LieAlgebras: Introduce WeightLattice

[lgoettgens]

Changes:

• Introduce WeightLattice, a formal parent for WeightLatticeElem
• character and friends now return a Dict{WeightLatticeElem, T} (with default T = Int)
• Weyl actions: remove some duplicate ugliness; instead add a warning to the docs page

preview: https://docs.oscar-system.org/previews/PR4344/Experimental/LieAlgebras/

[codecov]

Codecov Report

Attention: Patch coverage is 85.76512% with 40 lines in your changes missing coverage. Please review.

Project coverage is 84.31%. Comparing base (9da6d04) to head (faf6df4).
Report is 221 commits behind head on master.

Files with missing lines	Patch %	Lines
experimental/LieAlgebras/src/WeightLattice.jl	87.56%	23 Missing ⚠️
experimental/LieAlgebras/src/LieAlgebraModule.jl	51.72%	14 Missing ⚠️
experimental/LieAlgebras/src/RootSystem.jl	92.59%	2 Missing ⚠️
...xperimental/LieAlgebras/test/WeightLattice-test.jl	92.30%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4344      +/-   ##
==========================================
- Coverage   84.32%   84.31%   -0.02%     
==========================================
  Files         649      651       +2     
  Lines       86430    86483      +53     
==========================================
+ Hits        72880    72915      +35     
- Misses      13550    13568      +18     

Files with missing lines	Coverage Δ
...BasisLieHighestWeight/src/BasisLieHighestWeight.jl	100.00% <ø> (ø)
...imental/BasisLieHighestWeight/src/MainAlgorithm.jl	97.76% <100.00%> (ø)
...l/BasisLieHighestWeight/test/MainAlgorithm-test.jl	97.50% <ø> (ø)
experimental/LieAlgebras/src/LieAlgebras.jl	100.00% <ø> (ø)
experimental/LieAlgebras/src/Types.jl	96.73% <100.00%> (+0.05%)	⬆️
experimental/LieAlgebras/src/WeylGroup.jl	90.25% <100.00%> (-0.03%)	⬇️
...rimental/LieAlgebras/test/LieAlgebraModule-test.jl	100.00% <100.00%> (ø)
experimental/LieAlgebras/test/RootSystem-test.jl	97.16% <100.00%> (ø)
experimental/LieAlgebras/test/WeylGroup-test.jl	97.77% <ø> (ø)
...xperimental/LieAlgebras/test/WeightLattice-test.jl	92.30% <92.30%> (ø)
... and 3 more

[lgoettgens]

can we get this merged? @fingolfin or someone else?

[lgoettgens]

Re-drafting until conflicts with #4339 are resolved.

[lgoettgens]

CI is happy with my merge resolution. So this is again ready for merge

[joschmitt]

This is none of my business, but I spent too much time transposing-matrices-until-the-result-looks-correct to not comment here:
So far, my understanding was that all group actions are from the right in OSCAR (at least by default) and we happily break textbook conventions at least in the linear algebra and invariant theory to have this consistent. Why not here?

[lgoettgens]

Short answer: this is still in discussion with Max (before this migrates to src/). This is the current state of things, and I wanted to document how it is right now (but subject to change). The removal of some *_left_* and *_right_* functions in this PR is to clean things up that partially made it possible to do both action directions, but this didn't seem like a healthy way forward (and it didn't think of all places where this was an issue). So I would like to clean this up again, further discuss with Max and afterwards tackle this more systematically.

[joschmitt]

Okay, thanks!

[joschmitt]

The Aachen people seem to be happy with it.