Add isomorphism(PermGroup, ::WeylGroup) for missing irreducible types

[TWiedemann]

Adds support for all missing irreducible types (B, C, D, E, F, G) in isomorphism(PermGroup, ::WeylGroup) and also for non-canonical orderings. Reducible types are still missing.

@lgoettgens I don't know whether this should be merged already, but I think the code is mature enough for someone else to have a look.

[TWiedemann]

This is a continuation of #4264, I guess.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.40%. Comparing base (91f076a) to head (c5def11).
Report is 71 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4478      +/-   ##
==========================================
+ Coverage   84.36%   84.40%   +0.03%     
==========================================
  Files         663      672       +9     
  Lines       87805    88708     +903     
==========================================
+ Hits        74077    74873     +796     
- Misses      13728    13835     +107     

Files with missing lines	Coverage Δ
experimental/LieAlgebras/src/WeylGroup.jl	94.73% <100.00%> (+5.60%)	⬆️
experimental/LieAlgebras/test/WeylGroup-test.jl	100.00% <ø> (ø)

... and 76 files with indirect coverage changes

[lgoettgens]

Thanks! I have a few comments, mostly documentation-related. Once they are resolved, I would be happy to merge this PR. If you prefer to wait until reducible types are working, this would be fine for me as well.

[TWiedemann]

Thanks for your comments! I resolved everything. I plan to look into the reducible types soonish, but I see no harm in merging already.

[lgoettgens]

Thanks for the adaptions! Could you please have a look into the two failing CI jobs? Both should have some instructions in the failure log. Once that's done, this is good to go from my POV.

[TWiedemann]

Thanks for the adaptions! Could you please have a look into the two failing CI jobs? Both should have some instructions in the failure log. Once that's done, this is good to go from my POV.

Sure, will do that next week.

[TWiedemann]

I applied JuliaFormatter and bibtool and fixed the bib entry (changed "article" to "Article"). Now it's all fine (except for the nightly test).

[fingolfin]

as a general rule of thumb, use lowercase first letters for variables, and reserver Upper case for types. Main except for me is for single letter variables; but even there I'd recommend sym or S here.

But this is not a blocker for this PR, just a general remark for future reference :-)

[TWiedemann]

Thanks, I will keep that in mind :)

[fingolfin]

I would suggest that we instead install a variant of this line as a method for map_word on WeylGroupElem, and then call map_word here.

Of course this can wait for a future PR!

[TWiedemann]

Sounds good. This would, in particular, remove the potential error source of not converting "i in word(w)" from UInt to Int.