Programming Assignment 1

Polynomial

In this assignment, you will implement a polynomial and operations on it using a linked list.

Worth 60 points (6% of course grade)

Background

Read Section 3.1 in the textbook for background on polynomials and polynomial arithmetic.

A polynomial may be represented using a linked list as follows: for every term in the polynomial there is one entry in the linked list consisting of the term's coefficient and degree. The entries are ordered according to ASCENDING values of degree, i.e. lowest degree term first, then next lowest degree term and so on, all the way up to the highest degree term. IMPORTANT: Zero-coefficient terms are NOT stored.

For example, the following polynomial (the symbol '^' is used to mean 'raised to the power'):

 4x^5 - 2x^3 + 2x +3 

can be represented as the linked list of terms:

 (3,0) -> (2,1) -> (-2,3) -> (4,5) 

where each term is a (coefficient,degree) pair.

Notes about representation:

• Terms are stored in ASCENDING order of degrees from front to rear in a non-circular linked list.
• Zero-coefficient terms are NOT stored.
• An EMPTY (zero) polynomial is represented by a linked list with NO NODES in it, i.e. referenced by NULL.
• Coefficients are real numbers
• Degrees are POSITIVE integers, except if there is a constant term, in which case the degree is zero.
• There will not be more than one term in the same degree.

If you do not represent all your polynomials (the initial inputs as well as those you get out of doing arithmetic on polynomials) as above, you will lose credit even if your results are mathematically correct.

Running the program

There are three sample input files for you to test (they should be under the project folder in Eclipse):

• A file ptest1.txt that contains the polynomial

  4x^5 - 2x^3 + 2x + 3

• A file ptest2.txt that contains the polynomial

  8x^4 + 4x^3 - 3x + 9

• A file ptest1opp.txt that contains the polynomial

  -4x^5 + 2x^3 - 2x - 3

  (the negation of the polynomial in ptest1)

In each of these files, each line is a term, with the first value being the coefficient, and the second value being the degree. The terms are listed in descending order of degrees and the respective non-zero coefficients. Remember that when you store a polynomial in a linked list, you will store it in ascending order of degrees. (This is actually already implemented by the Polynomial constructor when it reads a polynomial from an input file. All you have to do is make sure you stick with this rule when you add and multiply.)

You may assume that we will NOT test with an invalid polynomial file, i.e. every test input file will either have at least one term in the correct format, or will be empty (see Notes about empty (zero) polynomialsbelow). So you don't need to check for validity of input.

Here's a sample run of the driver, Polytest. Apart from ptest1.txt, ptest2.txt, and ptest1opp.txt, a fourth test polynomial file, ptestnull.txt is also used. This is an empty file that stands for a null (zero) polynomial - you will need to create this yourself. See notes after the test run for special instructions regarding zero polynomials.

Enter the name of the polynomial file => ptest1.txt 4.0x^5 + -2.0x^3 + 2.0x + 3.0 1. ADD polynomial 2. MULTIPLY polynomial 3. EVALUATE polynomial 4. QUIT Enter choice # => 1 Enter the file containing the polynomial to add => ptest2.txt 8.0x^4 + 4.0x^3 + -3.0x + 9.0 Sum: 4.0x^5 + 8.0x^4 + 2.0x^3 + -1.0x + 12.0 1. ADD polynomial 2. MULTIPLY polynomial 3. EVALUATE polynomial 4. QUIT Enter choice # => 1 Enter the file containing the polynomial to add => ptest1opp.txt -4.0x^5 + 2.0x^3 + -2.0x + -3.0 Sum: 0 1. ADD polynomial 2. MULTIPLY polynomial 3. EVALUATE polynomial 4. QUIT Enter choice # => 1 Enter the file containing the polynomial to add => ptestnull.txt 0 Sum: 4.0x^5 + -2.0x^3 + 2.0x + 3.0 1. ADD polynomial 2. MULTIPLY polynomial 3. EVALUATE polynomial 4. QUIT Enter choice # => 2 Enter the file containing the polynomial to multiply => ptest2 8.0x^4 + 4.0x^3 + -3.0x + 9.0 Product: 32.0x^9 + 16.0x^8 + -16.0x^7 + -20.0x^6 + 52.0x^5 + 38.0x^4 + -6.0x^3 + -6.0x^2 + 9.0x + 27.0 1. ADD polynomial 2. MULTIPLY polynomial 3. EVALUATE polynomial 4. QUIT Enter choice # => 3 Enter the evaluation point x => 2 Value at 2.0: 119.0 1. ADD polynomial 2. MULTIPLY polynomial 3. EVALUATE polynomial 4. QUIT Enter choice # => 4 

The sample tests we have given you are just for starters. You will need to create other tests of your own on which you can run your code. For every test you run, be careful to keep your test input in the same format as the test files provided, otherwise Polytest will not work correctly. And make sure your test file is in the same folder as the other files, i.e. under Polynomial.

Note on translation from internal to output representation:

The toString method in the Polynomial class returns a string with the terms in descending order, fit for printing. (It processes the ascending ordered terms of the input linked list in reverse order.) For illustration, see how the add method in Polytest prints the resulting polynomial:

 System.out.println("Sum: " + Polynomial.toString(Polynomial.add(poly1,poly2)) + " "); 

Notes about empty (zero) polynomials:

• If you want to test with an empty polynomial input, you should create a file with nothing in it. In Eclipse, you can do this by right clicking on the project name in the package explorer view, then selecting New, then selecting File. Give a name, and click Finish. You new file will show up under the project name folder in the package explorer view, and the file will be opened in the text editor view. But don't type anything in the file.
• Remember that when you add two terms of the same degree, if you get a zero coefficient result term, it should not be added to the result polynomial. As listed in the "Notes about representation" in the Background section, zero-coefficient terms are not stored.
• The string representation of a zero polynomial is "0" - see the toString method of the Polynomial class. So, the Polytest driver will print a zero for a zero polyomial input, or a zero polynomial that results from an operation performed on two polynomials.