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module CoeffPoly where

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-- COMP2600 -- Assignment 1, 2003
-- Modified by Joseph Curtis (3952239)

-- Represent a polynomial as a list of coefficients, such that the
-- exponent of each term corresponds to the list index of each component.

type Coeff = Float
type Expon = Int
type Poly  = [Coeff]

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add :: Poly -> Poly -> Poly
add [] [] = []
add x [] = x
add [] y = y
add (x:xs) (y:ys) 
    | sum xs + sum ys == 0 = [] -- if the rest of both lists contains
    				-- only zeroes then just output the
				-- empty list.  This takes care of
				-- having trailing zeroes thus putting
				-- it in normal form.
    | otherwise = (x+y):add (xs) (ys) -- adds the two current list items
    				      -- together and joins this to the
				      -- list recursivly returned by the
				      -- adding of the rest of the polys.

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sub :: Poly -> Poly -> Poly
sub [] [] = []
sub x [] = x
sub [] y = map ((-) 0) y
sub (x:xs) (y:ys) = (x-y):sub (xs) (ys) -- very similar to the addition
					-- function.  See above.

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eval :: Float -> Poly -> Float
eval x [] = 0
eval x ys = ((last ys) * (x ^ fromInt (length (ys)-1))) + eval x (init ys)
-- Firstly if the set is empty it evaluates to zero.  For all other cases
-- the evaluation is performed as follows.  The last (higest exponent) list
-- item is taken and is multiplied by x to the power of the number of items
-- in the list minus 1.  This gets the correct exponent because the first
-- is the zero exponent.  Then this product is added to the sum of the rest
-- of the recursivly evaluated polynomial.

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