • pseudo-Riemannian manifolds: #24622 (merged in Sage 8.2.rc0)
    • Euclidean spaces and vector calculus: #24623 (merged in Sage 8.3.beta0)
    • Geometry of pseudo-Riemannian submanifolds: #25438 (merged in Sage 8.3.beta8)
    • Declaring a metric along with its components: #25457
    • Energy momentum tensor, Einstein tensor and Einstein space-time: #25500
    • Degenerate manifolds and submanifolds: #26355 (merged in Sage 9.1.beta0)
    • Degenerate submanifolds: new features: #29080
    • Tutorial about vector calculus: #27703 (merged in Sage 8.9.beta0)
    • More control on the numerical ODE solver for integrated curves and geodesics: #28707 (merged in Sage 9.0.beta6)
  • Lie groups:
    • Nilpotent Lie groups: #26344 (merged in Sage 8.4.rc0)

Bug fixes and performance improvements

  • List functionality of free module bases: #22518 (merged in Sage 7.6.rc0)
  • Display of tensors on free modules of finite rank: #22520 (merged in Sage 7.6.rc0)
  • Checking validity of coordinate values on a chart: #22535 (merged in Sage 7.6.rc0)
  • Symbolic derivatives in simplification of coordinate functions: #22503 (merged in Sage 7.6.rc0)
  • Pullback on parallelizable manifolds: #22563 (merged in Sage 8.0.beta0)
  • Tensor field restrictions on parallelizable manifolds: #22637 (merged in Sage 8.0.beta1)
  • Inverse metric on parallelizable manifolds: #22667 (merged in Sage 8.0.beta1)
  • Improvements in Jacobian determinants of transition maps: #22789 (merged in Sage 8.0.beta2)
  • Arithmetics of coordinate functions and scalar fields without zero check of the result: #22859 (merged in Sage 8.0.beta5)
  • Characteristic of coordinate function rings: #23329 (merged in Sage 8.1.beta2)
  • Faster comparison of manifold points: #23592 (merged in Sage 8.1.beta2)
  • Fast comparison to zero (method is_trivial_zero()) for coordinate functions and scalar fields: #23623 (merged in Sage 8.1.beta4)
  • Minor errors in integrated curves: #23838 (merged in Sage 8.1.beta6)
  • Simplifications in calculus on manifolds with derivatives of symbolic functions: #24199 (fixed by #24232)
  • Simplifications in calculus on manifolds via the expression tree: #24232 (merged in Sage 8.2.beta0)
  • Make simplifications in SymPy calculus on manifolds rely on SymPy only: #24290
  • Better handling of matrix output for operator [:] acting on sets of tensor components: #24884 (merged in Sage 8.2.beta8)
  • Better restrictions on manifolds: #25417 (merged in Sage 8.3.beta3)
  • py3: implement __hash__ method in ContinuousMap: #25502 (merged in Sage 8.3.beta5)
  • Declared coordinate range not taken into account when a symbolic bound is involved: #25510 (merged in Sage 8.3.beta5)
  • Improvements to integrated curves and geodesics on manifolds: #25936 (merged in Sage 8.5.beta1)
  • Fix bug concerning restrictions of tensor fields: #26012 (merged in Sage 8.4.beta1)
  • Parallelization of two functions (tensor calculus): #26168 (merged in Sage 8.5.beta5)
  • Remove deprecated method view() in tensor: #26392 (merged in Sage 8.4.rc0)
  • py3: make all doctests passed with Python3 in src/sage/manifolds: #26475 (merged in Sage 8.5.beta0)
  • py3: fix regression in Python3 tests in manifolds: #26569 (merged in Sage 8.5.beta2)
  • py3: make all doctests passed with Python3 in src/sage/tensor: #26601 (merged in Sage 8.5.beta2)
  • Remove deprecated stuff in manifolds: #26609 (merged in Sage 8.5.beta2)
  • Make simplifications effective in the computation of the inverse of a transition map: #26701 (merged in Sage 8.5.beta4)
  • Bug in parallelization on manifolds: #26777 (merged in Sage 8.5.beta6)
  • Remove deprecated ScalarField's method function_chart: #27409 (merged in Sage 8.7.beta7)
  • Bug in parallelized computations involving symbolic functions: #27492
  • Bug in wedge of unnamed differential forms: #27576 (merged in Sage 8.8.beta1)
  • Error in testing whether a scalar field belongs to a module of differential forms: #27658 (merged in Sage 8.8.beta3)
  • Tangent vectors should act as derivations on scalar fields: #27856 (merged in Sage 8.8.rc0)
  • Issue in calculus on manifolds with incomplete set of transition maps: #28072 (merged in Sage 8.9.beta2)
  • AttributeError when computing manifold chart after computing its vector field module: #28331 (merged in Sage 8.9.beta7)
  • Fix some issues with submanifolds and improve their documentation: #28344 (merged in Sage 8.9.beta8)
  • Use something instead of time() to ensure Manifold uniqueness in tests: #28365 (merged in Sage 8.9.beta8)
  • Change keyword argument verbose to check in CoordChange.set_inverse() and set the default to True: #28422 (merged in Sage 8.9.rc0)
  • Bug in computing the second fundamental form of a Riemannian submanifold: #28462 (merged in Sage 8.9.rc0)
  • Improve computation of connection coefficients: #28543 (merged in Sage 9.0.beta1)
  • Output dicts and lists copied: #28563 (merged in Sage 9.0.beta1)
  • Fix wedge product on the right with a scalar field: #28579 (merged in Sage 9.0.beta1)
  • Use standard notation for pullback and pushforward on manifolds: #28600 (merged in Sage 9.0.beta3)
  • set_restriction behaviour when the subdomain is the domain: #28628 (merged in Sage 9.0.beta4)
  • Unnecessary coordinate check while initializing an integrated curve: #28669 (merged in Sage 9.0.beta5)
  • Vector bundles: section module name fix: #28690 (merged in Sage 9.0.beta5)
  • Scalar field raise AttributeError on show_identifiers call: #28769 (merged in Sage 9.0.beta8)
  • More flexible coercions in mixed form algebra: #28916 (merged in Sage 9.1.beta1)
  • Mixed forms: zero treatment for scalar multiplication: #28921 (merged in Sage 9.1.beta1)
  • Vector bundles: documentation improvements: #28963
  • Automorphism fields: notation of inverse: #28973 (merged in Sage 9.1.beta1)
  • Bug in setting the calculus method on manifolds: #29021 (merged in Sage 9.1.beta1)
  • Documentation improvements of characteristic classes: #28854

