User manual for module 'factorial'
==================================

The n-th factorial is defined mathematically as:
    n! = (n)(n-1)(n-2)...(3)(2)(1)
(This definition really only makes sense if n is a positive whole number.)  The factorial is useful, for instance, in combinatorics: n! tells you the number of permutations (unique orderings) of a set of n different objects.

This module provides a single function, factorial(n), which computes the n-th factorial.  The function takes exactly one parameter, which must be a positive number (zero is okay).

To use the function, first import it:
>>> from factorialtest import factorial

Now we can calculate, say, 6! = (6)(5)(4)(3)(2)(1):
>>> factorial(6)
720

Zero-factorial is defined as 1:
>>> factorial(0)
1

Here are the first ten factorials, from 0! up to 9!:
>>> [factorial(n) for n in range(10)]
[1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]

The factorials get really big, really fast:
>>> factorial(30)
265252859812191058636308480000000

It's okay to give the factorial function a float, as long as it is a whole number:
>>> factorial(30.0)
265252859812191058636308480000000
>>> factorial(30.1)
Traceback (most recent call last):
    ...
ValueError: n must be exact integer

It also doesn't make sense to take the factorial of a negative number:
>>> factorial(-1)
Traceback (most recent call last):
    ...
ValueError: n must be >= 0

There are also limits on how big of a factorial this function can compute:
>>> factorial(1e100)
Traceback (most recent call last):
    ...
OverflowError: n too large

Have fun computing factorials!  For more reading, check out <a href="http://en.wikipedia.org/wiki/Stirling%27s_approximation">
Stirling's approximation</a> for large factorials