# Add polynomials

### From HaskellWiki

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)]