Generate Primitive Pythagorean Triples using Euclid's formula.

primitive_pythagorean_triples.py

#!/usr/bin/python
"""
Exercise in generate Primitive Pythagorean Triples using Euclid's formula.
Ref: http://bit.ly/1MOK3kY
"""

import fractions
import math

def pythagorean_triple(s, t):
	"""
	Returns a triple (a, b, c) based on following definition:
	  s > t >= 1, s and t are positive odd integers, with no common factor.
	  a^2 + b^2 = c^2
	  a = st
	  b = (s^2 - t^2) / 2
	  c = (s^2 + t^2) / 2
	"""
	a = s * t
	b = (s**2 - t**2)>>1
	c = (s**2 + t**2)>>1

	return (a, b, c)

def s_t_generator(upper_bound):
	"""
	Generate (s,t) tuples based on the following definition:
	  s > t >= 1, s and t are positive odd integers, with no common factor.

	`upper_bound` sets the max (inclusive) value for s.
	"""
	limit = upper_bound + 1
	for t in xrange(1, limit - 2, 2):
		for s in xrange(t + 2, limit, 2):

			# Check if s & t are coprime
			if fractions.gcd(s, t) != 1:
				continue

			yield (s, t)

def main():
	for s, t in s_t_generator(9):
		a, b, c = pythagorean_triple(s, t)
		print "%d, %d, %d" % (a, b, c)

if __name__ == "__main__":
	main()