We generalize FiniteRankFreeModule.tensor_module by giving it optional arguments sym, antisym; if given, a submodule of the tensor module spanned by the tensors with these prescribed symmetries is created.

The new methods symmetric_power and dual_symmetric_power provide two important special cases.

The implementation makes the standard bases of tensor modules (and of their new submodules) explicit objects. The basis method now works for tensor modules, not just the base module, and returns an instance of the new class TensorFreeSubmoduleBasis_sym, which represents the standard basis corresponding to an instance of the Components class (or one of its subclasses).

Follow-ups:

• TensorFreeModule.isomorphism_with_fixed_basis #34427 TensorFreeModule.isomorphism_with_fixed_basis
• Make ExtPowerFreeModule a quotient of TensorFreeModule #30242 Make ExtPowerFreeModule a quotient of TensorFreeModule
• Refactor Components into parent & element #30307 Refactor Components into parent (a ModuleWithBasis) & element

Depends on #30300
Depends on #34424
Depends on #34451
Depends on #34474

CC: @egourgoulhon @tscrim @mjungmath @slel @honglizhaobob

Component: linear algebra

Author: Matthias Koeppe

Branch/Commit: fc66ad1

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/30229