..testcode::

import collections

import math

import operator

import random

def take(n, iterable):

"Return first n items of the iterable as a list"

return list(islice(iterable, n))

data[2] = 1

return iter_index(data, 1) if n > 2 else iter([])

def factor(n):

"Prime factors of n."

# factor(97) --> 97

# factor(98) --> 2 7 7

# factor(99) --> 3 3 11

for prime in sieve(n+1):

while True:

quotient, remainder = divmod(n, prime)

if remainder:

break

yield prime

n = quotient

if n == 1:

return

def flatten(list_of_lists):

"Flatten one level of nesting"

return chain.from_iterable(list_of_lists)

Now, we test all of the itertool recipes

>>>import operator

>>>import collections

>>>import math

>>>import random

>>>take(10, count())

>>>set(sieve(10_000)).isdisjoint(carmichael)

list(factor(0))

[]

list(factor(1))

[]

list(factor(2))

[2]

list(factor(3))

[3]

list(factor(4))

[2, 2]

list(factor(5))

[5]

list(factor(6))

[2, 3]

list(factor(7))

[7]

list(factor(8))

[2, 2, 2]

list(factor(9))

[3, 3]

list(factor(10))

[2, 5]

all(math.prod(factor(n)) == n for n in range(1, 1000))

True

all(set(factor(n)) <= set(sieve(n+1)) for n in range(1, 1000))

True

all(list(factor(n)) == sorted(factor(n)) for n in range(1, 1000))

True

>>>list(flatten([('a','b'), (), ('c','d','e'), ('f',), ('g','h','i')]))