LieAlgebras: Adapt Demazure operator

[janikapeters]

Implemented by the request of @lgoettgens and @gfourier.
See the commit messages for details.

Currently this is based on #4399 and I will rebase it once this is merged

[lgoettgens]

Some comments below. Please also add the new docstrings (2 reflect, 2 reflect!, 1 reflection) to the corresponding documentation pages (in experimental/LieAlgebras/docs/src/root_systems.md or weight_lattice.md.

[codecov]

Codecov Report

Attention: Patch coverage is 84.90566% with 8 lines in your changes missing coverage. Please review.

Project coverage is 84.38%. Comparing base (cd79a0b) to head (b1b04f5).
Report is 17 commits behind head on master.

Files with missing lines	Patch %	Lines
src/LieTheory/RootSystem.jl	20.00%	8 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4384      +/-   ##
==========================================
- Coverage   84.38%   84.38%   -0.01%     
==========================================
  Files         658      663       +5     
  Lines       87157    87934     +777     
==========================================
+ Hits        73551    74199     +648     
- Misses      13606    13735     +129     

Files with missing lines	Coverage Δ
experimental/LieAlgebras/src/RootSystem.jl	100.00% <100.00%> (+1.00%)	⬆️
...rimental/LieAlgebras/test/LieAlgebraModule-test.jl	100.00% <ø> (ø)
src/Groups/spinor_norms.jl	82.91% <100.00%> (ø)
src/LieTheory/Types.jl	97.61% <100.00%> (ø)
src/LieTheory/WeightLattice.jl	89.11% <100.00%> (+1.55%)	⬆️
src/LieTheory/WeylGroup.jl	91.95% <100.00%> (+0.61%)	⬆️
src/LieTheory/RootSystem.jl	88.86% <20.00%> (-1.65%)	⬇️

... and 26 files with indirect coverage changes

[lgoettgens]

Looks good from my POV, thanks! But it would be great to hear the opinion of @felix-roehrich as well.

[fingolfin]

Suggested change

	Computes the action of the Demazure operator associated to the positive root `r` on the given element of the groupring $\mathbb{Z}[P]$.
	Computes the action of the Demazure operator associated to the positive root `r` on the given element of the group ring $\mathbb{Z}[P]$.

[fingolfin]

(it would be far preferable if the input was an actual group ring element, but this may not currently be an option... though my understanding is that recently some code for this (group rings over larger groups via dices) has been added to Hecke by @thofma ?

[lgoettgens]

I did some tinkering with group algebras over the weight lattice (as an additive group) to represent characters a few weeks ago. This is indeed the preferred goal, but I wasn't satisfied with the usability of these objects yet (this is the main reason why these things are still in experimental).
This would be something I or @janikapeters could look into at some point in the future, and upstream all necessary improvements to Hecke. And if we then are satisfied with the result, we can convert both the input here and the outputs of all character-like functions.