module Newton ( newton ) where
next :: Double -> Double -> Double
next m 0 = error "Division by zero"
next m x = (x + m/x)/2
repeatedly :: (Double -> Double) -> Double -> [Double] 
repeatedly f a = a : repeatedly f (f a)
relative :: Double -> [Double] -> Double
relative tau (a:b:rest) 
   | abs (a/b-1) <= tau = b
   | otherwise          = relative tau (b:rest)
newton x0 tau m = relative tau (repeatedly (next m) x0)