Root system documentation

[lgoettgens]

In preparation for #4263.

cc @felix-roehrich

previews:

• https://docs.oscar-system.org/previews/PR4297/Experimental/LieAlgebras/cartan_matrix/
• https://docs.oscar-system.org/previews/PR4297/Experimental/LieAlgebras/root_systems/
• https://docs.oscar-system.org/previews/PR4297/Experimental/LieAlgebras/weyl_groups/

[lgoettgens]

While looking through the existing documentation, I noticed that this contact section is a bit outdated.
Is it fine for you (@felix-roehrich) to be listed here (and then similarly after moving things to src in the contact section there)?
In the src/ documentation, I would find it beneficial to have someone more permanent than Felix and me there, and would additionally put @fingolfin (if that's fine for you).

[fingolfin]

Fine by me

[lgoettgens]

This is now ready for review IMO. There are a thousand things that could be changed/improved, but that can be iterated later, even after moving to src/.
Please look for straight up wrong statements/typos in the documentation and docstrings. Or if you have suggestions for some changes, I am happy to look at them.

Previews to the three new pages are linked in the initial comment.

[codecov]

Codecov Report

Attention: Patch coverage is 96.07843% with 8 lines in your changes missing coverage. Please review.

Project coverage is 84.51%. Comparing base (aa41156) to head (f5ca39c).
Report is 11 commits behind head on master.

Files with missing lines	Patch %	Lines
experimental/LieAlgebras/src/RootSystem.jl	95.34%	8 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4297      +/-   ##
==========================================
+ Coverage   84.50%   84.51%   +0.01%     
==========================================
  Files         644      644              
  Lines       85606    85685      +79     
==========================================
+ Hits        72339    72419      +80     
+ Misses      13267    13266       -1     

Files with missing lines	Coverage Δ
...imental/BasisLieHighestWeight/src/MainAlgorithm.jl	97.76% <100.00%> (-0.13%)	⬇️
...l/BasisLieHighestWeight/test/MainAlgorithm-test.jl	97.50% <ø> (ø)
experimental/LieAlgebras/src/CartanMatrix.jl	97.29% <100.00%> (-0.02%)	⬇️
experimental/LieAlgebras/src/LieAlgebraIdeal.jl	43.75% <ø> (ø)
experimental/LieAlgebras/src/LieAlgebras.jl	100.00% <ø> (ø)
experimental/LieAlgebras/src/LieSubalgebra.jl	58.71% <ø> (ø)
experimental/LieAlgebras/src/LinearLieAlgebra.jl	90.25% <ø> (ø)
experimental/LieAlgebras/src/Types.jl	96.68% <100.00%> (ø)
experimental/LieAlgebras/src/WeylGroup.jl	90.28% <100.00%> (ø)
experimental/LieAlgebras/test/CartanMatrix-test.jl	100.00% <ø> (ø)
... and 3 more

---- 🚨 Try these New Features:

• Flaky Tests Detection - Detect and resolve failed and flaky tests

[felix-roehrich]

Lgtm.

[lgoettgens]

gentle bump @fingolfin

[lgoettgens]

The nightly failure is thofma/Hecke.jl#1687.

[lgoettgens]

@fingolfin could we get this merged even though you didn't have time to look at it in detail? We have some following work in the pipeline and I am a bit scared of potential conflicts (as this PR here touches and moves a lot of stuff). You'll of course be given the opportunity to look through everything here before we move things to src/.

[fingolfin]

Looks good to me, thank you!