Streamline FreeAssAlgebra and Hecke.AssociativeAlgebraElem

[lgoettgens]

At the Friday meeting today it was discussed that while @Sequenzer works on associative algebras in Oscar, we can use the opportunity to streamline the already existing things in AbstractAlgebra and Hecke (both naming and interface).
From a first look, there seems to be:

• AbstractAlgebra.FreeAssAlgebra
• AbstractAlgebra.FreeAssAlgElem
• Hecke.AbstractAssociativeAlgebraElem
• Hecke.AssociativeAlgebraElem

I haven't checked what all of them offer, what the differences are, possibilities, etc. This issue exists just to have some place for discussions.

cc @Sequenzer @thofma @micjoswig @fieker

[thofma]

I think we can just rename FreeAssAlgebra to FreeAssociativeAlgebra and similar for the element. They have nothing else in common that would warrant an "interface".

[fieker]

@lgoettgens is promising a resolution by this afternoon... hold thumbs
(it just a renaming)

[lgoettgens]

The renaming of the two AA types is done in Nemocas/AbstractAlgebra.jl#1779.

What remains is to rename FreeAssAlgIdeal to FreeAssociativeAlgebraIdeal. Since this would create a hell of a lot of conflicts with #4035, I would ask @Sequenzer to include this change in #4035. It should be a simple search-and-replace and adding Base.@deprecate_binding FreeAssAlgIdeal FreeAssociativeAlgebraIdeal to the bottom of deprecations.jl.

[micjoswig]

Indeed, @Sequenzer please do as proposed.

What remains is to rename FreeAssAlgIdeal to FreeAssociativeAlgebraIdeal. Since this would create a hell of a lot of conflicts with #4035, I would ask @Sequenzer to include this change in #4035. It should be a simple search-and-replace and adding Base.@deprecate_binding FreeAssAlgIdeal FreeAssociativeAlgebraIdeal to the bottom of deprecations.jl.

[Sequenzer]

I would wait for the changes in AbstractAlgebra to propagate to OSCAR. But then I will do it.

[lgoettgens]

It's already available as AA 0.42.3. You just need to update the compat entry in Oscar's Project.toml.