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
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