Polynomial

java.lang.Object
- eecs2030.lab2.Polynomial

All Implemented Interfaces:

java.lang.Comparable<Polynomial>
```
public class Polynomial
extends java.lang.Object
implements java.lang.Comparable<Polynomial>
```
The Polynomial class represents a polynomial of a single indeterminate with double coefficients. A polynomial is an an expression consisting of variables with non-negative integer exponents and real coefficients. The set of operations supported by the Polynomial class includes: addition, subtraction, multiplication, function composition, polynomial derivative, and evaluation.
Examples of polynomials with a single indeterminate, x, are:
```
 p(x) = x^2 - 5.0x + 1.0
 p(x) = x^6 + 4.1x^4 + 0.5x - 7.2
 p(x) = 1.0
 
```
Author:

EECS2030 Summer 2019

Field Summary

Fields
Modifier and Type Field and Description

private double[] cf
Array of the polynomial coefficients.

private int degree
The degree of the polynomial.

Fields
Modifier and Type	Field and Description
`private double[]`	`cf` Array of the polynomial coefficients.
`private int`	`degree` The degree of the polynomial.

Constructor Summary

Constructors
Constructor and Description
`Polynomial()` Creates a polynomial with zero degree and one zero coefficient.
`Polynomial(double[] cf)` Creates a new polynomial from array of coefficients.
`Polynomial(double a, int i)` Creates a new polynomial `a * x^i`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`int`	`compareTo(Polynomial q)` Compares this polynomial `p` and the other polynomial `q` by their degree.
`Polynomial`	`compose(Polynomial q)` Returns the composition of this polynomial `p` and the specified polynomial `q`.
`Polynomial`	`derive()` Returns the result of deriving this polynomial `p`.
`boolean`	`equals(java.lang.Object obj)` Compares this polynomial to the other object `obj`.
`double`	`evaluate(double x)` Returns the result of evaluating this polynomial `p` at the value x.
`private void`	`findDegree()` Finds the polynomial `degree`, which is the largest exponent with non zero coefficient.
`int`	`getDegree()` Returns the degree of the polynomial.
`int`	`hashCode()` Returns a hash code for this polynomial.
`Polynomial`	`minus(Polynomial q)` Returns the result of subtracting the specified polynomial `q` from this polynomial `p`.
`Polynomial`	`plus(Polynomial q)` Returns the sum of this polynomial `p`} and the other polynomial `q` the argument.
`Polynomial`	`times(Polynomial q)` Returns the product of this polynomial `p` and the specified polynomial `q`.
`java.lang.String`	`toString()` Return a string representation of this polynomial in the standard form.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - cf
```
private double[] cf
```
    Array of the polynomial coefficients.
```
 p(x) = cf[0] * x^0 + ... + cf[n-1] * x^(n-1)
 
```
  - degree
```
private int degree
```
    The degree of the polynomial. That is the largest exponent with non zero coefficient. If all the coefficients are zero, the degree is zero. To set the value of degree, implement and call findDegree() method every time the polynomial is created or an operation is performed
- Constructor Detail
  - Polynomial
```
public Polynomial(double a,
                  int i)
```
    Creates a new polynomial a * x^i
    
    Parameters:
    
    a - the leading coefficient
    
    i - the exponent
    
    Throws:
    
    java.lang.IllegalArgumentException - if i is negative
  - Polynomial
```
public Polynomial(double[] cf)
```
    Creates a new polynomial from array of coefficients. The new polynomial has the form
```
 cf[0] * x^0 + ... + cf[n-1] * x^(n-1)
 
```
    where n is the length of the coefficients array.
    Parameters:
    
    cf - the coefficients array
    
    Throws:
    
    java.lang.IllegalArgumentException - if cf is empty
  - Polynomial
```
public Polynomial()
```
    Creates a polynomial with zero degree and one zero coefficient.
```
 p(x) = 0
 
```
- Method Detail
  - findDegree
```
private void findDegree()
```
    Finds the polynomial degree, which is the largest exponent with non zero coefficient. If all the coefficients are zero, the degree is zero.
  - getDegree
```
public int getDegree()
```
    Returns the degree of the polynomial. A polynomial with zero coefficients has a zero degree.
    
    Returns:
    
    the degree of the polynomial
  - plus
```
public Polynomial plus(Polynomial q)
```
    Returns the sum of this polynomial p} and the other polynomial q the argument.
    
    Parameters:
    
    q - the other polynomial
    
    Returns:
    
    the polynomial whose value is (p(x) + q(x))
  - minus
```
public Polynomial minus(Polynomial q)
```
    Returns the result of subtracting the specified polynomial q from this polynomial p.
    
    Parameters:
    
    q - the other polynomial
    
    Returns:
    
    the polynomial whose value is (p(x) - q(x))
  - times
```
public Polynomial times(Polynomial q)
```
    Returns the product of this polynomial p and the specified polynomial q.
    
    Parameters:
    
    q - the other polynomial
    
    Returns:
    
    the polynomial whose value is (p(x) * q(x))
  - compose
```
public Polynomial compose(Polynomial q)
```
    Returns the composition of this polynomial p and the specified polynomial q.
    
    Parameters:
    
    q - the other polynomial
    
    Returns:
    
    the polynomial whose value is (p(q(x)))
  - derive
```
public Polynomial derive()
```
    Returns the result of deriving this polynomial p.
    
    Returns:
    
    the polynomial whose value is p'(x)
  - evaluate
```
public double evaluate(double x)
```
    Returns the result of evaluating this polynomial p at the value x.
    
    Parameters:
    
    x - the value at which to evaluate the polynomial
    
    Returns:
    
    the value of evaluating (p(x))
  - hashCode
```
public int hashCode()
```
    Returns a hash code for this polynomial. The hash code value is equal to the degree of the polynomial multiplied with 31 plus the hashcode of the coefficients array.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    31 * degree + Arrays.hashCode(cf)
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Compares this polynomial to the other object obj. The result is true if and only if the argument is a polynomial object having the same degree and coefficients as this polynomial.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    obj - an object to compare
    
    Returns:
    
    true if this polynomial equals to the specified object; and false otherwise
  - compareTo
```
public int compareTo(Polynomial q)
```
    Compares this polynomial p and the other polynomial q by their degree. If the degrees are equal, the polynomial coefficients are compared, and so on.
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<Polynomial>
    
    Parameters:
    
    q - the other polynomial
    
    Returns:
    
    the value -1 if this polynomial is less than the argument polynomial; +1 if this polynomial is greater than the argument polynomial; and 0 if this polynomial is equal to the argument polynomial.
  - toString
```
public java.lang.String toString()
```
    Return a string representation of this polynomial in the standard form. The standard form of a polynomial is to put the terms with the highest degree first. The following are examples of the returned string for different polynomials.
```
        new Polynomial();                              //0.0
        new Polynomial(1,0)                            //1.0
        new Polynomial(1,1);                           //1.0x
        new Polynomial(new double[] {1,1});            //1.0x + 1.0
        new Polynomial(new double[] {0,0,2});          //2.0x^2
        new Polynomial(new double[] {0,1,2});          //2.0x^2 + 1.0x
        new Polynomial(new double[] {1,0,2});          //2.0x^2 + 1.0
        new Polynomial(new double[] {0.0001213,1,2});  //2.0x^2 + 1.0x + 1.213E-4
 
```
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a string representation of this polynomial

Class Polynomial

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

cf

degree

Constructor Detail

Polynomial

Polynomial

Polynomial

Method Detail

findDegree

getDegree

plus

minus

times

compose

derive

evaluate

hashCode

equals

compareTo

toString