Group theory

This is one of the cases where I've simply got bored of solving a problem the conventional way and decided it could be a much better use of my time writing a program rather than pressing multiply on my calculator repeatedly.

Here's a simple python program to find the order of an element of a group modulo some number (the binary operation being multiplication):

#!/usr/bin/env python
import sys

def element_order_mul(n,g):
    r=g
    o=1
    while r%n != 1:
        print "not",r
        r=r*g
        o=o+1
    return o

# calculates the element order under multiplication mod n.
# takes: n, element
n=int(sys.argv[1])
g=int(sys.argv[2])
o=element_order_mul(n,g)
print g,"^",o,"is congruent to 1 mod",n

To find the order of g=4 in the group G={1,2,4,5,7,8} with the binary operation being multiplication modulo 9:

[simon@simon ~]$ ./order.py 9 4
not 4
not 16
4 ^ 3 is congruent to 1 mod 9

Excellent!