I away from my computer at the moment. When I get back I will show you my code. The gist is I am making a simple permutation group theory script(i am not talking about simple groups, i mean a simple script). Anyway, what I have so far is trying to conjugate a group with itself, so i can nub out the resulting duplicates and get all the conjugacy classes of the group.
--- Original Message --- From: "Dan Bron" <[email protected]> Sent: July 10, 2014 8:38 PM To: [email protected] Subject: Re: [Jprogramming] Comaring Arrays Good point. We could fix this up by asking an additional question: are the items of A unique? There's a million ways to ask that, but maybe we're in a cutesy mood today: e. *./@:*. ~:@:] Though with the ~:, I'm not sure this would have any performance advantage over sorting. Maybe we should go back to i. : #@:] (e. < *./@:~:@:]) i. That is, look up A in B and tell me whether all elements are unique and that there are no missing elements ((#A) e. A i. B). -Dan Please excuse typos; sent from a phone. > On Jul 10, 2014, at 6:48 AM, Ben Gorte - CITG <[email protected]> wrote: > > Now we should ask Jon what he wants in this case: > > ]A=.3 2$1 1 1 2 1 1 > 1 1 > 1 2 > 1 1 > ]B=.3 2$1 2 1 2 1 1 > 1 2 > 1 2 > 1 1 > > Should the result be: > A *./@:e. B > 1 > or does he prefer: > (/:~A)-:/:~B > 0 > ? > > (I agree the first looks quicker) > > Ben > > _ > _______________________________________ > From: [email protected] > [[email protected]] on behalf of Dan Bron > [[email protected]] > Sent: Thursday, July 10, 2014 12:33 > To: [email protected] > Subject: Re: [Jprogramming] Comaring Arrays > > Sorting might be overkill (and/or a little expensive) for this situation. > > If A and B are the same shape (and they'd better be, or A is definitely not a > permutation of B), then you really only need to know if all the items (rows) > of A are also items (rows) of B. > > So let's just ask that: > > A e. B > 1 1 1 1 > A *./@:e. B > 1 > > Now, if we needed slightly more information (and we're willing to pay for > it), in particular, exactly how A is permuted from B, we could use i. instead > of e. : > > > A i. B > 2 0 1 3 > > And from here, we can figure out exactly how far Jon would have had to go in > his quest to check every possible permutation: > > A A.@:i. B > 12 > A C.@:i. B > +-----+-+ > |2 1 0|3| > +-----+-+ > > Looks like about halfway ( (!#A)%2 ) . Not surprising. > > -Dan > > Please excuse typos; sent from a phone. > >> On Jul 10, 2014, at 4:17 AM, Ben Gorte - CITG <[email protected]> wrote: >> >> B=:4 4$2 3 0 1 3 2 1 0 1 0 3 2 0 0 0 0 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
