For any such computation you need to check it on non-integer exponents. Integer exponents are no problem at all: x^n ←→ */n$x or */(-n)$%x.
On Tue, Aug 5, 2014 at 8:08 AM, Dan Bron <[email protected]> wrote: > I wrote: > > Jon Hough's suggestion looks very promising: > > > > x^y = (1 +(x-1))^y > > e^pi = (1+(e-1))^pi = 1+ pi*e + pi*(pi - 1)*e*e/2! +... > > http://en.wikipedia.org/wiki/Binomial_series > > Ok, here's a whack at that: > > binser =: (( ( (#@:] # {.@:[) ; (-~{:)~ ; >:@:]) )&> <\@:i.)~ > <@, > > ('x^k';('y-i.k');'k!') , 5 binser 7 4 > +---------+---------+---------+ > |x^k |y-i.k |k! | > +---------+---------+---------+ > |7 |4 |1 | > +---------+---------+---------+ > |7 7 |4 3 |1 2 | > +---------+---------+---------+ > |7 7 7 |4 3 2 |1 2 3 | > +---------+---------+---------+ > |7 7 7 7 |4 3 2 1 |1 2 3 4 | > +---------+---------+---------+ > |7 7 7 7 7|4 3 2 1 0|1 2 3 4 5| > +---------+---------+---------+ > > 1 + +/ *`%/"1 */&> 5 binser 7 4 > 4096 > > Note the 1 + ... part would not be required if <\ included the empty > prefix (which is really neat if you think about it). Unfortunately, while > this seems to work ok for 7^4, it breaks on 4^7, 7^4.5, and basically > everything else. But I think I've played with this enough for the moment. > > -Dan > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
