Fix Chevalley basis; add more functionality

[lgoettgens]

Reported by Willem de Graaf on slack. The example was added to the conformance tests, the conformance tests were improved to fail on that example, and then the algorithm was fixed (or rather: implemented properly instead of hoping for the best).

Release notes

• Fix chevalley_basis (sometimes returning wrong results)
• Add change_base_ring(::Field, ::LieAlgebra)
• Add structure_constant_table(::LieAlgebra, basis)

[lgoettgens]

@aaruni96 would this also be able to get backported? If you decide not to due to the amount of new functionality that I needed to add to allow for a proper implementation to fix the bug, that is fine for me as well.

And of course this first needs a review (bump @fingolfin), so please don't wait unnecessarily long with releasing 1.3.1 just because of this. If we do a 1.3.2 sometime, we can then consider this, or it would need to wait for 1.4.0

[aaruni96]

I am vary of adding new functionality to a patch release (if I understand correctly, major version bump = change whatever you want, point version bump = maintain backwards compatibility, patch version bump = bugfixes and very important changes only).

Maybe if we break this PR out into two, one fixing the chevalley_basis, and another for the rest, we could add in the bugfix to 1.3.1 ?

I am of course happy to defer to @benlorenz's judgement.

[lgoettgens]

I am vary of adding new functionality to a patch release (if I understand correctly, major version bump = change whatever you want, point version bump = maintain backwards compatibility, patch version bump = bugfixes and very important changes only).

Maybe if we break this PR out into two, one fixing the chevalley_basis, and another for the rest, we could add in the bugfix to 1.3.1 ?

Unfortunately, there is no rest. The new functions are an essential part of the fix, but since they also seem to be useful on their own, I put them into their own functions.

The only split up I could think of is the following:

1. The fix, the corresponding tests, including all the helper functions (but rename the helper functions by prepending a _)
2. Remove the added _ from the names, thus making these helper functions "public"

But I am not really sure how useful this even is.

[aaruni96]

If adding functionality is a side effect of a bug fix, then, sure I guess (modulo approval from @fingolfin or so).

[benlorenz]

I think it is fine to add to 1.3.1.

This is also part of experimental so there are less strict rules anyway.