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Add polynomials

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

Revision as of 05:51, 5 November 2006

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 "Enter a person's name: "
       putStr $ show $ addPoly [(0,1),(2,1)] [(0,1)]
fibs = fix $ \f -> 1 : 1 : zipWith (+) f (tail f)