> Yes, but different ways give different insights. See: > http://www.jsoftware.com/jwiki/Essays/Pascal's_Triangle
For example, the n-th set of binomial coefficients are seen as the polynomial coefficients of the function (x+1)^n : (>: ^ 9:) t. i.10 1 9 36 84 126 126 84 36 9 1 (i.10)!9 1 9 36 84 126 126 84 36 9 1 Therefore the (2*n)-th set of binomial coefficients are the polynomial coefficients of (x+1)^(2*n), and the latter obtain efficiently by repeated polynomial squaring: polytimes=: +//.@(*/) ((i.65)!64x) -: polytimes~^:6 ] 1 1x 1 10 timer '(i.65)!64x' 0.00483466 10 timer 'polytimes~^:6 ] 1 1x' 0.00187677 ----- Original Message ----- From: Roger Hui <[email protected]> Date: Monday, February 15, 2010 17:35 Subject: Re: [Jprogramming] Constant functions To: Programming forum <[email protected]> > Yes, but different ways give different insights. See: > http://www.jsoftware.com/jwiki/Essays/Pascal's_Triangle > > As an exercise, see how many ways you can come > up with to generate the identity matrix. > http://www.jsoftware.com/jwiki/Essays/Identity_Matrix > > > > ----- Original Message ----- > From: Alex Gian <[email protected]> > Date: Monday, February 15, 2010 16:26 > Subject: Re: [Jprogramming] Constant functions > To: Programming forum <[email protected]> > > > On Mon, 2010-02-15 at 10:24 +0000, Ian Clark wrote: > > > > > One can learn a lot of tacit J just by analysing that > > example: bc=: > > > < 0&(, + ,~) 1: > > > > Can't pretend I understand much of it, but I intend to take it > > apart in > > tonight's "Learning J" session! Great to see all this stuff. > > > > Now forgive me if I'm missing something in all this (as a > newb) but > > wouldn't a simpler way of generating binomial coefficients > just be: > > > > !/~i.10 > > > > 1 1 1 1 1 1 1 1 1 1 > > 0 1 2 3 4 5 6 7 8 9 > > 0 0 1 3 6 10 15 21 28 36 > > 0 0 0 1 4 10 20 35 56 84 > > 0 0 0 0 1 5 15 35 70 126 > > 0 0 0 0 0 1 6 21 56 126 > > 0 0 0 0 0 0 1 7 28 84 > > 0 0 0 0 0 0 0 1 8 36 > > 0 0 0 0 0 0 0 0 1 9 > > 0 0 0 0 0 0 0 0 0 1 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
