isSmallPrime :: Int -> Bool
isSmallPrime 2 = True
isSmallPrime 3 = True
isSmallPrime 5 = True
isSmallPrime 7 = True
isSmallPrime _ = False

equivalent :: Bool -> Bool -> Bool
equivalent True True = True
equivalent False False = True
equivalent _ _ = False

implies :: Bool -> Bool -> Bool
implies True False = False
implies _ _ = True

invertO :: (Int, Int) -> (Int, Int)
invertO (x,y) = (-x,-y)

isOnNegId :: (Int, Int) -> Bool
isOnNegId (x,y) = (-x==y)

add :: (Int, Int) -> (Int, Int) -> (Int, Int)
add (x,y) (a,b) = if y == b then (x+a,y)
                        else (x*b+a*y,b*y)

multiply :: (Int, Int) -> (Int, Int) -> (Int, Int)
multiply (x,y) (a,b) = (x*a, y * b)

divide :: (Int, Int) -> (Int, Int) -> (Int, Int)
divide (x,y) (a,b) = (x*b,y*a)