Rank is different. FYI,
-- Raul On Fri, Nov 19, 2021 at 2:33 AM 'Nollaig MacKenzie' via Chat <[email protected]> wrote: > > Hmmph. *&.^. is equivalent. Commutativity etc are obvious. Oh well. > > > On Nov 18, 2021, at 11:36, Raul Miller <[email protected]> wrote: > > > > (^^.)/"1((i.6 4) A.i.4){2 3 4 5 > > 5.46861 5.46861 5.46861 5.46861 > > 5.46861 5.46861 5.46861 5.46861 > > 5.46861 5.46861 5.46861 5.46861 > > 5.46861 5.46861 5.46861 5.46861 > > 5.46861 5.46861 5.46861 5.46861 > > 5.46861 5.46861 5.46861 5.46861 > > > > is kind of fun > > > > And so is the symmetry with reciprocal pairs. > > > > Thanks, > > > > -- > > Raul > > > > On Thu, Nov 18, 2021 at 2:25 PM 'Nollaig MacKenzie' via Chat > > <[email protected]> wrote: > >> > >> Some years ago on some group somewhere someone raised thequestion "Is > >> there another simple function which, like* and +, is commutative and > >> associative?". "Simple" was,as I recall, left to intuition. > >> The nice answer was: F(x,y) = x^ln(y) > >> It's easy to see that F satisfies the conditions: Take thelogarithm of > >> each side of the putative identities. > >> F goes nicely into J: pl=: ^ ^. > >> KEI used to encourage experimenting at the terminal. So > >> V=: 2 3 4 5 > >> 4 4$pl/"1 ((i.16) A. i.4){V > >> > >> 5.46861 5.46861 5.46861 5.46861 > >> > >> 5.46861 5.46861 5.46861 5.46861 > >> > >> 5.46861 5.46861 5.46861 5.46861 > >> > >> 5.46861 5.46861 5.46861 5.46861 > >> Idly experimenting, I tried: > >> pl/%V > >> > >> 5.46861 > >> That surprised me. It shouldn't have; ^. % x is just - ^. x > >> I don't know of any application for pl. But it's neat. > >> Cheers, Nollaig > >> > >> Sent using Hushmail > >> ---------------------------------------------------------------------- > >> 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
