x gcd y is <./&.(_&q:) x,y
x lcm y is >./&.(_&q:) x,y

lcm % gcd is (>.-<.)/&.(_&q:)

lcm * gcd is (>.+<.)/&.(_&q:) , which equals +/&.(_&q:) 
which is just *



----- Original Message -----
From: Oleg Kobchenko <[email protected]>
Date: Tuesday, February 3, 2009 10:32
Subject: Re: [Jprogramming] Examples of dyadic forks
To: Programming forum <[email protected]>

> > From: John Randall <[email protected]>
> > 
> > Thanks to all, especially Roger, for the dyadic fork examples.
> > 
> > I regard the tautologies as a bit meta, but I do like >. - 
> <. .  I had a
> > more complicated example along the same lines.
> > 
> > Before posing the question, I followed Oleg's advice in that I 
> eyeballed> the dyads in J Phrases: almost all use [ ] @ @: or 
> constant functions.
> 
> Also
> 
>   GCD * LCM  is  (*. * +.)  tautology  *
> 
> 
> I don't know what LCM % GCD is, but it is always whole
> and has some pattern
> 
>    load'viewmat'
>    viewmat    (*. % +.)"0/~ 2+i.100
>    viewmat |  (*. % +.)"0/~ 2+i:50
>    viewmat |%:(*. % +.)"0/~ 2+i.100
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