Re: [Jchat] pl=: ^ ^.

[Raul Miller]

   (^^.)/"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
<c...@jsoftware.com> 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
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