Python mathy functions, in no particular order

funcs.py

import math
import operator

# primality test
def is_prime(i):
	if i <= 1: return False
	if i <= 3: return True
	if i%3 == 0 or i%2 == 0: return False
	return sum((1 for y in xrange(5, int(i**0.5)+1, 6) if i%y == 0 or i%(y+2) == 0)) == 0

# traditional generator
# generate primes up to i
def prime_gen(i):
	num = 2
	while num < i:
		yield num
		num += 1
		while not is_prime(num):
			num += 1
			
# like itertools.count but only for primes
def infinite_prime_gen(num=2):
	while True:
		yield num
		num += 1
		while not is_prime(num):
			num += 1
	
# faster prime "generator", returns list		
prime_gen_memo_arr = [2]
def prime_gen_memo(i):
	while prime_gen_memo_arr[-1] < i:
		num = prime_gen_memo_arr[-1]+1
		while not is_prime(num):
			num += 1
		prime_gen_memo_arr.append(num)
		
	return prime_gen_memo_arr

# returns a list of factors, including 1 and n, non distinct
def get_factors(n):    
    return list(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5)+1) if n % i == 0)))
    
def prod(factors):
    return reduce(operator.mul, factors, 1)
    
factorial = lambda num : prod([i for i in range(1,num+1)])
reverse_digits = lambda n: int(''.join(list([i for i in str(n)][::-1])))
is_palindrome = lambda n: str(n) == str(n)[::-1]


# babylonian/hero's method
# for positive i
# alternative to gmpy.is_square(i)
def is_square(i):
	x = i//2
	last = x
	while x*x != i:
		x = (x + (i//x))//2
		if last == x: 
			return False
		last = x
		
	return True
 


# long division for an arbitrary amount of precision
def long_divide(n, d, num_digits):
	dividend = n
	divisor = d
	count = 0
	while dividend:
		quotient = dividend // divisor
		yield quotient
		dividend = dividend % divisor * 10
		if count >= num_digits:
			return
			
		count += 1


# Euclidean Alg for finding Greatest Common Divisor
# http://codereview.stackexchange.com/questions/66450/simplify-a-fraction
# (dev in progress)
def gcd(a,b):
	q = 0
	r = 1
	while r != 0:
		q, r = a//b, a%b
		a, b = b, r
		
	return q