how do i code the java polynomial interface and the public class polynomial?

An example of such a polynomial is f(x)=3x - 5x+ 2x - 4. This polynomial has four terms. The degree of a polynomial is defined as the highest power of the variable in a term. In the above example, the degree of the polynomial is 4. The polynomials we deal with have only positive, integral powers. The coefficients of our polynomials are also integral numbers. Tho polynomials are the same if they contain the same terms. Several algebraic operations are possible with polynomials. The simplest one is evaluating the polynomial for a specific value of the variable. For example, for a polynomial f(x)=3x5x+ 2x - 4. its value at x=2.5 is defined as: (2.5) = 3 (2.5)-5. (2.5)+2. (2.5) - 4 which is 40.0625. Polynomials can be added together to create a new polynomial. The addition is performed by combining all the terms and adding the coefficients of the terms with the same power. For example 3x - 5x+ 2x - 4 + 2x + 2x + 4 = 3x - 3x+2x+ 2x. The degree of the sum is the maximum of the degrees of the two polynomials. 2. What to do Design an interface Polynomial that defines the above operations. This is your polynomial abstract data type and specifies the contract Polynomial (s) will adhere to. Specifically this interface should have the following method signatures: A method add text that takes a coefficient and a power (both integral numbers) and adds the resulting term to the polynomial. (This will enable you to build a polynomial term-by-term.) It should throw an IldegalAETUIENTExsertina if a negative power is passed to it. A method zemexedeza that takes a power and removes any and all terms in the polynomial with that power. A method getRegere that returns the degree of this polynomial. A method gesterffisient that takes a power and returns the coefficient for the term with that power. A method evaluate that takes a double-precision decimal number and returns a double- precision result. A method add that takes another Polynomial object and returns the polynomial obtained by adding the two polynomials. Any implementation should ensure that this method does not mutate either polynomial. The implementation may assume that the given Polynomial is the of the same concrete class as this object; if it is a different class, the method may throw an IldegadAtstumentExSERLINA: Now implement this interface in a class BR XORIJLord Beyond implementing the Polynomial interface, this implementation should have the following features/obey these constraints: This class should store the polynomial using the a linked list with nodes. This representation must be implemented by you (i.e. you are not allowed to use existing List classes in Java). This class should store only terms with non-zero coefficients. This class should store the polynomial terms in decreasing order of their powers. This class should have a constructor with no parameters that creates a polynomial with no terms, i.e. the polynomial (think about how to represent this?). This class should have a second constructor that takes a polynomial as a string, parses it and creates the polynomial accordingly. The string contains the polynomial, with each term separated by a space. The following examples should work with your constructor: *4x^3 +3x^1 -5 "-3x^4 -2x^5 -5 +11x41" Hint: Break the string into substrings and process. You may find the Ssaranzand string classes helpful to do this. Furthermore one can convert "23" into the integer 23 by using JetSREBRESSIAS ("23"). o While you are free to write helper methods, you are not allowed to write any other public methods other than those in the interface and the above two constructors. This class should include a tretzing method that returns a string that contains the polynomial. The following examples should help you infer the required format. Note that the spacing and placement in the String representations below are purposeful and not a formatting error: 5x2 + 4x - 2 creates the string "5x^2 +4x^1 -2" -50x + x + 3 creates the string-50x^3 +1x^2 +3" 4x + 2x - 3x - 10 creates the string "2x^5 -3x^2 +4x^1 -10" O O O Write tests that thoroughly test this implementation. As always, it is recommended to write the test before completing the Red Xardiak botol implementation. 3.Hints: How to tackle the assignment Start by creating empty interfaces and classes for polynomials and nodes. Now select a method from the ADT and implement it end-to-end. Write tests for it before writing the implementation, and when your implementation passes your tests, move on to the next method. Tackle the parsing constructor at the end: you should not need it to test other methods. For the add method: one approach is to think about how you can "accumulate" the result. There are other approaches; do not feel compelled to follow this line of thinking. NB: These are hints and suggestions. You are not required to follow these suggestions if you are more comfortable with an alternate approach