I very much look forward to the inclusion of Akos Seress' fast random
algorithms for permutation groups into Gap 3.4, and can certainly wait
a while in order to make sure they are smoothly integrated into the
However, if these algorithms are going to run without the user being
aware then they must provide a certain result when they return a result
at all. If there is some probability of the answer being wrong then
the user must be alerted to this fact, and hopefully also be provided
with the probability of an error. For example, if the group order is
said to be n, then for certain algorithms the order is at least n,
but may be greater than n with a small probability. Such functions
are very very useful when playing around in groups to, say, find a
subgroup of a given order, but in the end we must have a proof.
I expect these considerations have already been well thought out by
the Gap designers, but I just wanted to make my concerns clear.
When I use a function (such as the very useful but undocumented
MakeStabChainRandom in Gap 3.3), I always want to know precisely
to what extent the results are certain.
Sincerely, Leonard Soicher.