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