Change History (156)

comment:1 Changed 6 years ago by egourgoulhon

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comment:2 Changed 5 years ago by egourgoulhon

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comment:3 Changed 5 years ago by egourgoulhon

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  • Summary changed from SageManifolds meta-ticket to SageManifolds metaticket

comment:4 Changed 5 years ago by egourgoulhon

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comment:8 Changed 5 years ago by egourgoulhon

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comment:9 Changed 5 years ago by egourgoulhon

  • Keywords manifold tensor added; manifolds tensors removed

comment:10 Changed 5 years ago by egourgoulhon

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comment:11 Changed 5 years ago by egourgoulhon

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comment:12 Changed 5 years ago by egourgoulhon

  • Milestone changed from sage-6.9 to sage-6.10

All the tickets, except for #18786, are now ready for review.

comment:13 Changed 5 years ago by egourgoulhon

All the tickets are now based on the category ticket #18175, so that the manifold categories are

  • Manifolds(K) for topological manifolds over a topological field K
  • Manifolds(K).Differentiable() for differentiable manifolds
  • Manifolds(K).Smooth() for smooth manifolds

comment:14 follow-up: Changed 5 years ago by tscrim

Something I would like to see once the basics are done is a catalog of examples and common interesting manifolds:

  • n-sphere
  • n-torus
  • real/complex projective n-space
  • surfaces
  • (Affine) Grassmannians
  • Classical Lie groups (more for my info, a description of charts is on page 5 of https://www.dpmms.cam.ac.uk/~agk22/mfds.pdf, but this probably isn't a good atlas for doing computations)

