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 at > http://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
