Add minimal_normal_subgroups and maximal_normal_subgroups functions

[RuchitJagodara]

• Added the function
  This patch implements a minimal_normal_subgroups function in PermutationGroup_generic class.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

NA

[tscrim]

The result should be converted back into Sage (permutation) (sub)groups.

Also, I don't see why $S_8$ should be a test (which are hidden in the final html doc) rather than a normal example.

[RuchitJagodara]

I have done some necessary changes. But I just found that these methods can be implemented for all groups as the functions MaximalNormalSubgroups and MinimalNormalSubgroups works for all groups in gap, so I am considering implementing this in Sage for all groups, but I am having difficulty in finding the appropriate location to define these functions. Can you help me with this?

[tscrim]

You can add it to the Groups() category, but that wouldn't work because not all groups in Sage have a corresponding GAP version (see, e.g., right-angled Artin groups). However, there is a base class for all GAP groups, so you can implement it there.

[RuchitJagodara]

I have relocated the function, but I believe the implementation is suboptimal. This is because it will consume a significant amount of time, as it needs to generate the generators first and then convert them into a subgroup (as demonstrated below). I attempted to explore alternative options but was unsuccessful. Do you have any suggestions for the fix for this?

sage/src/sage/groups/libgap_wrapper.pyx

Line 359 in 297e8b2

return [self.subgroup(gap_subgroup.GeneratorsOfGroup()) for gap_subgroup in self.gap().MinimalNormalSubgroups()]

Also, were you referring to this particular Class? Because now for permutation groups it is giving an AttributeError (seems like permutationgroups are not derived from this class).

[tscrim]

Within ParentLibGAP, there is the _subgroup_constructor() method that you should use since you already have the GAP group (and always takes a GAP group object from doing a grep search).

[RuchitJagodara]

I have implemented the modifications; however, I remain uncertain about the location of these functions. I am unable to invoke these functions when I have a permutation group(It is giving me AttributeError). Because this class is never inherited in the PermutationGroup class. So what should I do ? Because I am not sure whether inheriting that function in PermutationGroup class will be good or not.

[tscrim]

Something that is annoying is that permutation groups don't seem to use libgap. I think you need to have your previous implement in permgroup. Then that should cover the most number of cases I think...

[tscrim]

Please also squash and give at least a little bit better commit messages for the first two. These automated ones from github are not good (I want to fire that "feature" into the sun).

[RuchitJagodara]

Done! I have applied all the changes that you suggested. Thank you for your help, @tscrim throughout :) . I learned a lot while working on this, and I won't make these types of mistakes again.

[tscrim]

No problem. Thank you for the changes. This is just dealing with some trickier parts of Sage with how things are implemented because of the interfaces.

I am cc-ing @dimpase in case he has some comments.

[dimpase]

@fchapoton did some work on removing pexpect GAP and replacing it with libgap just last week.

Maybe it should be taken into account here

[tscrim]

Good point. I rebased this off the latest develop, which should have #36889 included. Since there are no merge conflicts and @RuchitJagodara wrote the code with future-proofing in mind, there shouldn’t be any issues (which will be reflected in the tests all passing). I also don’t see any way to make additional improvements at this point either.

[github-actions]

Documentation preview for this PR (built with commit fa26be9; changes) is ready! 🎉