Opened 5 years ago
Last modified 27 hours ago
#18528 new task
SageManifolds metaticket 1
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 )
This is the implementation of manifolds resulting from the SageManifolds project, developed by the following authors.
This metaticket covers the implementation up to Sage 9.2. See the metaticket #30525 for Sage >= 9.3.
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)
- Index notation for tensors should allow for unicode characters: #29248 (merged in Sage 9.2.beta9)
- Basis-dependent isomorphism from
FiniteRankFreeModule
to an object in the categoryModulesWithBasis
: #30094 (merged in Sage 9.2.beta7) ModulesWithBasis.linear_combination
should be a method ofModules
: #30179 (merged in Sage 9.2.beta7)- Immutable elements of
FreeModuleTensor
: #30181 (merged in Sage 9.2.beta8) FiniteRankFreeModule
needs__classcall__
: #30169 (merged in Sage 9.2.beta8)- Extend
FreeModule
factory to construction ofFiniteRankFreeModule
andCombinatorialFreeModule
: #30194 (merged in Sage 9.2.beta8) FiniteRankFreeModule
: Simplify unique representation code for dependent modules: #30250 (merged in Sage 9.2.beta8)- Simplify
_repr_
ofExtPowerFreeModule
andExtPowerDualFreeModule
: #30251 (merged in Sage 9.2.beta9) TensorFreeModule._an_element_
: Create a default basis in the base module if necessary: #30254 (merged in Sage 9.2.beta8)FiniteRankFreeModule
: Move all module identifications to methodsexterior_power
,dual_exterior_power
,tensor_module
: #30255 (merged in Sage 9.2.beta8)sage.tensor.modules.free_module_basis
: Add testsuite: #30287 (merged in Sage 9.2.beta8)
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)
- 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)
- add manifold orientability: #30178 (merged in Sage 9.2.beta9)
- Immutability for scalar fields: #30266 (merged in Sage 9.2.beta8)
- Coercion via restriction of chart functions: #30267 (merged in Sage 9.2.beta8)
- Scalar Field Arithmetics: Trivial Cases: #30291 (merged in Sage 9.2.beta8)
- 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)
- Constructing a vector frame from a family of vector fields: #28716 (merged in Sage 9.0.beta8)
- Apply a function to all components of a tensor field: #29244 (merged in Sage 9.1.beta8)
- Let
diff()
act on chart functions and differentiable forms: #29953 (merged in Sage 9.2.beta4) - Action for bundle connections: #30209 (merged in Sage 9.2.beta9)
- Declare sections with name only: #30228 (merged in Sage 9.2.beta7)
- List assignment for bundle connections: #30208 (merged in Sage 9.2.beta8)
- Immutability of tensor fields: #30274 (merged in Sage 9.2.beta8)
- Add
copy()
method to affine connections: #30285 (merged in Sage 9.2.beta8) - Immutability of affine connections: #30280 (merged in Sage 9.2.beta8)
- Immutability for sections: #30288 (merged in Sage 9.2.beta8)
- 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)
- Degenerate manifolds and submanifolds: #26355 (merged in Sage 9.1.beta0)
- Degenerate submanifolds: new features: #29080 (merged in Sage 9.1.beta4)
- 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)
- Add
EuclideanSpace
to category of metric spaces: #30062 (merged in Sage 9.2.beta7) - Dot and cross products along a differentiable map: #30318 (merged in Sage 9.2.beta8)
- 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)
- 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 inContinuousMap
: #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 methodfunction_chart
: #27409 (merged in Sage 8.7.beta7) - 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
tocheck
inCoordChange.set_inverse()
and set the default toTrue
: #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
onshow_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 (merged in Sage 9.1.beta6)
- 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 (merged in Sage 9.1.beta6)
- Improve doctests of degenerate submanifolds: #29440 (merged in Sage 9.1.rc0)
- Correct documentation of characteristic classes: #29470 (merged in Sage 9.1.rc0)
- Wrong parent when using
diff_form
of degree zero: #29570 (merged in Sage 9.1.rc3) - Wedge product of multivector field with scalar field: #29628 (merged in Sage 9.2.beta0)
- Bug in initialization of vector field with rational components: #29639 (merged in Sage 9.2.beta0)
