TensorFreeModule.isomorphism_with_fixed_basis

[mkoeppe]

We generalize FiniteRankFreeModule.isomorphism_with_fixed_basis so that it works with tensor modules.

Depends on #34424
Depends on #30300
Depends on #30229

CC: @egourgoulhon @tscrim

Component: linear algebra

Author: Matthias Koeppe

Branch/Commit: 08d6a65

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/34427

[mkoeppe]

Branch: u/mkoeppe/tensorfreemodule_isomorphism_with_fixed_basis

[mkoeppe]

Last 10 new commits:

b7e5319	Merge #34424
fb1ce42	src/sage/tensor/modules/ext_pow_free_module.py: No need to override basis() any more
30d4eec	TensorFreeModule.basis: Pass all args
d1376fd	TensorFreeModule.basis: Add documentation
2bcfc21	src/sage/tensor/modules: Use keyword order: category, ambient
6e9bec5	src/sage/tensor/modules/finite_rank_free_module.py: Move ambient_module, is_submodule to FiniteRankFreeModule_abstract
fd5ba8c	src/sage/tensor/modules/tensor_free_module.py: No more need for TensorFreeModule.irange
544ffab	Merge #30229
a4d65bc	FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Move here from FiniteRankFreeModule, rewrite using Family
280424e	FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Add example with codomain from sage.modules

[mkoeppe]

Commit: 280424e

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Changed commit from 280424e to b0b8d19

[sagetrac-git]

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

e452316	FreeModuleTensor: Handle TensorFreeSubmoduleBasis_comp
b0b8d19	FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Handle codomain=MatrixSpace

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

18aa856

FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Add example with symmetric binary forms

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

dafd47d

FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Better example with symmetric binary forms

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

c354770

FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Add example with codomain= tensor square of a CombinatorialFreeModule

[mkoeppe]

Author: Matthias Koeppe

[sagetrac-git]

Changed commit from c354770 to 454f0b0

[sagetrac-git]

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

694e665	TensorFreeSubmoduleBasis_comp._repr_: New
adc2b45	Merge #30229
454f0b0	src/sage/tensor/modules/finite_rank_free_module.py: Update doctest output

[mjungmath]

comment:9

This looks great! I think this also solves the problem that tensor bundles currently return the preferred local frame of the tangent bundle.

Moreover, tensor powers and exterior powers of vector bundles should be easy to implement by following the same strategy as for tensor bundles. The only reason I haven't done it so far was exactly that those powers in the free module case had no bases.

However, perhaps it is a better idea to start with some sort of unifocation first, to avoid redundancies. Otherwise we have to write similar code twice (for tangent bundles and for vector bundles). After all, tangent bundles are just special cases of vector bundles. I am still not sure though what a good implemention strategy would be to achive that.

Speaking of which: what about fiber bundles?

[mkoeppe]

comment:10

Thanks for taking a look!

For exterior powers, I still hope to come back to the approach of #30242, making them quotients. This will basically come for free when #30229 is complete.

Right now I don't have an opinion on how this should be generalized to tensor/vector/fiber bundles

[sagetrac-git]

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

a1de064	TensorFreeSubmodule_comp: Default name, latex_name for the case Sym^n(M)
320d00b	TensorFreeSubmodule_comp: Default name, latex_name for more cases
e8ba509	TensorFreeSubmodule_comp: Fix default name, latex_name for indices without symmetries
0277d80	TensorFreeSubmodule_comp: Add example for module with sym and antisym
17137cf	FiniteRankFreeModule.tensor_module: Add parameters sym, antisym; add methods symmetric_power, dual_symmetric_power
eb517b2	Merge #30229
06e0cd8	src/sage/tensor/modules/finite_rank_free_module.py: WIP isomorphism_with_fixed_basis with codomain=symmetric matrices

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Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

e2d2ea8

src/sage/tensor/modules/finite_rank_free_module.py: isomorphism_with_fixed_basis with codomain=symmetric matrices

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

993b343	TensorFreeModule._element_constructor_: Pass parent=self to element_class
5b8ccde	src/sage/tensor/modules/tensor_free_module.py: Update doctest output
b0812b1	TensorFreeSubmoduleBasis_comp._element_constructor_: Full implementation
8cd3cc4	TensorFreeSubmoduleBasis_comp._element_constructor_: Fix for zero; implement retract
ae2ff23	TensorFreeSubmoduleBasis_comp.reduce: New; use it in _element_constructor_
9ace3e2	Merge #30229

[sagetrac-git]

