I don't think one can rely on this. It is not guaranteed to work, although in practice you might often see this. Typically, it uses A.Hulpke's method, which is randomised: http://www.math.colostate.edu/~hulpke/paper/permclass.pdf So you are relying on a pseudorandom generator to give you exactly the same sequence--- not good, as you can imagine.
On Jan 26, 10:53 pm, David Joyner <wdjoy...@gmail.com> wrote: > On Tue, Jan 26, 2010 at 8:01 AM, Dima Pasechnik <dimp...@gmail.com> wrote: > > David, > > GAP does not fix an ordering of the conj. classes, or an ordering of > > the irreducibles. They depend upon the way > > the group comes in, and as conj. classes and irreds are often computed > > by randomised procedures, > > it's very hard to predict them. > > (and not fun to deal with issues that somtimes arise due to this...) > > I thought that if you input a group into GAP in exactly the same way > twice (using same generators both times) then you will get the same > listing of conjugacy classes. Is that false? > > > > > > > What is fixed, are these orderings in the character table library. > > (and whenever applicable, they can be matched to the orderings used > > in Atlas of Finite Groups (the big red book...)) > > > Dima > > > On Jan 26, 8:38 pm, David Joyner <wdjoy...@gmail.com> wrote: > >> On Tue, Jan 26, 2010 at 6:27 AM, Alex Ghitza <aghi...@gmail.com> wrote: > >> > On Tue, 26 Jan 2010 06:19:16 -0500, David Joyner <wdjoy...@gmail.com> > >> > wrote: > > >> >> What Dima means is that the ordering returned by the character > >> >> must of course agree with the internal ordering of the conjugacy > >> >> classes. > >> >> I assume (without having looked at your patch) that you are not > >> >> changing the functions at all but only the doctests of the functions? > >> >> Otherwise, you will somehow have to check that your character value > >> >> ordering is "in sync" with the conjugacy class ordering. > > >> > Ah, excellent. All I do is sort *the list of characters*, not the list > >> > of values appearing in each character. (If you think of the character > >> > table as having the characters listed as rows and conjugacy classes > >> > listed as columns, I'm permuting the rows but leaving the columns > >> > intact.) Does this make sense? (I've been staring at a laptop screen > >> > for a bit too long today...) > > >> Mathematically? Yes. > >> To implement in Sage? I think it is it more complicated than that. > > >> > I don't have the time to look into this at this very moment, so the rest > >> > of this is speculation: we might want to give the same treatment to the > >> > function that returns the list of conjugacy classes, to avoid similar > >> > problems. That would mean that we're permuting the columns. Still, > >> > we're doing the same operations across, so the table won't get "out of > >> > sync", it will just be ordered differently. > > >> You want the ordering of the characters to be consistent with the > >> ordering of the conjugacy classes always. For most groups, there is > >> no natural ordering but for some there are. My understanding is that > >> you can't "fix" the ordering in any way you like unless you are at least > >> sure that it preserves the ordering of groups for which a natural > >> ordering exists (eg, the symmetric group). > > >> My suggestion is to leave the ordering the way GAP (and I think > >> also Magma) have fixed them. If you think that should change, for > >> whatever reason, i think more GAP group people at least should > >> be consulted on how to resolve the problem. However, if you just > >> want to sort the output in the doctests (or even have a non-default > >> "sorted" method added to the conj class and char functions, > >> whcih would be a huge amount or work IMHO) then that is > >> a different matter. > > >> > Best, > >> > Alex > > >> > -- > >> > Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne > >> > -- Australia --http://www.ms.unimelb.edu.au/~aghitza/ > > >> > -- > >> > To post to this group, send an email to sage-devel@googlegroups.com > >> > To unsubscribe from this group, send an email to > >> > sage-devel+unsubscr...@googlegroups.com > >> > For more options, visit this group > >> > athttp://groups.google.com/group/sage-devel > >> > URL:http://www.sagemath.org > > > -- > > To post to this group, send an email to sage-devel@googlegroups.com > > To unsubscribe from this group, send an email to > > sage-devel+unsubscr...@googlegroups.com > > For more options, visit this group > > athttp://groups.google.com/group/sage-devel > > URL:http://www.sagemath.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
