Implement Orthogonal C1 symplectic type

[maxhauck]

Add the following functions:

• [x] OmegaStabilizerOfNonSingularVector in ReducibleMatrixGroups.gi
• [x] SolveQuadraticEquation, FindGamma and FancySpinorNorm in Utils.gi
• [x] QuadraticForm in Forms.gi

Modify the following functions:

• [x] ReflectionMatrix in Utils.gi
• [x] ConjugateToSesquilinearForm and ConjugateToStandardForm in Forms.gi

Tests have now been added as well, lines not covered are almost exclusively error messages.

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.

[maxhauck]

@fingolfin Two things:

1. After being a bit puzzled for a while, we discovered that GAP uses different standard orthogonal forms for SO(epsilon, d, q) and Omega(epsilon, d, q) ... - we therefore decided to conjugate the constructed subgroup so that it is inside Omega(epsilon, d, q) and consequently not inside SO(epsilon, d, q), which should be what we want, right?

2. We added "Constructing maximal subgroups of orthogonal subgroups" to the bibliography by mimicking what you did as best as we could, but we could not for the life of us figure out what to put as MRNUMBER and MRREVIEWER in ClassicalMaximals.bib ... - so what to put there?

[codecov[bot]]

Codecov Report

Merging #85 (087e5ad) into main (927d284) will decrease coverage by 0.46%. The diff coverage is 90.10%.

@@            Coverage Diff             @@
##             main      #85      +/-   ##
==========================================
- Coverage   93.56%   93.09%   -0.47%     
==========================================
  Files          14       14              
  Lines        2485     2665     +180     
==========================================
+ Hits         2325     2481     +156     
- Misses        160      184      +24     

Impacted Files	Coverage Δ
gap/Forms.gi	89.67% <88.37%> (+0.54%)	:arrow_up:
gap/Utils.gi	92.93% <89.55%> (-1.10%)	:arrow_down:
gap/ReducibleMatrixGroups.gi	98.01% <91.42%> (-1.39%)	:arrow_down:
gap/Forms.gd	100.00% <100.00%> (ø)
gap/SubfieldMatrixGroups.gi	97.79% <100.00%> (ø)
gap/ClassicalMaximals.gi	83.27% <0.00%> (-1.40%)	:arrow_down:
gap/TensorInducedMatrixGroups.gi	98.38% <0.00%> (+0.27%)	:arrow_up:

[fingolfin]

Regarding Omega: this is known, see https://github.com/gap-system/gap/issues/500. Since it's been like this "forever", we can't simply change it without risking to break existing code out there. The solution we came up with is that in GAP 4.12, various constructors will allow the user to optionally specify a form.