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

89a5893	src/sage/tensor/modules/tensor_free_[sub]module.py (_basis_comp): Add docstrings
c8d9877	TensorFreeSubmodule_comp._is_symmetry_coarsening_of: Add docstring
e31bdac	TensorFreeModule._an_element_: Pass parent to element class
e7d5e77	TensorFreeModule._an_element_: Use element constructor
18d3dbe	TensorFreeSubmodule_comp._is_symmetry_coarsening_of: Update example
3f1c33d	TensorFreeSubmoduleBasis_comp.__init__: Add doctest
9378a78	src/sage/tensor/modules/finite_rank_free_module.py: Update doctest output
1c8b0a1	Merge #30229
f496223	FiniteRankFreeModule_abstract._test_isomorphism_with_fixed_basis: Do nothing if there is no basis method
d341422	src/sage/tensor/modules/finite_rank_free_module.py: Update doctest output

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Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

c42118a

src/sage/manifolds/differentiable/tangent_space.py: Add example: isomorphism with inner product space

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Changed commit from c42118a to b79aebe

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

877d17e	Merge #30300
b79aebe	Merge #30229

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

aaf46cc	DifferentiableManifold.tangent_space, TangentSpace: Accept keyword 'base_ring'
6cd438c	StandardSymplecticSpace: Add example: isomorphism with inner product space

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

1e7430a	src/sage/tensor: In examples, use FiniteRankFreeModule.tensor_module(..., sym=...) instead of FiniteRankFreeModule_sym
046887c	TensorFreeModule.basis: Add example from egourgoulhon
3a65d2d	CompWithSym._canonicalize_sym_antisym: Factor out from __init__
07ab991	src/sage/tensor: Allow _sym, _antisym attributes to be tuples
3619b4c	src/sage/tensor, src/sage/manifolds: Sort _sym, _antisym, store as tuples of tuples
970c6c8	src/sage/tensor, src/sage/manifolds: Sort _sym, _antisym, store as tuples of tuples (fixup)
9f15e00	src/sage/tensor: Allow _sym, _antisym attributes to be tuples (fixup)
6547ab9	Merge #34451
04706dd	FiniteRankFreeModule.tensor_module: Canonicalize sym, antisym
6ca796c	Merge #30229

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

726e562	src/sage/tensor/modules/finite_rank_free_module.py: Remove unused import
bd38eac	Merge #30229

[sagetrac-git]

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

421c660	src/sage/tensor/modules/finite_rank_free_module.py: Add doctest
a1a3f36	CompWithSym.__init__: Accept keyword 'trivial_symmetries', add tests
8a2c71a	VectorFieldModule.tensor, VectorFieldFreeModule.tensor: Use CompWithSym._canonicalize_sym_antisym
e34306b	Revert "FiniteRankFreeModule.tensor: Restore error when trivial symmetries are passed"
c6b6b2e	src/sage/tensor, src/sage/manifolds: Remove parameter 'trivial_symmetries' again
39bfe8d	Merge #34451
bec2f65	CompWithSym._canonicalize_sym_antisym: Refactor, fix index validation, add tests
66009e7	src/sage/tensor/modules/comp.py: Fix docstring
64e3c1d	Merge #34451
ebc98d4	Merge #30229

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

7474abb	FiniteRankFreeModule_abstract.tensor_product: Handle submodules with symmetries
ed3c8d9	src/sage/tensor/modules/finite_rank_free_module.py (FiniteRankFreeModule_abstract.is_submodule): Fix typo in doctest
fd89892	src/sage/tensor/modules/tensor_free_submodule[_basis].py, finite_rank_free_module.py: Update AUTHORS
644933a	src/sage/tensor/modules/finite_rank_free_module.py: Update copyright according to git blame -w --date=format:%Y FILE | sort -k2
a7c79de	Merge #30229

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

45bf6f3	FiniteRankFreeModule_abstract.tensor_product: Add comment
803f7e4	Make FiniteRankFreeModule.tensor_module(0, 1) return the dual (#34474)
0648daa	Merge #34474
fc66ad1	FiniteRankFreeModule.dual_symmetric_power: Update for changes in #34474
08d6a65	Merge #30229

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Changed commit from a7c79de to 08d6a65

[egourgoulhon]

Reviewer: Eric Gourgoulhon

[egourgoulhon]

comment:27

Looks nice. Thanks.

[mkoeppe]

comment:28

Thank you!

[vbraun]

Changed branch from u/mkoeppe/tensorfreemodule_isomorphism_with_fixed_basis to 08d6a65