Add polynomials
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Polynomial Algebra
#!/usr/local/bin/runhugs
module Main where
type Poly = [(Int,Int)]
-- assume sorted by increasing exponent.
-- data Rational = (Poly, Poly)
-- an interesting thing to observe:
-- when adding, the null polynomial is zero.
-- when multiplying it is one. This concept emerges implicitly
-- in these definitions.
addPoly :: Poly -> Poly -> Poly
addPoly [] ys = ys
addPoly xs [] = xs
addPoly ((a,b):xs) ((c,d):ys)
| a == c = ((a,b+d):(addPoly xs ys))
| a < c = ((a,b):(addPoly xs ((c,d):ys)))
| a > c = ((c,d):(addPoly ((a,b):xs) ys))
addManyPolys :: [Poly] -> Poly
addManyPolys ps = foldl 0 addPoly ps
multiply :: [Int] -> [Int] -> [Int]
--multiply polynomials together.
multiply [] ys = ys
multiply xs [] = xs
multiply ((a,b):xs) ((c,d):ys)
main = do
putStr $ show $ addPoly [(0,1),(2,1)] [(0,1)]