- Multiprocessing in tensor computations does not work under macOS: #29755
- More efficient contruction of free module bases: #30061 (merged in Sage 9.2.beta7)
- Unable to coerce free module over Q into Category of vector spaces over Q: #30094 (merged in Sage 9.2.beta7)
- Not equal operator for mixed forms: #30108 (merged in Sage 9.2.beta7)
- Coercion from
ChartFunctionRing
toScalarFieldAlgebra
: #30112 (merged in Sage 9.2.beta6) - Failed conversion yields unconclusive error message: #30191 (merged in Sage 9.2.beta7)
- Error in display of a continuous map between open intervals: #30289 (merged in Sage 9.2.beta8)
- Unions of subsets of a fixed open set X are not known to be subsets of X: #30401 (merged in Sage 9.2.beta12)
- Replace
AssertionError
withValueError
when immutable elements are tried to be changed: #30275 (merged in Sage 9.2.beta13) set_default_frame()
too restrictive on parallelizable manifolds: #30320 (merged in Sage 9.2.beta13)- Fix check of orientation in volume form: #30519 (merged in Sage 9.2.beta13)
Change History (190)
comment:1 Changed 5 years ago by
- Description modified (diff)
comment:2 Changed 5 years ago by
- Cc bpillet added
- Description modified (diff)
comment:3 Changed 5 years ago by
- Description modified (diff)
- Summary changed from SageManifolds meta-ticket to SageManifolds metaticket
comment:4 Changed 5 years ago by
- Description modified (diff)
comment:5 Changed 5 years ago by
- Description modified (diff)
comment:6 Changed 5 years ago by
- Description modified (diff)
- Milestone changed from sage-6.8 to sage-6.9
comment:7 Changed 5 years ago by
- Description modified (diff)
comment:8 Changed 5 years ago by
- Description modified (diff)
comment:9 Changed 5 years ago by
- Keywords manifold tensor added; manifolds tensors removed
comment:10 Changed 5 years ago by
- Description modified (diff)
comment:11 Changed 5 years ago by
- Description modified (diff)
comment:12 Changed 5 years ago by
- Milestone changed from sage-6.9 to sage-6.10
comment:13 Changed 5 years ago by
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 5 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 5 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 5 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 5 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 5 years ago by
Thanks!
comment:19 Changed 5 years ago by
- Description modified (diff)
- Milestone changed from sage-6.10 to sage-7.0
comment:20 Changed 5 years ago by
- Description modified (diff)
- Milestone changed from sage-7.0 to sage-7.1
comment:21 Changed 5 years ago by
- Description modified (diff)
comment:22 Changed 4 years ago by
- Description modified (diff)
- Milestone changed from sage-7.1 to sage-7.3
comment:23 Changed 4 years ago by
- Description modified (diff)
comment:24 Changed 4 years ago by
- Description modified (diff)
comment:25 Changed 4 years ago by
- Description modified (diff)
comment:26 Changed 4 years ago by
- Description modified (diff)
comment:27 Changed 4 years ago by
- Milestone changed from sage-7.3 to sage-7.4
comment:28 Changed 4 years ago by
- Description modified (diff)
comment:29 Changed 4 years ago by
- Milestone changed from sage-7.4 to sage-7.5
comment:30 Changed 4 years ago by
- Description modified (diff)
comment:31 Changed 4 years ago by
- Description modified (diff)
comment:32 Changed 4 years ago by
- Description modified (diff)
comment:33 follow-up: ↓ 41 Changed 4 years ago by
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
- Description modified (diff)
comment:35 Changed 4 years ago by
- Description modified (diff)
comment:36 Changed 4 years ago by
- Description modified (diff)
- Milestone changed from sage-7.5 to sage-7.6
comment:37 Changed 4 years ago by
- Description modified (diff)
comment:38 Changed 4 years ago by
- Description modified (diff)
comment:39 Changed 4 years ago by
- Description modified (diff)
comment:40 Changed 4 years ago by
- Description modified (diff)
comment:41 in reply to: ↑ 33 ; follow-up: ↓ 42 Changed 3 years ago by
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: ↓ 43 Changed 3 years ago by
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, V^{p}(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 V^{p}(M) x V^{q}(M) --> V^{p+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 V^{p}(M). Would this be an issue for you?
