Script to enumerate rational numbers

rationals.py

from itertools import izip, imap
from fractions import Fraction, gcd

def main():
	for x in rationals():
		print x

def rationals():
	yield Fraction()
	
	for x in combine(imap(const, naturals())):
		yield x
		yield -x

def naturals():
	n = 1
	while True:
		yield n
		n += 1

def combine(streams):
	tmp = []
	
	while True:
		tmp.append(next(streams))
		for stream in tmp:
			yield next(stream)

def const(k):
	yield Fraction(k, 1)
	
	i = 2
	while True:
		if gcd(k, i) == 1:
			yield Fraction(k, i)
		
		i += 1

if __name__ == '__main__':
	main()