Orthogonal C1 NonDegenerate

[TristanPfersdorff]

Adds the construction for the stabilizer of the canonical non-degenerate-subspace according to Lemma 4.3 in [HR10] via the function OmegaStabilizerOfNonDegenerateSubspace along with some error handling tests for StandardGeneratorsOfOrthogonalGroup and StandardOrthogonalForm as well as a minor addition to StandardGeneratorsOfOrthogonalGroup, see my comment below for details.

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.
• [ ] 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 #100 (5244aec) into main (bad7060) will increase coverage by 0.30%. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #100      +/-   ##
==========================================
+ Coverage   95.24%   95.55%   +0.30%     
==========================================
  Files          14       14              
  Lines        3072     3194     +122     
==========================================
+ Hits         2926     3052     +126     
+ Misses        146      142       -4     

Impacted Files	Coverage Δ
gap/ReducibleMatrixGroups.gi	98.48% <100.00%> (+0.44%)	:arrow_up:
gap/Utils.gi	93.26% <100.00%> (+0.05%)	:arrow_up:
gap/Forms.gi	87.88% <0.00%> (+1.38%)	:arrow_up:

[TristanPfersdorff]

I had to add the special case d = 1 to StandardGeneratorsOfOrthogonalGroup, since otherwise a few statements involving d - 2 cause errors. It feels a little hacky but is mathematically justified. The field generatorsOfOmega could also be an empty list in that case (GAP even does this by default, calling GeneratorsOfGroup on a trivial group returns an empty list), but this would cause some issues in OmegaStabilizerOfNonDegenerateSubspace and probably also future construction functions, so my current solution of returning just the identity matrix as a generator seems like a good choice, but this is subject to review. In other news, one of the tests causes a weird Error, !!!, similar (but not necessarily related) to this RECOG-issue.