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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
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