org.matheclipse.core.polynomials

Class PolynomialsUtils

java.lang.Object

org.matheclipse.core.polynomials.PolynomialsUtils

public class PolynomialsUtils
extends java.lang.Object

A collection of static methods that operate on or return polynomials.

Since:

2.0

Version:

$Id: PolynomialsUtils.java 1517203 2013-08-24 21:55:35Z psteitz $

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	PolynomialsUtils.RecurrenceCoefficientsGenerator Interface for recurrence coefficients generation.

Method Summary

Modifier and Type	Method and Description
static IAST	buildPolynomial(int degree, IExpr x, java.util.List<org.apache.commons.math4.fraction.BigFraction> coefficients, PolynomialsUtils.RecurrenceCoefficientsGenerator generator) Get the coefficients array for a given degree.
static IAST	createChebyshevPolynomial(int degree, IExpr x) Create a Chebyshev polynomial of the first kind.
static IAST	createHermitePolynomial(int degree, IExpr x) Create a Hermite polynomial.
static IAST	createLaguerrePolynomial(int degree, IExpr x) Create a Laguerre polynomial.
static IAST	createLegendrePolynomial(int degree, IExpr x) Create a Legendre polynomial.

Methods inherited from class java.lang.Object

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

Method Detail

createChebyshevPolynomial

public static IAST createChebyshevPolynomial(int degree,
                                             IExpr x)

Create a Chebyshev polynomial of the first kind.

Chebyshev polynomials of the first kind are orthogonal polynomials. They can be defined by the following recurrence relations:

  T0(X)   = 1
  T1(X)   = X
  Tk+1(X) = 2X Tk(X) - Tk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Chebyshev polynomial of specified degree

createHermitePolynomial

public static IAST createHermitePolynomial(int degree,
                                           IExpr x)

Create a Hermite polynomial.

Hermite polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

  H0(X)   = 1
  H1(X)   = 2X
  Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Hermite polynomial of specified degree

createLaguerrePolynomial

public static IAST createLaguerrePolynomial(int degree,
                                            IExpr x)

Create a Laguerre polynomial.

Laguerre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

        L0(X)   = 1
        L1(X)   = 1 - X
  (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)
 

Parameters:

degree - degree of the polynomial

Returns:

Laguerre polynomial of specified degree

createLegendrePolynomial

public static IAST createLegendrePolynomial(int degree,
                                            IExpr x)

Create a Legendre polynomial.

Legendre polynomials are orthogonal polynomials. They 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)
 

Parameters:

degree - degree of the polynomial

Returns:

Legendre polynomial of specified degree

buildPolynomial

public static IAST buildPolynomial(int degree,
                                   IExpr x,
                                   java.util.List<org.apache.commons.math4.fraction.BigFraction> coefficients,
                                   PolynomialsUtils.RecurrenceCoefficientsGenerator generator)

Get the coefficients array for a given degree.

Parameters:

degree - degree of the polynomial

coefficients - list where the computed coefficients are stored

generator - recurrence coefficients generator

Returns:

coefficients array