Bottom of def get_number renders as the Registered Trademark unicode instead of ®.

You can be a little more concise with the code by modifying how __memo is set up.

def __init__(self):
self.__memo = {0:0,1:1}

Then you can do:

def __get_matrix_power(self, M, p):
"""Matrix exponentiation (it is expected that p that is equal to the power of 2)."""
return self.__memo.get(p,self.non_memoized(M,p))
def non_memoized(self, M,p):
K = self.__get_matrix_power(M, int(p/2))
R = self.__multiply_matrices(K, K)
self.__memo[p] = R
return R

I know it essentially does the same thing, IMHO it's a little cleaner code thou ;)

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You can be a little more concise with the code by modifying how __memo is set up.

Then you can do:

I know it essentially does the same thing, IMHO it's a little cleaner code thou ;)