On 2013-04-11, Jason B. Hill <ja...@jasonbhill.com> wrote: > --e89a8f64674d73946104da0e3a61 > Content-Type: text/plain; charset=ISO-8859-1 > >> no, no, that's not what you want to do, certainly. A much more efficient >> way >> is to compute a strong generating set w.r.t. a "canonical" minimal base. >> > data into a canonical form of a permutation group. > > There is no "canonical" minimal base, unless one specifies the group action > to such an extent that most permutation group representations are excluded. > > Seriously, if you need some sort of canonical form for permutation groups, > you must restrict to primitive actions. In the real world, this just isn't > a sensible approach. Each abstract group has infinitely many permutation > group representations. ONLY the primitive representations are currently > classified in any detail below a given degree, and as such those are the > only canonical representations that would even be available.
perhaps a more sensible idea for a canonical form would be via centralizer algebras. Centralizer algebras are easy to construct, and checking that two of them are isomorphic is indeed a kind of coloured graph isomorphism, except that the size of objects has a much nicer dependence on the group order --- if we talk about transitive permutation groups, at least. In most cases you will have a suborbit on which the point stabilizer acts faithfully, so this provides you some sort of reduction. The full permutation group isomorphism test is still not there, but this looks like a good way to limit the possible choices. Dima > > Jaosn > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
