Schreiben Sie eine kleine Bibliothek zum Rechnen mit Polynomen. Hierzu sei der Datentyp Poly gegeben.
> module Poly where
> import Data.Ratio
> import Data.List
> data Monom = M Rational Int
> deriving (Show,Eq)
> newtype Poly = P [Monom]
> deriving (Show,Eq)
> infix 8 #^
> a #^ b = P [M a b]
> polyEx = 3#^2
> class ToLaTeX a where
> toLaTeX :: a -> String
> instance (Integral a,Eq a,Num a,Show a) => ToLaTeX (Ratio a)where
> toLaTeX r
> |n==1 = show z
> |otherwise = "\\frac{"++show z++"}{"++show n++"}"
> where
> z = numerator r
> n = denominator r
> instance ToLaTeX Monom where
> toLaTeX (M k 0) = toLaTeX k
> toLaTeX (M k 1)
> |k==1 = "x"
> |otherwise = toLaTeX k++"*x"
> toLaTeX (M k e)
> |k==1 = "x^{"++show e++"}"
> |otherwise = toLaTeX k++"*x^{"++show e++"}"
> instance ToLaTeX Poly where
> toLaTeX (P []) = "0"
> toLaTeX (P (x:xs))
> = (toLaTeX x)
> ++ (foldl (++) ""
> $ map (\m@(M k e)->
> (if (k>=0) then "+" else "")++toLaTeX m)
> xs)
> infix 9 §
> (§) :: Poly -> Rational -> Rational
> (P xs)§x = 0
> normalize :: Poly -> Poly
> normalize = id
> add :: Poly -> Poly -> Poly
> add p1 p2 = P[]
> negat :: Poly -> Poly
> negat = id
> mult :: Poly -> Poly -> Poly
> mult p1 p2 = P[]
> infix 2 /%
> (/%) :: Poly -> Poly -> (Poly,Poly)
> p1 /% p2 = (p1,p2)
> derivation :: Poly -> Poly
> derivation = id
> instance Num Poly where
> fromInteger x = error "not implemented"
> negate p = negat p
> p1 + p2 = add p1 p2
> abs (P xs) = error "not implemented"
> signum _ = error "not implemented"
> p1 * p2 = mult p1 p2
> example1 = 6 #^ 6 - 2#^5 - 4#^3 + 3#^1 + 3
> example2 = 2#^3 + 2#^1 - 3
> res1 = example1 /% example1
> res2 = example1 /% example2
Subato
