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

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.polynomial.root.Polyroot

All Implemented Interfaces:

Solver

public class Polyroot
extends java.lang.Object
implements Solver

A solver for polynomial equations.

A root (or a zero) of a function f is a member x in the domain of f such that f(x) vanishes at x. That is

f(x) = 0

This is a wrapper class that solves for a Polynomial equation with non-negative, whole number exponents, e.g.,

ax⁴ + bx³ + cx² + dx + e = 0

By the fundamental theorem of algebra, every polynomial of degree n has n roots. The roots can be both real (in double) or Complex.

By default, all polynomial equations are solved using Jenkins-Traub algorithm. Customized solvers of various types, such as Linear, Quadratic, Cubic, Quartic, can be registered via the constructor.

By Abel–Ruffini theorem, we have analytical solution for polynomials of degree up to 4.

See Also:

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

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.polynomial.root.Solver

Solver.RootFindingException, Solver.Type

Constructor Summary

Polyroot(Solver... solvers)
Construct a Polyroot instance to solve polynomial equations.

Method Summary

NumberList	solve(Polynomial polynomial) Call the appropriate solver to find roots/zeros for the polynomial.
Solver.Type	type() Get the type of the solver.

Methods inherited from class java.lang.Object

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

Constructor Detail

Polyroot

public Polyroot(Solver... solvers)

Construct a Polyroot instance to solve polynomial equations.

Customized solver for a particular type of polynomial can be registered via the solvers argument. For example,

Polyroot solver = new Polyroot(new Cubic(), new Quartic());

The default polynomial solver, JenkinsTraubReal, can be used to solve any polynomial equations.

Parameters:

solvers - customized solver implementations

Method Detail

type

public Solver.Type type()

Description copied from interface: Solver

Get the type of the solver.

Specified by:

type in interface Solver

Returns:

the solver type

solve

public NumberList solve(Polynomial polynomial)

Call the appropriate solver to find roots/zeros for the polynomial.

Specified by:

solve in interface Solver

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 variable