module Polynomial where

-- import Data.List
--
--
-- data Equation = Equation { left :: Polynomial, right :: Polynomial }
-- type Polynomial = [Term]
-- data Term = Term { coefficient :: Float, exponent :: Int }
--
-- instance Eq Term where
--     (Term _ e1) == (Term _ e2) = e1 == e2
--
-- instance Ord Term where
--     compare (Term _ e1) (Term _ e2) = compare e1 e2
--
-- instance Show Term where
--     show (Term 0 e) = ""
--     show (Term c 0) = show (round c)
--     show (Term c e) = show (round c) ++ " * X^" ++ show e
--
-- instance Show Equation where
--     show (Equation l r) = showPolynomial (filterNull l)
--                           ++ " = "
--                           ++ showPolynomial (filterNull r)
--         where showPolynomial [] = "0"
--               showPolynomial p  = dropWhile (`elem` " +") $ foldl f "" (map show p)
--                 where f s "" = s
--                       f s (c:cs)
--                         | c == '-'  = s ++ " - " ++ cs
--                         | otherwise = s ++ " + " ++ (c:cs)
--
--
-- filterNull :: Polynomial -> Polynomial
-- filterNull = filter (\t -> coefficient t /= 0)
--
-- equationMap :: (Polynomial -> Polynomial) -> Equation -> Equation
-- equationMap f (Equation l r) = Equation (f l) (f r)
--
-- degree :: Polynomial -> Int
-- degree [] = 0
-- degree p  = Equation.exponent (maximum p)
--
-- reduce :: Equation -> Equation
-- reduce equ = Equation (merge (left stdForm) (right stdForm)) []
--     where stdForm = equationMap (\a -> (reducePolynomial $ sort a)) equ
--           merge [] rs = rs
--           merge ls [] = ls
--           merge (l:ls) (r:rs)
--             | l == r = (subTerm l r) : merge ls rs
--             | l < r  = l : merge ls (r:rs)
--             | r < l  = r : merge (l:ls) rs
--             where subTerm (Term c1 e) (Term c2 _) = Term (c1 - c2) e
--           reducePolynomial []         = []
--           reducePolynomial [t]        = [t]
--           reducePolynomial (t1:t2:ts)
--             | t1 == t2  = (addTerm t1 t2) : reducePolynomial ts
--             | otherwise = t1 : reducePolynomial (t2:ts)
--             where addTerm (Term c1 e) (Term c2 _) = Term (c1 + c2) e
--
-- solveDegree2 :: Float -> Float -> Float -> [Float]
-- solveDegree2 a b c
--     | phi < 0   = []
--     | phi == 0  = [(-b) / (2.0 * a)]
--     | phi > 0   = [ (-b + mySqrt phi) / (2.0 * a) -- not alowed
--                   , (-b - mySqrt phi) / (2.0 * a)
--                   ]
--     where phi = b * b - 4.0 * a * c
--
-- solveDegree1 :: Float -> Float -> Float
-- solveDegree1 b c = -c / b
--
-- solve :: Polynomial -> [Float]
-- solve [t0]         = []
-- solve [t0, t1]     = [solveDegree1 (coefficient t1) (coefficient t0)]
-- solve [t0, t1, t2] = solveDegree2 (coefficient t2) (coefficient t1) (coefficient t0)
-- solve _            = undefined
--
-- mySqrt :: Float -> Float
-- mySqrt n
--   | n < 0     = undefined
--   | otherwise = mySqrt' (n / 2)
--     where mySqrt' x = if abs (x * x - n) < 0.01
--                          then x
--                          else mySqrt' xn
--             where xn = b - (a * a) / (2 * b)
--                     where a = (n - x * x) / (2 * x)
--                           b = x + a