groups-ann.py

from __future__ import print_function
import sys
import getopt
import math

g = None
m = None

argv = sys.argv[1:]
opts, args = getopt.getopt(argv, "m:")
for opt, arg in opts:
    if opt == '-m':
        m = int(arg)
    else:
        raise Exception("Unrecognised option: {0}".format(opt))
if args:
    raise Exception("Not matching options: {0}".format(args))

if m < 1:
    raise Exception("Must specify -m, must be positive integer")

print("Groups modulo {0}".format(m))
for g in range(m):
    group_el = []
    for e in range(m+1):
        val = pow(g, e, m)
        if val in group_el:
            break
        group_el.append(val)
    print('g: {0:>{width}}, len: {2:>{width}}, {1}'.format(
                                        g, group_el,
                                        len(group_el),
                                        width=int(math.ceil(math.log10(m)))))