comment:43 in reply to: ↑ 42 ; follow-up: ↓ 44 Changed 3 years ago by
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 V^{p} x V^{q} -> V^{p+q} and Schouten bracket V^{p} x V^{q} -> V^{p+q-1}. One would also like to have interior contractions with forms Omega^{p} x V^{q} -> V^{q-p} and V^{p} x Omega^{q} -> Omega^{q-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 V^{p}(M). Would this be an issue for you?
I don't foresee any issue.
comment:44 in reply to: ↑ 43 ; follow-up: ↓ 51 Changed 3 years ago by
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 V^{p} x V^{q} -> V^{p+q} and Schouten bracket V^{p} x V^{q} -> V^{p+q-1}. One would also like to have interior contractions with forms Omega^{p} x V^{q} -> V^{q-p} and V^{p} x Omega^{q} -> Omega^{q-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 V^{p}(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 3 years ago by
- Description modified (diff)
comment:46 Changed 3 years ago by
- Description modified (diff)
comment:47 Changed 3 years ago by
- Description modified (diff)
comment:48 Changed 3 years ago by
- Description modified (diff)
comment:49 Changed 3 years ago by
- Description modified (diff)
comment:50 Changed 3 years ago by
- Description modified (diff)
comment:51 in reply to: ↑ 44 ; follow-up: ↓ 52 Changed 3 years ago by
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 V^{p} x V^{q} -> V^{p+q} and Schouten bracket V^{p} x V^{q} -> V^{p+q-1}. One would also like to have interior contractions with forms Omega^{p} x V^{q} -> V^{q-p} and V^{p} x Omega^{q} -> Omega^{q-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: ↓ 53 Changed 3 years ago by
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
- Description modified (diff)
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
- Description modified (diff)
comment:55 Changed 3 years ago by
- Description modified (diff)
comment:56 Changed 3 years ago by
- Description modified (diff)
comment:57 Changed 3 years ago by
- Description modified (diff)
- Milestone changed from sage-7.6 to sage-8.1
comment:58 Changed 3 years ago by
- Description modified (diff)
comment:59 Changed 3 years ago by
- Description modified (diff)
comment:60 Changed 3 years ago by
- Description modified (diff)
comment:61 Changed 3 years ago by
- Description modified (diff)
comment:62 Changed 3 years ago by
- Description modified (diff)
comment:63 Changed 3 years ago by
- Description modified (diff)
comment:64 Changed 3 years ago by
- Description modified (diff)
- Milestone changed from sage-8.1 to sage-8.2
comment:65 Changed 3 years ago by
- Description modified (diff)
comment:66 Changed 3 years ago by
- Description modified (diff)
comment:67 Changed 3 years ago by
- Description modified (diff)
comment:68 Changed 3 years ago by
- Description modified (diff)
comment:69 Changed 2 years ago by
- Description modified (diff)
comment:70 Changed 2 years ago by
- Description modified (diff)
comment:71 Changed 2 years ago by
- Description modified (diff)
comment:72 Changed 2 years ago by
- Description modified (diff)
- Milestone changed from sage-8.2 to sage-8.3
- Type changed from enhancement to task
comment:73 Changed 2 years ago by
- Description modified (diff)
comment:74 Changed 2 years ago by
- Description modified (diff)
comment:75 Changed 2 years ago by
- Description modified (diff)
comment:76 Changed 2 years ago by
- Description modified (diff)
comment:77 Changed 2 years ago by
- Description modified (diff)
comment:78 Changed 2 years ago by
- Description modified (diff)
comment:79 Changed 2 years ago by
- Description modified (diff)
comment:80 Changed 2 years ago by
- Description modified (diff)
comment:81 Changed 2 years ago by
- Milestone changed from sage-8.3 to sage-8.4
update milestone 8.3 -> 8.4
