Start of almost simple in defining characteristic

[danielrademacher]

Start of a file for the almost simple groups in defining characteristic (chapter 5 in the book by colva). In this PR we are also adding two functions to show how these groups can be generated in GAP.

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 #41 (e9f832a) into main (3c6b318) will decrease coverage by 12.29%.
The diff coverage is 7.69%.

@@             Coverage Diff             @@
##             main      #41       +/-   ##
===========================================
- Coverage   81.95%   69.65%   -12.30%     
===========================================
  Files          14       15        +1     
  Lines        2028     2432      +404     
===========================================
+ Hits         1662     1694       +32     
- Misses        366      738      +372     

Impacted Files	Coverage Δ
gap/AlmostSimpleDefiningCharacteristic.gi	7.69% <7.69%> (ø)
gap/ClassicalMaximals.gd	100.00% <0.00%> (ø)

[ssiccha]

The ValueOption abomination should be replaced by adding a variadic argument. This whole option business accesses and modifies a global state, from the docs 8 Options Stack: "GAP supports a global options system".

[fingolfin]

Why does it even have to be variadic? Can't this function simply have two arguments, the second being general,l and people are free to pass in false for it?

BTW, while I agree options are problematic, they are often used to substitute for a feature GAP sadly is lacking: keyword arguments. In GAP you can end up with function calls like func(true, true, false) that can be rather confusing, compared to something like func(general:=true, checks:=true, format_drive:=false)

[fingolfin]

I guess what I tried to say with my last remark is: dang, we really should have keyword arguments in GAP ;-). I once started working on that but quickly decided to put it aside, because while I think implementing it would be fun, I really should be spending my time on other things sigh. But if anybody is ever interested in diving into the GAP kernel and implementing some language extensions, I'd be happy to teach you the ropes.

[ssiccha]

I guess what I tried to say with my last remark is: dang, we really should have keyword arguments in GAP ;-).

That would be a dream come true. :D

[ssiccha]

I had the impression that, at least in the magma version, these functions share a lot of code. It may make sense to have one very abstract function, which then delegates to more specialized functions. E.g. I think many of the magma functions first build a tensor module "V tensor V", then compute the constituents, and then looks for a constituent with a given dimension. The only thing that changes between this part of these functions is the dimension we're looking for.

[fingolfin]

Sorry for this nitpick, but:

That's a rather cryptic name... I have no idea what this function is supposed to compute. Maybe at least add a comment, perhaps we can also find a slightly more helpful name? (Also, global variables/functions in GAP normally start with an uppercase letter?)

[ssiccha]

Yepp, the current name is taken from magma. The abstract function could have a name like ConstructDefiningCharacteristicRepresentationOfAlmostSimpleGroup, that's what's happening here. The function l3qdim6 constructs one of these embeddings, namely the representation of an SL_3(q) on the symmetric-square module of dimension 6. There's a lot of these constructions which are extremely similar, which is why I'm suggesting something like ConstructDefiningCharacteristicRepresentationOfAlmostSimpleGroup or maybe ConstructDefiningCharacteristicRepresentationOfAlmostSimpleGroupOnSymmetricPowerModule

[ssiccha]

Did you copy, paste that? Could we instead extend the function in recog such that you can also use it here?

[fingolfin]

Any news on this? Would it help / make sense to meet to discuss this?

[danielrademacher]

Anna and I haven't had time to continue working on the project until now. Hopefully we'll get back to it during the semester break.