TensorFreeModule._an_element_: Create a default basis in the base module if necessary

[mkoeppe]

Likewise for ExtPowerFreeModule etc.

The current code creates an element without components if the base module has no default basis. Such elements are not useful for running the test suite because adding them gives a "no common basis" error.

That currently all tests work depends in a subtle way on the order in which modules are created.

In this ticket, we propose to change the _an_element_ method to create a default basis in the base module if none already exists -- this matches what FiniteRankFreeModule._an_element_ already does.

This will simplify further refactoring of the code, such as the identification of modules discussed in #30241.

CC: @egourgoulhon @tscrim @mjungmath

Component: linear algebra

Author: Matthias Koeppe

Branch/Commit: eec19fd

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/30254

[mkoeppe]

Branch: u/mkoeppe/tensorfreemodule__an_element___create_a_default_basis_in_the_base_module_if_necessary

[sagetrac-git]

Commit: d2d7f42

[sagetrac-git]

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

d2d7f42

ExtPowerDualFreeModule._an_element_: Make sure a default basis is available

[sagetrac-git]

Changed commit from d2d7f42 to eec19fd

[sagetrac-git]

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

9e739e5	FreeModuleLinearGroup._an_element_: Make sure a default basis is available
eec19fd	TensorFreeModule._an_element_: Make sure a default basis is available

[mkoeppe]

Author: Matthias Koeppe

[egourgoulhon]

comment:5

Thanks for fixing this!

[egourgoulhon]

Reviewer: Eric Gourgoulhon

[mkoeppe]

comment:6

Thanks!

[vbraun]

Changed branch from u/mkoeppe/tensorfreemodule__an_element___create_a_default_basis_in_the_base_module_if_necessary to eec19fd