Pythagorean Tuples, by Paul Franklin

|| #4
|| I'm generating all tuples (a,b,c) that match a^2+b^2 = c^2,
|| sorted by c, where a,b,c>=0, b>=a

|| Several optimizations are possible...
||   We know b != a, and that a,b>1 (maybe even a,b>2).
||   We could keep track of a^2, b^2, c^2, to avoid constantly
||     evaluating that.

pyth_merge ((xa,xb):xt) ((ya,yb):yt) = (xa,xb):(pyth_merge xt ((ya,yb):yt)), (xa*xa+xb*xb)<(ya*ya+yb*yb)
				     = (ya,yb):(pyth_merge yt ((xa,xb):xt)), otherwise

|| pyth_tuples must spit out the first one
|| so pyth_merge will start spitting out stuff

pyth_tuples a = (a,a):(pyth_merge (pyth_tuples (a+1)) [(a,n) | n <- [(a+1)..]])

pyth_filt ((a,b):abt) c = (a,b,c):(pyth_filt abt c), ((a*a)+(b*b))=(c*c)
			= pyth_filt ((a,b):abt) (c+1), ((a*a)+(b*b))>(c*c)
			= pyth_filt abt c, otherwise

pyth = pyth_filt (pyth_tuples 1) 1