As far as I know, once you have a backtracking algorithm for equivalence/stabilizer, then you have also an algorithm for canonical representative.
But GAP does not provides such functionalities ... However, for the special action "OnSets", there is a function "SmallestImageSet" available from the GRAPE package that does the job. Mathieu On Wed, Jan 12, 2011 at 08:04:13PM +0800, Gordon Royle wrote: >> Dear Gapsters.. >> >> Consider the following generic problem... given a permutation group >> G acting on a set X, I have a (potentially) large collection of >> k-subsets of X and wish to keep only one representative of each >> G-orbit on k-subsets. >> >> GAP can tell me if two k-subsets are equivalent under G using >> RepresentativeAction and so in principle, I can build up a list >> by starting with the first one, then testing to see if the second >> is equivalent to the first and keeping it only if it is not, and >> so on. This works, but each new one requires one more test than >> the previous one and things rapidly become unmanageable. >> >> For winnowing large lists of graphs, the standard procedure is >> not to test them pairwise but rather to compute a "canonically >> labelled" version of each input graph and then simply throw out >> the duplicates... >> >> Is there any way of computing a "canonically labelled" version >> of each k-subset? Or is this well known to be more difficult >> than computing equivalence? >> >> Thanks >> >> Gordon >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
