Data commit

Task/Pisano-period/Python/pisano-period.py

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+from sympy import isprime, lcm, factorint, primerange
+from functools import reduce
+
+
+def pisano1(m):
+    "Simple definition"
+    if m < 2:
+        return 1
+    lastn, n = 0, 1
+    for i in range(m ** 2):
+        lastn, n = n, (lastn + n) % m
+        if lastn == 0 and n == 1:
+            return i + 1
+    return 1
+
+def pisanoprime(p, k):
+    "Use conjecture π(p ** k) == p ** (k − 1) * π(p) for prime p and int k > 1"
+    assert isprime(p) and k > 0
+    return p ** (k - 1) * pisano1(p)
+
+def pisano_mult(m, n):
+    "pisano(m*n) where m and n assumed coprime integers"
+    return lcm(pisano1(m), pisano1(n))
+
+def pisano2(m):
+    "Uses prime factorization of m"
+    return reduce(lcm, (pisanoprime(prime, mult)
+                        for prime, mult in factorint(m).items()), 1)
+
+
+if __name__ == '__main__':
+    for n in range(1, 181):
+        assert pisano1(n) == pisano2(n), "Wall-Sun-Sun prime exists??!!"
+    print("\nPisano period (p, 2) for primes less than 50\n ",
+          [pisanoprime(prime, 2) for prime in primerange(1, 50)])
+    print("\nPisano period (p, 1) for primes less than 180\n ",
+          [pisanoprime(prime, 1) for prime in primerange(1, 180)])
+    print("\nPisano period (p) for integers 1 to 180")
+    for i in range(1, 181):
+        print(" %3d" % pisano2(i), end="" if i % 10 else "\n")