I understand that some of these could be considered more wishlist than others. Some other wishlist items:

  • Morse theory to compute homology of manifolds.
  • Manifolds with boundary
  • Cartesian products of manifolds (or more generally, fiber bundles)
  • DeRham? cohomology (see, e.g., lecture notes above)

comment:15 in reply to: ↑ 14 Changed 5 years ago by egourgoulhon

Replying to tscrim:

Something I would like to see once the basics are done is a catalog of examples and common interesting manifolds:

Thanks for these suggestions. For sure, one should have a catalog of standard manifolds. For the time being, there are only examples available as worksheets at http://sagemanifolds.obspm.fr/examples.html, for instance

I understand that some of these could be considered more wishlist than others. Some other wishlist items:

  • Morse theory to compute homology of manifolds.
  • Manifolds with boundary
  • Cartesian products of manifolds (or more generally, fiber bundles)
  • DeRham? cohomology (see, e.g., lecture notes above)

All the above seem indeed desirable extensions. Even if they are not implemented yet, we should have them in mind when setting the basics.

comment:16 Changed 5 years ago by egourgoulhon

PS: could you point to some existing catalog in Sage, in order to have some example?

comment:17 follow-up: Changed 5 years ago by tscrim

  • algebras.<tab> in sage/algebras/catalog.py
  • crystals.<tab> in sage/combinat/crystals.catalog.py
  • designs.<tab> in sage/combinat/designs.designs_catalog.py
  • groups.<tab> in sage/groups/groups_catalog.py

comment:18 in reply to: ↑ 17 Changed 5 years ago by egourgoulhon

Thanks!

comment:19 Changed 5 years ago by egourgoulhon

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comment:24 Changed 4 years ago by tscrim

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comment:32 Changed 4 years ago by egourgoulhon

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comment:33 follow-up: Changed 4 years ago by tscrim

Would there be any interest in Kontsevich graphs, which are related to Poisson structures on manifolds from what I saw? In particular, in https://arxiv.org/abs/1702.00681, there is reference to a C++ package https://github.com/rburing/kontsevich_graph_series-cpp (with the MIT license).

comment:34 Changed 4 years ago by egourgoulhon

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comment:37 Changed 4 years ago by egourgoulhon

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comment:40 Changed 4 years ago by egourgoulhon

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comment:41 in reply to: ↑ 33 ; follow-up: Changed 4 years ago by bpym

Replying to tscrim:

Would there be any interest in Kontsevich graphs, which are related to Poisson structures on manifolds from what I saw? In particular, in https://arxiv.org/abs/1702.00681, there is reference to a C++ package https://github.com/rburing/kontsevich_graph_series-cpp (with the MIT license).

With collaborators (independent from the above) we have developed a Sage package for calculations with Kontsevich graphs, Poisson brackets and deformation quantizations; the preliminary version will be released later this year. We certainly would like to interface our code with SageManifolds.

The main thing we would need is a SageManifolds implementation of the algebra of multivector fields (exterior algebra of the tangent bundle) and its Schouten bracket https://en.wikipedia.org/wiki/Schouten%E2%80%93Nijenhuis_bracket. Are there any plans in this direction?

comment:42 in reply to: ↑ 41 ; follow-up: Changed 4 years ago by egourgoulhon

Replying to bpym:

With collaborators (independent from the above) we have developed a Sage package for calculations with Kontsevich graphs, Poisson brackets and deformation quantizations; the preliminary version will be released later this year. We certainly would like to interface our code with SageManifolds.

Very good!

The main thing we would need is a SageManifolds implementation of the algebra of multivector fields (exterior algebra of the tangent bundle) and its Schouten bracket https://en.wikipedia.org/wiki/Schouten%E2%80%93Nijenhuis_bracket. Are there any plans in this direction?

