«K12/K13» Q.hs «PDF», «POD»

{-# OPTIONS_GHC -fglasgow-exts #-}
module Q where

import EqClass
import GHC.Real

data Q  z = Q (z,z)
type Q' z = EqClass (Q z)

instance (Real z, Integral z) => Show (Q z) where
  show z = "Q[" ++ show (toRational z) ++ "]"

instance (Num z, Eq z) => Eq (Q z) where
  (Q (a,b)) == (Q (c,d)) = a * d == c * b

instance (Num z, Integral z) => Num (Q z) where
  (Q (a,b)) + (Q (c,d)) = Q (a*d + c*b, b*d)
  (Q (a,b)) - (Q (c,d)) = Q (a*d - c*b, b*d)
  (Q (a,b)) * (Q (c,d)) = Q (a*c, b*d)

  signum (Q (a,b)) = fromInteger . toInteger $ signum (a*b)

  abs x = x * signum x

  fromInteger n = Q (fromInteger n, 1)

instance (Num z, Integral z) => Fractional (Q z) where
  (Q (a,b)) / (Q (c,d)) = Q (a*d, b*c)
  fromRational (a :% b) = Q (fromInteger a, fromInteger b)

instance (Num z, Ord z) => Ord (Q z) where
  (Q (a,b)) <= (Q (c,d)) | b * d > 0 = a * d <= c * b
  (Q (a,b)) <= (Q (c,d)) | b * d < 0 = a * d  > c * b

instance (Real z, Integral z) => Real (Q z) where
  toRational (Q (a,b)) = toRational a / toRational b