Software packages such as Mathematica and Maple have features that allow a user to manipulate symbolic algebraic expressions. For example, the user can enter a pair of polynomials, say x2 + 1 and 3x4 +7 and software will print out 3x4 +x2 +8. In this programming project, we will develop a way of accomplishing this using linked lists. The idea is to represent each term in the polynomial using a node structure containing a field for the coefficient and a field for the exponent.

Begin by writing an interface called Polynomial that specifies these public methods. LinkedPolynomial will then implement the Polynomial interface. 1. getCoefficient - takes an integer argument and returns the coefficient of the term that has the argument as its exponent. 2. value - takes a double argument and returns the value of this polynomial at the argument 3. add - takes a LinkedPolynomial; returns a new Polynomial that is the sum of this and the argument. 4. subtract - takes a LinkedPolynomial; returns a new Polynomial that is the difference of this and the argument. 5. negate - returns the negative of the LinkedPolynomial 6. equals - takes a Polynomial; returns true if the Polynomials are equal, false otherwise. 7. hashCode - returns a hash code for the Polynomial 8. toString - returns a String representation of the Polynomial

Implement a class called LinkedPolynomial. LinkedPolynomials are to be immutable. LinkedPolynomial is to implement the Polynomial interface. You are not to use any of the Java Collections Framework for this assignment. You are to implement your linked list directly. The class LinkedPolynomial will have an integer exponent field and a double coefficient field. The constructor for LinkedPolynomial should take a String argument representing the polynomial. The strings will be formatted like this: (3.5, 4, 1.0, 2, 8.6, 0). Successive pairs represent a single term. This sequence represents 3.5x4 + x2 + 8.6.

Write a main method to test your code. Test your code thoroughly! You will be graded on the completeness of your tests.