Introduction to Programming
                    Assignment 2, 2 Sep, 2008
                       Due Tue 9 Sep, 2008

Note: Remember to always supply a type definition for every
      function you write, including any auxiliary functions that
      you may define to solve the given problem.

Polynomials
-----------

Let us consider polynomials in a single variable x with integer
coefficients: for instance, 3x^4 - 17x^2 - 3x + 5.  Each term of
the polynomial can be represented as a pair of integers
(coefficient,exponent).  The polynomial itself is then a list of
such pairs.  Thus, we have:

   type Coefficient = Int
   type Exponent = Int
   type Polynomial = [(Coefficient,Exponent)]

We have the following constraints to guarantee that each
polynomial has a unique representation:

-- Terms are sorted in descending order of exponent
-- No term has a zero cofficient
-- No two terms have the same exponent
-- Exponents are always nonnegative

For example, the polynomial introduced earlier is represented as

   [(3,4),(-17,2),(-3,1),(5,0)]

The zero polynomial, 0, is represented as the empty list [],
since it has no terms with nonzero coefficients.

Write Haskell functions for the following operations:

  addpoly  :: Polynomial -> Polynomial -> Polynomial
  multpoly :: Polynomial -> Polynomial -> Polynomial

These functions add and multiply two polynomials, respectively.

You may assume that the inputs to these functions follow the
representation given above.  Correspondingly, the outputs from
these functions should also obey the same constraints.

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