VectorFieldModule, TensorFieldModule, DiffFormModule: Add methods tensor_product, tensor_power, update category of TensorFieldModule

[mkoeppe]

... as previously done for FiniteRankFreeModule etc.

We introduce abstract base classes ReflexiveModule_* to unify the implementations of VectorFieldModule... and FiniteRankFreeModule/VectorFieldFreeModule...

Follow-up: #34621 Method dual_pairing for modules in sage.tensor

CC: @egourgoulhon @tscrim @mjungmath

Component: manifolds

Author: Matthias Koeppe

Branch/Commit: 74601e6

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/34589

[mkoeppe]

Dependencies: #34448

[mkoeppe]

Branch: u/mkoeppe/vectorfieldmodule_tensor_product

[mkoeppe]

Commit: 31b17b5

[mkoeppe]

comment:3

Probably best to create a class VectorFieldModule_abstract

---

Last 10 new commits:

620df16	src/sage/tensor/modules/tensor_free_submodule.py: Remove tensor_factors, add doctest for construction
4c9be6b	src/sage/manifolds/differentiable/diff_form_module.py: doc: add that the case p=1 of M parallelizable is implemented via VectorFieldDualFreeModule
06710c1	src/sage/manifolds/differentiable/diff_form_module.py, vectorfield_module.py: Update copyright using 'git blame -w --date=format:%Y FILE.py | sort -k2', add to AUTHORS
bb614c1	Merge #34501
4a4a29d	Merge tag '9.7' into t/34448/put_tensor_modules_of_finiterankfreemodule_in_modules___tensorproducts__
1f4fb90	Merge tag '9.8.beta0' into t/34448/put_tensor_modules_of_finiterankfreemodule_in_modules___tensorproducts__
7c04959	src/sage/manifolds/differentiable/diff_form_module.py: Fix typo in docstring
fc31cbf	Merge #34501
f0def92	src/sage/tensor/modules/tensor_free_module.py: Remove redundant method
31b17b5	WIP

[sagetrac-git]

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

e10f9cf	src/sage/manifolds/differentiable/vectorfield_module.py: Revert change to VectorFieldModule.tensor (not needed yet)
ff00c11	VectorFieldModule: Add tensor_product, tensor_power
8d753dc	src/sage/manifolds/differentiable/vectorfield_module.py (VectorFieldModule_abstract): New

[sagetrac-git]

Changed commit from 31b17b5 to 8d753dc

[sagetrac-git]

Changed commit from 8d753dc to 6bada9f

[sagetrac-git]

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

2830ebc	TensorFreeModule.tensor_factors: Go through methods tensor_type, base_module
6bada9f	TensorFieldModule.tensor_factors: New

[sagetrac-git]

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

347ffc0

TensorFieldModule: Put it in the category Modules.TensorProducts

[sagetrac-git]

Changed commit from 6bada9f to 347ffc0

[sagetrac-git]

Changed commit from 347ffc0 to 7194893

[sagetrac-git]

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

7194893

src/sage/manifolds/differentiable/tensorfield_module.py: Update copyright according to git blame -w --date=format:%Y FILE | sort -k2

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

comment:11

This new base class is of course not very pretty

+class VectorFieldModule_abstract(UniqueRepresentation, Parent):
+    r"""
+    Abstract base class for modules of vector fields.
+    """
+
+    tensor_power = FiniteRankFreeModule_abstract.tensor_power
+
+    tensor_product = FiniteRankFreeModule_abstract.tensor_product
+
+    tensor = FiniteRankFreeModule_abstract.tensor

It could be better to have a common base class for VectorFieldModule_abstract and FiniteRankFreeModule_abstract.

Perhaps that could be called ModuleWithDual_abstract? (see also #13372)

[mkoeppe]

comment:12

Algebra question - do we know / do we assume that a VectorFieldModule is reflexive?