It would certainly be easy to implement multivector fields at the level of a sequence of modules over the ring of scalar fields, in the same footing as what has been done for differential forms, cf. http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/diff_form_module.html Each module, Vp(M) say, will be the set of multivector fields with a fixed degree p, i.e. the set of p-vectors. Implementing the Schouten bracket atop of this as an exterior operator Vp(M) x Vq(M) --> Vp+q-1(M) should not be too difficult either. But in such a setting, we do not introduce explicitely the algebra of multivector fields, which is the direct sum of all the modules Vp(M). Would this be an issue for you?

comment:43 in reply to: ↑ 42 ; follow-up: Changed 4 years ago by bpym

Replying to egourgoulhon:

It would certainly be easy to implement multivector fields at the level of a sequence of modules over the ring of scalar fields, in the same footing as what has been done for differential forms ...

Great! This is indeed the sort of implementation I was imagining. One would like the operations of wedge product Vp x Vq -> Vp+q and Schouten bracket Vp x Vq -> Vp+q-1. One would also like to have interior contractions with forms Omegap x Vq -> Vq-p and Vp x Omegaq -> Omegaq-p, defined when q >= p.

But in such a setting, we do not introduce explicitely the algebra of multivector fields, which is the direct sum of all the modules Vp(M). Would this be an issue for you?

I don't foresee any issue.

comment:44 in reply to: ↑ 43 ; follow-up: Changed 4 years ago by egourgoulhon

Replying to bpym:

Replying to egourgoulhon:

It would certainly be easy to implement multivector fields at the level of a sequence of modules over the ring of scalar fields, in the same footing as what has been done for differential forms ...

Great! This is indeed the sort of implementation I was imagining. One would like the operations of wedge product Vp x Vq -> Vp+q and Schouten bracket Vp x Vq -> Vp+q-1. One would also like to have interior contractions with forms Omegap x Vq -> Vq-p and Vp x Omegaq -> Omegaq-p, defined when q >= p.

This seems quite straightforward to implement. Only a matter of finding time to do it...

But in such a setting, we do not introduce explicitely the algebra of multivector fields, which is the direct sum of all the modules Vp(M). Would this be an issue for you?

I don't foresee any issue.

Very good!

The question is then: what is your time scale? i.e. when would you like these features to be available?

comment:45 Changed 4 years ago by egourgoulhon

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comment:48 Changed 4 years ago by karimvanaelst

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comment:49 Changed 4 years ago by egourgoulhon

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comment:50 Changed 3 years ago by egourgoulhon

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comment:51 in reply to: ↑ 44 ; follow-up: Changed 3 years ago by egourgoulhon

Replying to egourgoulhon:

Replying to bpym:

Great! This is indeed the sort of implementation I was imagining. One would like the operations of wedge product Vp x Vq -> Vp+q and Schouten bracket Vp x Vq -> Vp+q-1. One would also like to have interior contractions with forms Omegap x Vq -> Vq-p and Vp x Omegaq -> Omegaq-p, defined when q >= p.

This seems quite straightforward to implement. Only a matter of finding time to do it...

The pure algebraic part of this has been implemented, including the interior products, see #23207. There remains to implement the differential part, in particular the Schouten bracket. On the Wikipedia page, there is some warning: "There are two different versions, both rather confusingly called by the same name." Do we agree that the thing to implement is the bracket given by the second formula in that page?

comment:52 in reply to: ↑ 51 ; follow-up: Changed 3 years ago by bpym

Replying to egourgoulhon:

The pure algebraic part of this has been implemented, including the interior products, see #23207.

Great, thank you!

There remains to implement the differential part, in particular the Schouten bracket. On the Wikipedia page, there is some warning: "There are two different versions, both rather confusingly called by the same name." Do we agree that the thing to implement is the bracket given by the second formula in that page?

Yes, we agree.

comment:53 in reply to: ↑ 52 Changed 3 years ago by egourgoulhon

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Replying to bpym:

Replying to egourgoulhon:

There remains to implement the differential part, in particular the Schouten bracket. On the Wikipedia page, there is some warning: "There are two different versions, both rather confusingly called by the same name." Do we agree that the thing to implement is the bracket given by the second formula in that page?

