[GAP Forum] Remarks on SmallGeneratingSet

[Hulpke,Alexander]

Dear Mathieu, Dear Forum,

I’m unsure whether the Forum is the best place for technical details. I have created an issue on github (https://github.com/gap-system/gap/issues/4636) where I will reply on the technical aspects.

Let me just, as author of this code, make a few general remarks:

- This is a method for generic permutation groups, but there is a special method for solvable groups (that guarantees minimal size). One thus should assume the group is not solvable

- The main use of the operation is to quickly reduce generating sets in size (say down from 30 to 5), but the cost for being off the optimal by 1 or 2, or to perform badly in untypical cases, is small.

- This is utility code that is needed for speed, but will never lead to a publication. It thus did not get written with an overarching strategy, but got incrementally adapted over 20 years to avoid particular shortcomings in examples I created. If you excounter examples in which the method performs badly, please let me know.

- A consequence of these incremental changes is that it is much easier and quicker to not refactor the overall decision process each time. Maybe it is time to do now — I will have a look at the points you mentioned. Thank you for taking the time to do so.

Best,

  Alexander Hulpke