polynoms.hs

data Polynomnom = P [Int]
instance Show Polynomnom where
    show (P polynom) = 
        let showp (P []) = "" 
            showp (P xs) = nom ++ showp (P (init xs))
                where nom 
                        | x == 0 = ""
                        | x < 0  = "-" ++ show (abs x) ++ temp
                        | otherwise = "+" ++ (if (x == 1) then "" else (show (abs x))) ++ temp
                        where x = last xs
                              temp
                                 | (x == 1)&&(l == 0) = "1"
                                 | (l == 0)&&(x /= 1) = ""
                                 | (l == 1)           = "x"
                                 | otherwise          = "x^" ++ show l
                                   where l = length xs - 1 in
        case showp (P (polynom)) of "" -> "0"
                                    '+':xs -> xs
                                    xs -> xs

simplify (P p1) = P $ fst $ foldr (\x acc@(xs,flag)-> if flag && x == 0 
                                                      then acc 
                                                      else (x:xs,False)) ([],True) p1
                                                      
instance Eq Polynomnom where
 (==) (P p1) (P p2) = (simplify p1) == (simplify p2)

arifm :: (Int -> Int -> Int) -> Polynomnom -> Polynomnom -> Polynomnom
arifm f (P p1) (P p2) = simplify $ P (zipWith f (p1 ++ (take (-degsub) zeros)) (p2 ++ (take degsub zeros)))
    where degsub = length p1 - length p2  
          zeros = repeat 0   

instance Num Polynomnom where
    (+) = arifm (+)
    (-) = arifm (-)
    (*) a b = simplify $ helper 0 a b
        where
            helper :: Int -> Polynomnom -> Polynomnom -> Polynomnom
            helper _ _ (P []) = P []
            helper c a@(P p1) (P (x:xs)) = P (zeros c ++ (map (*x) p1)) + (helper (c+1) a (P xs))
                where zeros x = take x $ repeat 0
    signum (P xs) = P (map signum xs)
    abs (P xs) = P (map abs xs)
    fromInteger x = P [fromIntegral x]

polynomFromList = P
    
main :: IO()
main = do
    let p1 = polynomFromList [1,0,0,0,0,0,1]
    putStrLn $ " polynom1 = " ++ show p1                  -- x^6+1
    putStrLn $ " p1 + p1  = " ++ (show $ p1 + p1)         -- 2x^6+2
    putStrLn $ " p1 - p1  = " ++ (show $ p1 - p1)         -- 0
    putStrLn $ " p1 * p1  = " ++ (show $ p1 * p1)         -- x^12+2x^6+1
    let p2 = P [1,2,1]
    putStrLn $ " polynom2 = " ++ (show p2)               -- x^2+2x^1+1
    putStrLn $ " p1 + p2  = " ++ (show $ p1 + p2)        -- x^6+x^2+2x^1+2
    putStrLn $ " p2 * x   = " ++ (show $ p2 * (P [0,1])) -- x^3+2x^2+x^1
    putStrLn $ " (p2 == p2 - (p2 - p1) + p2 - p1) is " ++ (show $ p2 == p2 - (p2 - p1) + p2 - p1) -- True