Polynomial

Collaboration diagram for Polynomial:

Functions
int	PolynomialDifferentiation (double a[], long Degree, double b[])
int	PolynomialEvaluation (double x, double a[], long Degree, double *Result)
int	PolynomialMultiplication (double a1[], long Degree1, double a2[], long Degree2, double b[])
int	PolynomialPrimitive (double a[], long Degree, double b[])
int	PolynomialRealRoots (double a[], long Degree, double RealRoot[], long *RealRootNumber, double Tolerance, int *Status)
double	Sign (double x)
double	xPlus (double x, double p)

Detailed Description

Function Documentation

PolynomialDifferentiation()

int PolynomialDifferentiation	(	double	a[],
		long	Degree,
		double	b[]
	)

Differentiation of the polynomial p(x) = (a[0] + Sum a[k] x^k). The degree of the input polynomial is Degree. There are (Degree+1) input coefficients. The degree of the output polynomial is (Degree-1). There are Degree output coefficients.

success: return(!ERROR); failure: return(ERROR)

PolynomialEvaluation()

int PolynomialEvaluation	(	double	x,
		double	a[],
		long	Degree,
		double *	Result
	)

Evaluates a polynomial: result = a[0] + Sum a[k] x^k. The degree of the polynomial is Degree. There are (Degree+1) coefficients.

success: return(!ERROR); failure: return(ERROR)

PolynomialMultiplication()

int PolynomialMultiplication	(	double	a1[],
		long	Degree1,
		double	a2[],
		long	Degree2,
		double	b[]
	)

Polynomial multuplication. Multiplication resulting in b[0] + Sum b[k] x^k = (a1[0] + Sum a1[k] x^k) (a2[0] + Sum a2[k] x^k).

The degree of the 1st input polynomial is Degree1. The degree of the 2nd input polynomial is Degree2. There are (Degree1+1) input coefficients for the first multiplicand. There are (Degree2+1) input coefficients for the second multiplicand. The degree of the output polynomial is (Degree1+Degree2). There are (Degree1+Degree2+1) output coefficients.

success: return(!ERROR); failure: return(ERROR)

PolynomialPrimitive()

int PolynomialPrimitive	(	double	a[],
		long	Degree,
		double	b[]
	)

Primitive of the polynomial p(t) = (a[0] + Sum a[k] t^k). The degree of the input polynomial is Degree. There are (Degree+1) input coefficients. The degree of the output polynomial is (Degree+1). There are (Degree+2) output coefficients.

success: return(!ERROR); failure: return(ERROR)

PolynomialRealRoots()

int PolynomialRealRoots	(	double	a[],
		long	Degree,
		double	RealRoot[],
		long *	RealRootNumber,
		double	Tolerance,
		int *	Status
	)

Find the real roots of the polynomial p(x) = (a[0] + Sum a[k] x^k). The degree of the polynomial is Degree. There are (Degree+1) input coefficients (a[]). The output array (RealRoot[]) must have size (Degree). Only the first (RealRootNumber) roots returned in RealRoot[] are valid. (RealRootNumber) -> -1 when the equation is indeterminate. The returned roots are sorted in ascendent order.

success: return(!ERROR); failure: return(ERROR)

Sign()

double Sign

(

double

x

)

Returns the sign of x with Sign(0) = 0.

xPlus()

double xPlus	(	double	x,
		double	p
	)

Computes the one-sided power function. xPlus(0, 0) = 1/2