Yes, we agree.

Multivector fields and their Schouten-Nijenhuis bracket are now ready (at least for review...): #23429.

comment:54 Changed 3 years ago by egourgoulhon

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update milestone 8.3 -> 8.4

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comment:99 Changed 20 months ago by embray

  • Milestone changed from sage-8.7 to sage-8.8

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

comment:100 Changed 20 months ago by egourgoulhon

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comment:101 Changed 20 months ago by egourgoulhon

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comment:102 Changed 20 months ago by egourgoulhon

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comment:103 Changed 20 months ago by egourgoulhon

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comment:104 Changed 20 months ago by egourgoulhon

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comment:105 Changed 20 months ago by egourgoulhon

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comment:106 Changed 20 months ago by egourgoulhon

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comment:107 Changed 20 months ago by egourgoulhon

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comment:108 Changed 20 months ago by egourgoulhon

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comment:109 Changed 18 months ago by egourgoulhon

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comment:110 Changed 18 months ago by embray

  • Milestone sage-8.8 deleted

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

comment:111 Changed 17 months ago by egourgoulhon

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comment:112 Changed 17 months ago by egourgoulhon

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comment:113 Changed 16 months ago by egourgoulhon

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comment:114 Changed 16 months ago by egourgoulhon

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comment:115 Changed 16 months ago by egourgoulhon

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comment:116 Changed 15 months ago by egourgoulhon

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comment:117 Changed 15 months ago by egourgoulhon

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comment:118 Changed 15 months ago by egourgoulhon

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comment:119 Changed 15 months ago by egourgoulhon

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comment:120 Changed 15 months ago by egourgoulhon

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comment:121 Changed 14 months ago by egourgoulhon

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comment:122 Changed 14 months ago by egourgoulhon

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comment:123 Changed 14 months ago by egourgoulhon

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comment:124 Changed 14 months ago by egourgoulhon

  • Authors changed from Eric Gourgoulhon, Michal Bejger, Marco Mancini to see ticket description

comment:125 Changed 14 months ago by egourgoulhon

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comment:126 Changed 14 months ago by egourgoulhon

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comment:127 Changed 14 months ago by egourgoulhon

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comment:128 Changed 14 months ago by egourgoulhon

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comment:129 Changed 13 months ago by egourgoulhon

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comment:130 Changed 13 months ago by egourgoulhon

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comment:131 Changed 13 months ago by egourgoulhon

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comment:132 Changed 13 months ago by egourgoulhon

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comment:133 Changed 13 months ago by egourgoulhon

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comment:134 Changed 13 months ago by egourgoulhon

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comment:135 Changed 13 months ago by egourgoulhon

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comment:136 Changed 13 months ago by egourgoulhon

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comment:137 Changed 13 months ago by egourgoulhon

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comment:138 Changed 13 months ago by egourgoulhon

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comment:139 Changed 12 months ago by egourgoulhon

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comment:140 Changed 12 months ago by egourgoulhon

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comment:141 Changed 12 months ago by egourgoulhon

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comment:142 Changed 12 months ago by egourgoulhon

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comment:143 Changed 12 months ago by egourgoulhon

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comment:144 Changed 12 months ago by gh-LBrunswic

  • Cc gh-LBrunswic added

comment:145 Changed 12 months ago by gh-LBrunswic

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comment:146 Changed 12 months ago by egourgoulhon

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comment:147 Changed 12 months ago by egourgoulhon

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comment:148 Changed 11 months ago by egourgoulhon

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comment:149 Changed 11 months ago by egourgoulhon

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comment:150 Changed 10 months ago by egourgoulhon

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comment:151 Changed 10 months ago by egourgoulhon

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comment:152 Changed 10 months ago by gh-LBrunswic

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comment:153 Changed 10 months ago by egourgoulhon

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comment:154 Changed 10 months ago by gh-LBrunswic

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comment:155 Changed 9 months ago by egourgoulhon

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comment:156 Changed 9 months ago by egourgoulhon

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