Opened 22 months ago

Last modified 5 days ago

#18528 new enhancement

SageManifolds metaticket

Reported by: egourgoulhon Owned by: egourgoulhon
Priority: major Milestone: sage-7.6
Component: geometry Keywords: manifold, tensor, differential geometry
Cc: mbejger, mmancini, tscrim, bpillet Merged in:
Authors: Eric Gourgoulhon, Michal Bejger, Marco Mancini 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.

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)

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)
  • 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)
  • 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)
    • Euclidean spaces: #19978

Bug fixes

  • 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
  • Tensor field restrictions on parallelizable manifolds: #22637
  • Inverse metric on parallelizable manifolds: #22667

Change History (40)

comment:1 Changed 22 months ago by egourgoulhon

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comment:2 Changed 22 months ago by egourgoulhon

  • Cc bpillet added
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comment:3 Changed 22 months ago by egourgoulhon

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  • Summary changed from SageManifolds meta-ticket to SageManifolds metaticket

comment:4 Changed 21 months ago by egourgoulhon

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comment:5 Changed 21 months ago by egourgoulhon

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comment:6 Changed 19 months ago by egourgoulhon

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  • Milestone changed from sage-6.8 to sage-6.9

comment:7 Changed 19 months ago by egourgoulhon

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comment:8 Changed 19 months ago by egourgoulhon

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comment:9 Changed 19 months ago by egourgoulhon

  • Keywords manifold tensor added; manifolds tensors removed

comment:10 Changed 19 months ago by egourgoulhon

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comment:11 Changed 19 months ago by egourgoulhon

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comment:12 Changed 18 months 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 17 months 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 17 months 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 17 months 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 17 months ago by egourgoulhon

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

comment:17 follow-up: Changed 17 months 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 17 months ago by egourgoulhon

Thanks!

comment:19 Changed 15 months ago by egourgoulhon

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  • Milestone changed from sage-6.10 to sage-7.0

comment:20 Changed 14 months ago by egourgoulhon

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  • Milestone changed from sage-7.0 to sage-7.1

comment:21 Changed 14 months ago by egourgoulhon

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comment:22 Changed 10 months ago by egourgoulhon

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  • Milestone changed from sage-7.1 to sage-7.3

comment:23 Changed 10 months ago by egourgoulhon

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comment:24 Changed 10 months ago by tscrim

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comment:25 Changed 10 months ago by egourgoulhon

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comment:26 Changed 10 months ago by egourgoulhon

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comment:27 Changed 7 months ago by egourgoulhon

  • Milestone changed from sage-7.3 to sage-7.4

comment:28 Changed 5 months ago by egourgoulhon

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comment:29 Changed 5 months ago by egourgoulhon

  • Milestone changed from sage-7.4 to sage-7.5

comment:30 Changed 4 months ago by egourgoulhon

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comment:31 Changed 4 months ago by egourgoulhon

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comment:32 Changed 2 months ago by egourgoulhon

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comment:33 Changed 7 weeks 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 3 weeks ago by egourgoulhon

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comment:35 Changed 3 weeks ago by egourgoulhon

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comment:36 Changed 3 weeks ago by egourgoulhon

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  • Milestone changed from sage-7.5 to sage-7.6

comment:37 Changed 3 weeks ago by egourgoulhon

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comment:38 Changed 2 weeks ago by egourgoulhon

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comment:39 Changed 10 days ago by egourgoulhon

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comment:40 Changed 5 days ago by egourgoulhon

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