Opened 6 years ago
Last modified 4 months ago
#18528 new task
SageManifolds metaticket — at Version 36
Reported by: | egourgoulhon | Owned by: | egourgoulhon |
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Priority: | major | Milestone: | |
Component: | geometry | Keywords: | manifold, tensor, differential geometry |
Cc: | mbejger, mmancini, tscrim, bpillet, gh-LBrunswic, gh-mjungmath, gh-honglizhaobob | 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 )
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)
- Fix bug in list functionality of free module bases: #22518
- Fix display of tensors on free modules of finite rank: #22520
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)
- fix bug with symbolic derivatives in simplification of coordinate functions: #22503
- 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:
Change History (36)
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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 KManifolds(K).Differentiable()
for differentiable manifoldsManifolds(K).Smooth()
for smooth manifolds
comment:14 follow-up: ↓ 15 Changed 6 years ago by
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 6 years ago by
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
- the 2-sphere at http://sagemanifolds.obspm.fr/examples/html/SM_sphere_S2.html
- the real projective plane at http://sagemanifolds.obspm.fr/examples/html/SM_projective_plane_RP2.html
- the hyperbolic plane at http://nbviewer.ipython.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v0.8/SM_hyperbolic_plane.ipynb
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 6 years ago by
PS: could you point to some existing catalog in Sage, in order to have some example?
comment:17 follow-up: ↓ 18 Changed 6 years ago by
algebras.<tab>
insage/algebras/catalog.py
crystals.<tab>
insage/combinat/crystals.catalog.py
designs.<tab>
insage/combinat/designs.designs_catalog.py
groups.<tab>
insage/groups/groups_catalog.py
comment:18 in reply to: ↑ 17 Changed 6 years ago by
Thanks!
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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).
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All the tickets, except for #18786, are now ready for review.