com.numericalmethod.suanshu.analysis.function.polynomial.root

Class PolyRoot

java.lang.Object

com.numericalmethod.suanshu.analysis.function.polynomial.root.PolyRoot

All Implemented Interfaces:

PolyRootSolver, java.io.Serializable

public class PolyRoot
extends java.lang.Object
implements PolyRootSolver

This is a solver for finding the roots of a polynomial equation. A root (or a zero) of a polynomial p is a member x in the domain of p such that p(x) vanishes. That is, p(x) = 0. By the fundamental theorem of algebra, every polynomial of degree n has n roots. The roots can be both real (double) or Complex. The Abel–Ruffini theorem says that we have analytical solution for polynomials of degree up to 4.

This implementation solves a polynomial of degree 1 by LinearRoot, degree 2 by QuadraticRoot, degree 3 by CubicRoot, degree 4 by QuarticRoot, and others by the Jenkins-Traub algorithm JenkinsTraubReal.

See Also:

• Wikipedia: PolyRoot (mathematics)
• Wikipedia: Fundamental theorem of algebra
• Wikipedia: Abel–Ruffini theorem
• Wikipedia: Jenkins-Traub algorithm

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
PolyRoot()

Method Summary

Modifier and Type	Method and Description
static java.util.List<Complex>	getComplexRoots(java.util.List<? extends java.lang.Number> roots) Get a copy of only the Complex but not real roots of a polynomial.
static java.util.List<java.lang.Double>	getRealRoots(java.util.List<? extends java.lang.Number> roots) Get a copy of only the real roots of a polynomial.
java.util.List<? extends java.lang.Number>	solve(Polynomial polynomial) Get the roots/zeros of a polynomial.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolyRoot

public PolyRoot()

Method Detail

solve

public java.util.List<? extends java.lang.Number> solve(Polynomial polynomial)

Get the roots/zeros of a polynomial.

Specified by:

solve in interface PolyRootSolver

Parameters:

polynomial - the polynomial to be solved

Returns:

the roots of the polynomial

Throws:

java.lang.IllegalArgumentException - if the polynomial is a constant, hence no solution

getRealRoots

public static java.util.List<java.lang.Double> getRealRoots(java.util.List<? extends java.lang.Number> roots)

Get a copy of only the real roots of a polynomial. The union of these and getComplexRoots(java.util.List) are all the roots.

Parameters:

roots - all the roots of a polynomial

Returns:

a copy of the real roots

getComplexRoots

public static java.util.List<Complex> getComplexRoots(java.util.List<? extends java.lang.Number> roots)

Get a copy of only the Complex but not real roots of a polynomial. The union of these and getRealRoots(java.util.List) are all the roots.

Parameters:

roots - all the roots of a polynomial

Returns:

a copy of the Complex roots