Programming for Mathematics
Assignment, 27 August 2014

Write a Python class Polynomial that stores polynomials in a
single variable x with integer coefficients: for instance, 3x^4 -
17x^2 - 3x + 5.

Choose a suitable internal representation. 

- For instance each term of the polynomial can be represented as
  a pair of integers (coefficient,exponent) and the polynomial
  could itself be a list of such pairs.

- Or you could use a dictionary where the key is the exponent and
  the value is the coefficient.

Your representation should store only terms with non-zero
coefficients.

a. The function __init__ should accept an initial polynomial of
   in the list format: i.e.
   [(coeff1,expo1),(coeff2,expo2),...,(coeffn,expon)]

   Assume that the terms could be in any order, possibly with
   repeated exponents, in which case the corresponding
   coefficients should be added up.

b. Define "magic functions" __add__ and __mul__ to add and
   multiply two polynomials.

c. Define __str__ that displays the polynomial in human readable
   form. Print the terms in some canonical order (e.g. in
   descending order of exponents)

d. Define __repr__ that returns a string of the form
   "Polynomial([(coeff1,expo1),(coeff2,expo2),...,(coeffn,expon)]"

e. Define functions getcoeff(exponent) and setcoeff(exponent) to
   get and set the coefficients of a particular term.  Make sure
   these work sensibly if there is currently no term with that
   exponent. 

f. Anything else you think is interesting!

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