Permutation check for smaller alphabets

from functools import reduce
from fractions import gcd


MAXLEN = 3 * 10**12
ALPHABET = '0123'


def index_function(char):
    return ord(char) - ord('0')


INDEX_FN = index_function


def lcm(*args):
    def reduction(previous, current):
        return previous * current / gcd(previous, current)
    return reduce(reduction, args, 1)


def _find_base(string1, string2, maxlen, alphabet):
    def holds(lcm_value, maximal):
        # The last condition is just to restrain the search to 64-bit integers
        return lcm_value > maxlen and maxlen * maximal**(len(alphabet) - 1) < 2**64

    # Calculate the maximal possible lcm value for a given maximal number, such that the above holds
    lcm_value = 2
    maximal = 2
    while not holds(lcm_value, maximal):
        maximal += 1
        lcm_value = lcm(lcm_value, maximal)

    # Retrieve the base for that lcm value
    base = []
    while lcm_value > 1 and maximal > 1:
        if lcm_value % maximal == 0:
            base.append(maximal)
            lcm_value = lcm_value / maximal
        maximal -= 1

    return base


find_base = _find_base


def _hash_for_power(string, power):
    return sum(power**INDEX_FN(c) for c in string)


get_hash = _hash_for_power


def is_permutation(string1, string2):
    if len(string1) != len(string2):
        return False
    base = find_base(string1, string2, MAXLEN, ALPHABET)
    return all(get_hash(string1, power) == get_hash(string2, power) for power in base)