bmabsout / fibulus Goto Github PK

for all p1, p2 in G, (p3 = p1 * p2) should be in G. In other words, p3 should not be a hole.

A hole is defined by a pair (a, b) such that a and b is in Fp and Fib(a, b) does not have an inverse.

inverse :: (Fractional a, Eq a) => Fib a -> Maybe (Fib a) inverse (Fib a b) | a == 0 && b /= 0 = Just $ Fib (1/(-b)) (1/b) | a /=0 && b^2 /= a*(a + b) = Just $ Fib ((a + b)/ (a^2 + a*b -b^2)) (-b/(a^2 + a*b - b^2)) | otherwise = Nothing

A finite field of order q exists if and only if q is a prime power p^k where k > 1.

When we were working in Fib a b where a and b are integers mod 5 we had a weird order of 20. This would contradict the statement above. We had all the properties of a field except that the order wasn't of the form p^k....