comment:82 Changed 2 years ago by
- Description modified (diff)
comment:83 Changed 2 years ago by
- Description modified (diff)
comment:84 Changed 2 years ago by
- Description modified (diff)
comment:85 Changed 2 years ago by
- Description modified (diff)
comment:86 Changed 2 years ago by
- Description modified (diff)
comment:87 Changed 2 years ago by
- Description modified (diff)
comment:88 Changed 2 years ago by
- Description modified (diff)
comment:89 Changed 2 years ago by
- Description modified (diff)
comment:90 Changed 2 years ago by
- Description modified (diff)
comment:91 Changed 2 years ago by
- Description modified (diff)
- Milestone changed from sage-8.4 to sage-8.5
comment:92 Changed 23 months ago by
- Description modified (diff)
comment:93 Changed 23 months ago by
- Description modified (diff)
comment:94 Changed 22 months ago by
- Description modified (diff)
comment:95 Changed 22 months ago by
- Description modified (diff)
comment:96 Changed 22 months ago by
- Description modified (diff)
comment:97 Changed 22 months ago by
- Description modified (diff)
comment:98 Changed 19 months ago by
- Description modified (diff)
- Milestone changed from sage-8.5 to sage-8.7
comment:99 Changed 18 months ago by
- 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 18 months ago by
- Description modified (diff)
comment:101 Changed 18 months ago by
- Description modified (diff)
comment:102 Changed 18 months ago by
- Description modified (diff)
comment:103 Changed 18 months ago by
- Description modified (diff)
comment:104 Changed 18 months ago by
- Description modified (diff)
comment:105 Changed 18 months ago by
- Description modified (diff)
comment:106 Changed 18 months ago by
- Description modified (diff)
comment:107 Changed 18 months ago by
- Description modified (diff)
comment:108 Changed 17 months ago by
- Description modified (diff)
comment:109 Changed 16 months ago by
- Description modified (diff)
comment:110 Changed 16 months ago by
- 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 15 months ago by
- Description modified (diff)
comment:112 Changed 15 months ago by
- Description modified (diff)
comment:113 Changed 14 months ago by
- Description modified (diff)
comment:114 Changed 14 months ago by
- Description modified (diff)
comment:115 Changed 14 months ago by
- Description modified (diff)
comment:116 Changed 13 months ago by
- Description modified (diff)
comment:117 Changed 13 months ago by
- Description modified (diff)
comment:118 Changed 13 months ago by
- Description modified (diff)
comment:119 Changed 13 months ago by
- Description modified (diff)
comment:120 Changed 13 months ago by
- Description modified (diff)
comment:121 Changed 12 months ago by
- Description modified (diff)
comment:122 Changed 12 months ago by
- Description modified (diff)
comment:123 Changed 12 months ago by
- Description modified (diff)
comment:124 Changed 12 months ago by
comment:125 Changed 12 months ago by
- Description modified (diff)
comment:126 Changed 12 months ago by
- Description modified (diff)
comment:127 Changed 12 months ago by
- Description modified (diff)
comment:128 Changed 12 months ago by
- Description modified (diff)
comment:129 Changed 11 months ago by
- Description modified (diff)
comment:130 Changed 11 months ago by
- Description modified (diff)
comment:131 Changed 11 months ago by
- Description modified (diff)
comment:132 Changed 11 months ago by
- Description modified (diff)
comment:133 Changed 11 months ago by
- Description modified (diff)
comment:134 Changed 11 months ago by
- Description modified (diff)
comment:135 Changed 11 months ago by
- Description modified (diff)
comment:136 Changed 11 months ago by
- Description modified (diff)
comment:137 Changed 11 months ago by
