Symplectic C6

[maxhauck]

Add functions constructing C6 subgroups of Sp(n, q) and a corresponding generic function in the ClassicalMaximals.gi

Note: Lines not covered by the tests in ExtraspecialNormalizerMatrixGroups.gi are exclusively due to problems with RECOG, but I have checked these manually; the changes in ClassicalMaximals.gi will be tested once the symplectic main function is complete and we implement its tests.

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]

Codecov Report

Merging #74 (168afa9) into main (be3b551) will decrease coverage by 1.38%.
The diff coverage is 62.88%.

@@            Coverage Diff             @@
##             main      #74      +/-   ##
==========================================
- Coverage   93.64%   92.26%   -1.39%     
==========================================
  Files          14       14              
  Lines        2141     2223      +82     
==========================================
+ Hits         2005     2051      +46     
- Misses        136      172      +36     

Impacted Files	Coverage Δ
gap/ClassicalMaximals.gi	89.96% <6.06%> (-5.49%)	⬇️
gap/ExtraspecialNormalizerMatrixGroups.gi	94.75% <92.06%> (-0.85%)	⬇️
gap/ClassicalMaximals.gd	100.00% <100.00%> (ø)

[fingolfin]

Is the error in recog you are alluding to the same as gap-packages/recog#295 ?

[fingolfin]

What do you mean here? Are you saying: "The Magma code does this, so we use this as justification for doing the same"? (that doesn't seem like a great argument, by the way ;-).

Or are you saying: "compared to the Magma code, we are better/different/whatever, and hence it suffices to do XYZ?

[maxhauck]

The former :D ... well, sadly the relevant paper does not really say much (or rather anything) concerning this particular case so I trusted the Magma code on this one - however, doing this did pass some sanity checks: (1) the group sizes do come out the right way and (2) this case is exactly where an exception occurs in the structure of these C6 subgroups according to the tables in [BHR13] (namely, they are a bit smaller), so it makes sense that this should suffice.

One could of course check "theoretically" that these generators are enough, but I am not sure if this maybe transcends our current mathematical horizon a bit ;)

[maxhauck]

Is the error in recog you are alluding to the same as gap-packages/recog#295 ?

Ummmm, I honestly don't know, but could be ... - the tests just produced a ton of RECOG errors, which we currently handle by simply removing the error-causing tests until there are no errors anymore :D ... sadly, this means that, sometimes, not many tests are left :/

[maxhauck]

I guess I can merge this, @fingolfin?

[fingolfin]

• the tests just produced a ton of RECOG errors, which we currently handle by simply removing the error-causing tests until there are no errors anymore

That's bad! Please at least turn those into bug reports for recog. Else they won't (can't!!) be fixed

[fingolfin]

There is a conflict now, which looks easy to resolve (basically two PRs were appending to the end of gap/ClassicalMaximals.gi). But I wonder if perhaps it would make sense to move the various cases C1, C3, etc. into separate source files, and only leave truly common stuff in gap/ClassicalMaximals.gi?

[fingolfin]

I've manually resolved the conflict (via the web interface -- nice feature!) Assuming tests pass, we can merge it next.