Symplectic Maximals

[TristanPfersdorff]

• Add MaximalSubgroupClassRepsSpecialUnitaryGroup
• Modify ClassicalMaximalsGeneric
• Various fixes for classes C2, C5, C6, C7
• Test MaximalSubgroupClassRepsSpecialUnitaryGroup

With this PR, the maximal geometric subgroups of the symplectic groups should be all done.

Checklist for the reviewer

General

• [ ] All functions have unit tests

Functions constructing generators of maximal subgroups

• [ ] The code which computes and then stores the sizes is correct. To do this one confers to the tables referenced by the code. Tests for the group size should use RECOG.TestGroup from the recog package.
• [ ] The test suite checks whether all constructed generators are sensible. That is it tests the generators'
  • [ ] determinants (and if applicable also the spinor norms are correct), and
  • [ ] compatibility with the correct form,
  • [ ] DefaultFieldOfMatrixGroup returns the correct field.

Functions assembling the list of all maximal subgroups of a certain group

• [ ] The code agrees with the tables in section 8.2 of the book "The Maximal Subgroups of the Low-dimensional Finite Classical Groups".

The reviewer doesn't need to compare our results to magma's results. That's the job of the person implementing the code.

[codecov[bot]]

Codecov Report

Merging #89 (56d2048) into main (30aa81a) will increase coverage by 3.04%. The diff coverage is 96.85%.

@@            Coverage Diff             @@
##             main      #89      +/-   ##
==========================================
+ Coverage   93.11%   96.15%   +3.04%     
==========================================
  Files          14       14              
  Lines        2686     2734      +48     
==========================================
+ Hits         2501     2629     +128     
+ Misses        185      105      -80     

Impacted Files	Coverage Δ
gap/ClassicalMaximals.gi	96.81% <95.91%> (+13.53%)	:arrow_up:
gap/ClassicalMaximals.gd	100.00% <100.00%> (ø)
gap/ImprimitiveMatrixGroups.gi	98.26% <100.00%> (+0.06%)	:arrow_up:
gap/ReducibleMatrixGroups.gi	98.07% <100.00%> (+0.05%)	:arrow_up:
gap/SemilinearMatrixGroups.gi	95.17% <100.00%> (-0.07%)	:arrow_down:
gap/SubfieldMatrixGroups.gi	97.82% <100.00%> (+0.03%)	:arrow_up:
gap/TensorProductMatrixGroups.gi	98.09% <100.00%> (-0.02%)	:arrow_down:

[TristanPfersdorff]

Alright, changes are implemented. While I was at it, I fixed all instances of silly x := Concatenation(x, ...) syntax that I could conceivably find with a keen eye and Ctrl + f (about 50 of them, wtf were we doing?!) and replaced it by Append(x, ...). I also added the safer checks to disallow stuff like MaximalSubgroupClassRepsSymplecticGroup(n, q, [1,2,4], 5) to some other functions since those checks are done in a few more functions inside ClassicalMaximals.gi.

[TristanPfersdorff]

As @maxhauck pointed out to me, not all of the constructed groups had been conjugated to the standard GAP forms after construction, which would cause issues if GAP ever changed its standard form. I hope to have taken care of that in the last commit, though some of the construction functions do not explicitly set the form before conjugating. Presumably, this is because we do not know the form in those cases. That issue should be largely fixed by #88 though.