I wrote:
> that J allows us to express LCM elegantly! Compare
> >./&.(_&q:) to the formulas given on the Wikipedia page.
> By the way, GCD (+.) is analogously <./&.(_&q:)
> (<. in place of >.).
Let's play with f/&.(_&q:) some more. First, let's make it a reusable
adverb:
ruf =: / ( &.(_&q:) ) NB. Reduce Under Factorization
N =: @:(>:@:i.) NB. First N positive ints
rufN =: ruf N
Now let's verify our observations:
>. rufN 20x NB. LCM
232792560
<. rufN 20x NB. GCD
1
Now, let's expand our minds:
+ rufN 20x NB. Guess!
2432902008176640000
! 20x NB. Hint....
2432902008176640000
That is, just as >. ruf is *. and <. ruf is +. , so + ruf is * ! It
bears repeating:
> A ... expression like *./ refreshes my appreciation of J's
> design; it's close to * / which is the "obvious" common
> multiple of the vector.
Are there any other f for which f ruf or f rufN are interesting?
-Dan
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