map_word and parabolic_subgroup for Weyl groups

[TWiedemann]

Adds parabolic_subgroup as discussed in #4483. This relies on the new map_word. I also added parabolic_subgroup_with_projection (maybe the name is not good) which, in addition, returns the projection homomorphism from the large Weyl group to the parabolic subgroup.

I set this to draft because:

1. Someone will have to tell me where precisely to put the exports. I assume they go to experimental/LieAlgebras/src/exports.jl. For the moment I put them there at the end of file (where I will sort them alphabetically once this is clarified).
2. Examples/jldoctests for parabolic_subgroup(_with_projection) are still missing.

[TWiedemann]

In my function map_word(::WeylGroupElem, ...), I had to call map_word(::Vector{Int}, ...) with Oscar.map_word while map_word(::Vector{Int}, ...) worked fine on the REPL. Not sure what is going on there. Probably related to the doctest failure:

WARNING: using LieAlgebras.map_word in module Oscar conflicts with an existing identifier.
[...]
ERROR: MethodError: no method matching map_word(::WeylGroupElem, ::Vector{Int64})

[thofma]

You need to add map_word here: https://github.com/TWiedemann/Oscar.jl/blob/tw/weyl_parabolics/experimental/LieAlgebras/src/LieAlgebras.jl#L72

[TWiedemann]

@thofma @fingolfin @lgoettgens Thanks for the help and suggestions! I fixed everything.

One non-nightly test fails: Am I not allowed to spread a string over several lines with "", as in WeylGroup.jl:398?

        @req is_zero_entry(cm, i, j) begin
          "Input vector does not describe a factor of the Weyl group, \
          so there is no projection homomorphism"
        end

This was apparently introduced in Julia 1.7, which might be the problem.

[lgoettgens]

Could you please also use map_word in the isomorphism functions in the same file (cf. #4478 (comment))? This would then provide as another indirect test of the newly added function

[codecov]

Codecov Report

Attention: Patch coverage is 93.54839% with 2 lines in your changes missing coverage. Please review.

Project coverage is 84.42%. Comparing base (d5e963e) to head (834868a).
Report is 19 commits behind head on master.

Files with missing lines	Patch %	Lines
experimental/LieAlgebras/src/WeylGroup.jl	93.54%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4519      +/-   ##
==========================================
+ Coverage   84.16%   84.42%   +0.26%     
==========================================
  Files         672      672              
  Lines       88768    89185     +417     
==========================================
+ Hits        74715    75298     +583     
+ Misses      14053    13887     -166     

Files with missing lines	Coverage Δ
experimental/LieAlgebras/src/LieAlgebras.jl	100.00% <ø> (ø)
experimental/LieAlgebras/test/WeylGroup-test.jl	100.00% <ø> (ø)
src/Groups/GAPGroups.jl	94.11% <ø> (+0.32%)	⬆️
experimental/LieAlgebras/src/WeylGroup.jl	94.25% <93.54%> (-0.49%)	⬇️

... and 64 files with indirect coverage changes

[TWiedemann]

Could you please also use map_word in the isomorphism functions in the same file (cf. #4478 (comment))? This would then provide as another indirect test of the newly added function

Done. Also added links to the new map_word in the docs of the old map_word functions.

I have removed the draft status.

[lgoettgens]

Looks good, thanks! @fingolfin could you please have a look again as well?

[fingolfin]

Looks good to me in principle, but I have a few small suggestions.

[TWiedemann]

@fingolfin Thanks! I will implement the remaining suggestions tomorrow.

[TWiedemann]

Fixed the last two issues (check_factor -> check and added documentation for check).