org.spaceroots.mantissa.algebra
Class Legendre

java.lang.Object
  org.spaceroots.mantissa.algebra.Polynomial
      org.spaceroots.mantissa.algebra.Polynomial.Rational
          org.spaceroots.mantissa.algebra.OrthogonalPolynomial
              org.spaceroots.mantissa.algebra.Legendre

All Implemented Interfaces:

Serializable

public class Legendre

extends OrthogonalPolynomial

This class implements Legendre polynomials.

Legendre polynomials can be defined by the following recurrence relations:

        P0(X)   = 1
        P1(X)   = X
  (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)
 

Version:

$Id: Legendre.java 1709 2006-12-03 21:16:50Z luc $

Author:

L. Maisonobe

See Also:

Serialized Form

Nested Class Summary

Nested classes inherited from class org.spaceroots.mantissa.algebra.Polynomial

Polynomial.DivisionResult, Polynomial.Double, Polynomial.Rational

Field Summary

Fields inherited from class org.spaceroots.mantissa.algebra.Polynomial.Rational

a

Constructor Summary

Legendre()
Simple constructor.

Legendre(int degree)
Simple constructor.

Methods inherited from class org.spaceroots.mantissa.algebra.Polynomial.Rational

add, euclidianDivision, getCoefficients, getDegree, getDenominatorsLCM, getDerivative, isIdentity, isOne, isZero, multiply, multiply, multiply, negate, subtract, toString, valueAt

Methods inherited from class org.spaceroots.mantissa.algebra.Polynomial

divide, divide, divide, multiply

Methods inherited from class java.lang.Object

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

Constructor Detail

Legendre

public Legendre()

Simple constructor. Build a degree 0 Legendre polynomial

Legendre

public Legendre(int degree)

Simple constructor. Build a degree d Legendre polynomial

Parameters:

degree - degree of the polynomial