ProGAL.math

Class Polynomial

java.lang.Object

ProGAL.math.Polynomial

public class Polynomial
extends java.lang.Object

A representation of a variable sized polynomial. To find the roots of the parabola f(x) = 2x^2 + 3x - 4, for instance, write Polynomial parabola = new Polynomial(new double[]{2,3,4}); double[] roots = parabola.calcRoots(); or simply double[] roots = Polynomial.calcRoots(2,3,4); Currently this only works for polynomials of degree 2 and 3.

Field Summary

Fields

Modifier and Type	Field and Description
double[]	coeff

Constructor Summary

Constructors

Constructor and Description
Polynomial(double[] pars) creates a polynomal

Method Summary

Modifier and Type	Method and Description
double[]	calcRoots() Find the roots of the polynomial.
static double[]	calcRoots(double[] parameters) Find the roots of the polynomial specified by the parameters.
static double[]	calcRoots(double a, double b, double c) Find the roots of a second degree polynomial.
static double[]	calcRoots(double a, double b, double c, double d) Find the roots of a third degree polynomial.
Polynomial	clone() returns a copy of the polynomial p
Polynomial	compose(Polynomial b)
Polynomial	differentiate()
boolean	dominates(Polynomial p)
boolean	equal(Polynomial b)
double	evaluate(int x)
static Polynomial	gcd(Polynomial a, Polynomial b)
int	getDeg()
boolean	isZeroPolynomial() returns TRUE if this polynomial is a zero polynomial
Polynomial	leadingTerm()
static void	main(java.lang.String[] args)
Polynomial	makeMonic()
Polynomial	minus(Polynomial b)
int	numberNegativeRoots()
int	numberPositiveRoots()
Polynomial	plus(Polynomial b)
static java.lang.Double[]	solveCubic(double[] c)
java.lang.Double	solveFirstDegree()
static double	solveHighDegree(double[] a)
static java.lang.Double[]	solveQuadric(double[] c)
static java.lang.Double[]	solveQuartic(double[] c)
java.lang.Double[]	solveSecondDegree()
static double[]	solveThirdDegree(double[] parameters) Solves cubic equation.
java.util.List<Polynomial>	squareFreeFact()
Polynomial	times(Polynomial b)
Polynomial	toMonic()
java.lang.String	toString()

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

coeff

public final double[] coeff

Constructor Detail

Polynomial

public Polynomial(double[] pars)

creates a polynomal

Parameters:

pars -

Method Detail

clone

public Polynomial clone()

returns a copy of the polynomial p

Overrides:

clone in class java.lang.Object

Returns:

copy of the polynomial p

isZeroPolynomial

public boolean isZeroPolynomial()

returns TRUE if this polynomial is a zero polynomial

Returns:

dominates

public boolean dominates(Polynomial p)

leadingTerm

public Polynomial leadingTerm()

getDeg

public int getDeg()

plus

public Polynomial plus(Polynomial b)

minus

public Polynomial minus(Polynomial b)

times

public Polynomial times(Polynomial b)

compose

public Polynomial compose(Polynomial b)

equal

public boolean equal(Polynomial b)

evaluate

public double evaluate(int x)

toMonic

public Polynomial toMonic()

differentiate

public Polynomial differentiate()

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

calcRoots

public double[] calcRoots()

Find the roots of the polynomial. The imaginary part is not returned.

Returns:

an array containing the roots of the polynomial

calcRoots

public static double[] calcRoots(double[] parameters)

Find the roots of the polynomial specified by the parameters. The imaginary part is not returned.

Parameters:

parameters - an array representing the coefficents of the polynomial

Returns:

an array containing the roots of the polynomial

calcRoots

public static double[] calcRoots(double a,
                                 double b,
                                 double c)

Find the roots of a second degree polynomial. The length of the returned array depends on how many roots the quadratic equation has. In other words: The imaginary part is removed completely.

Parameters:

a - coefficient of the squared term

b - coefficient of the linear term

c - coefficient of the constant

Returns:

an array containing the roots of the polynomial

calcRoots

public static double[] calcRoots(double a,
                                 double b,
                                 double c,
                                 double d)

Find the roots of a third degree polynomial. The length of the returned array depends on how many roots the cubic equation has. In other words: The imaginary part is removed completely.

Parameters:

a - coefficient of the cubed term

b - coefficient of the squared term

c - coefficient of the linear term

d - coefficient of the constant term

Returns:

an array containing the roots of the polynomial

solveFirstDegree

public java.lang.Double solveFirstDegree()

solveSecondDegree

public java.lang.Double[] solveSecondDegree()

solveThirdDegree

public static double[] solveThirdDegree(double[] parameters)

Solves cubic equation.

solveQuartic

public static java.lang.Double[] solveQuartic(double[] c)

solveCubic

public static java.lang.Double[] solveCubic(double[] c)

solveQuadric

public static java.lang.Double[] solveQuadric(double[] c)

squareFreeFact

public java.util.List<Polynomial> squareFreeFact()

gcd

public static Polynomial gcd(Polynomial a,
                             Polynomial b)

makeMonic

public Polynomial makeMonic()

numberPositiveRoots

public int numberPositiveRoots()

numberNegativeRoots

public int numberNegativeRoots()

solveHighDegree

public static double solveHighDegree(double[] a)

main

public static void main(java.lang.String[] args)