- Description modified (diff)
comment:138 Changed 11 months ago by
- Description modified (diff)
comment:139 Changed 10 months ago by
- Description modified (diff)
comment:140 Changed 10 months ago by
- Description modified (diff)
comment:141 Changed 10 months ago by
- Description modified (diff)
comment:142 Changed 10 months ago by
- Description modified (diff)
comment:143 Changed 10 months ago by
- Description modified (diff)
comment:144 Changed 10 months ago by
- Cc gh-LBrunswic added
comment:145 Changed 10 months ago by
- Description modified (diff)
comment:146 Changed 10 months ago by
- Description modified (diff)
comment:147 Changed 10 months ago by
- Description modified (diff)
comment:148 Changed 9 months ago by
- Description modified (diff)
comment:149 Changed 9 months ago by
- Description modified (diff)
comment:150 Changed 8 months ago by
- Description modified (diff)
comment:151 Changed 8 months ago by
- Description modified (diff)
comment:152 Changed 8 months ago by
- Description modified (diff)
comment:153 Changed 8 months ago by
- Description modified (diff)
comment:154 Changed 8 months ago by
- Description modified (diff)
comment:155 Changed 7 months ago by
- Description modified (diff)
comment:156 Changed 7 months ago by
- Description modified (diff)
comment:157 Changed 7 months ago by
- Description modified (diff)
comment:158 Changed 6 months ago by
- Description modified (diff)
comment:159 Changed 6 months ago by
- Description modified (diff)
comment:160 Changed 6 months ago by
- Description modified (diff)
comment:161 Changed 5 months ago by
- Description modified (diff)
comment:162 Changed 5 months ago by
- Description modified (diff)
comment:163 Changed 5 months ago by
- Description modified (diff)
comment:164 Changed 5 months ago by
- Description modified (diff)
comment:165 Changed 5 months ago by
- Description modified (diff)
comment:166 Changed 5 months ago by
- Description modified (diff)
comment:167 Changed 5 months ago by
- Description modified (diff)
comment:168 Changed 5 months ago by
- Description modified (diff)
comment:169 Changed 5 months ago by
- Description modified (diff)
comment:170 Changed 4 months ago by
- Description modified (diff)
comment:171 Changed 4 months ago by
- Description modified (diff)
comment:172 Changed 4 months ago by
- Description modified (diff)
comment:173 Changed 3 months ago by
- Description modified (diff)
comment:174 Changed 2 months ago by
- Cc gh-mjungmath added
comment:175 Changed 2 months ago by
- Description modified (diff)
comment:176 Changed 2 months ago by
- Description modified (diff)
comment:177 Changed 2 months ago by
- Description modified (diff)
comment:178 Changed 2 months ago by
- Description modified (diff)
comment:179 Changed 2 months ago by
- Description modified (diff)
comment:180 Changed 2 months ago by
- Description modified (diff)
comment:181 Changed 2 months ago by
- Description modified (diff)
comment:182 Changed 7 weeks ago by
- Description modified (diff)
comment:183 Changed 7 weeks ago by
- Description modified (diff)
comment:184 Changed 6 weeks ago by
- Description modified (diff)
comment:185 Changed 6 weeks ago by
- Description modified (diff)
comment:186 Changed 6 weeks ago by
- Description modified (diff)
comment:187 Changed 4 weeks ago by
- Description modified (diff)
comment:188 Changed 4 weeks ago by
- Description modified (diff)
comment:189 Changed 2 weeks ago by
- Description modified (diff)
- Summary changed from SageManifolds metaticket to SageManifolds metaticket 1
This metaticket is becoming too large; I am moving the tickets not closed in Sage 9.2 to the new metaticket #30525.
comment:190 Changed 27 hours ago by
- Description modified (diff)
All the tickets, except for #18786, are now ready for review.