RatOps

module RatOps where
type Rat = (Int,Int)

asop :: Num z => (z -> z -> z) -> (z,z) -> (z,z) -> (z,z)
asop op (z1,n1)(z2,n2) = ((z1*n2) `op` (z2*n1), (n1*n2))

short :: Num z => (z -> z) -> (z,z) -> (z,z)
short (z1,n1) = ((z1/gcd z1 n1), (gcd z1 n1)

negn :: Rat -> Bool
negn (z1,n1) = if n1 = 0
			then True
				else False

negz :: Rat -> Bool
negz (z1,n1) = if z1 = 0
			then True
				else False

switch :: Rat -> Rat
switch (z,n) = (n,z)

addR :: Rat -> Rat -> Rat
addR x y|negz x = True || (snd y == 1) = (0, 1)
		|negn y = True || (fst x == 0) = (0, 0)
		|otherwise = short $ asop(+) x y

subR :: Rat -> Rat -> Rat
subR x y|negz x = True || (snd y == 1) = (0, 1)
		|negn y = True || (fst x == 0) = (0, 0)
		|otherwise = short $ asop(-) x y

mulR :: Rat -> Rat -> Rat
mulR x y|negz x = True || (snd y == 1) = (0, 1)
		|negn y = True || (fst x == 0) = (0, 0)
		|otherwise = short ((fst x * fst y),(snd x * snd y)

divR :: Rat -> Rat -> Rat
divR x y|negz x = True || (snd y == 1) = (0, 1)
		|negn y = True || (fst x == 0) = (0, 0)
		|otherwise = short $ x `mulR` (switch y)