Octic Class Reference

Octic polynomials. More...

#include <nonic.h>

Public Member Functions
	Octic ()
	Empty.
	Octic (const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &, const double &)
	Creates a Octic polynomial.
	~Octic ()
	Empty.
constexpr double &	operator[] (int)
	Access to the coefficients of the sextic.
constexpr double	operator[] (int) const
	Overloaded.
int	CheckDegree () const
	Check the degree of the octic.
Octic	operator- () const
	Unary.
Octic &	operator+= (const Octic &)
	Destructive sum of two octics.
Octic &	operator-= (const Octic &)
	Destructive difference of two octics.
Octic &	operator*= (const double &)
	Scale an octic by a double value.
Octic &	operator/= (const double &)
	Scale an octic by a double value.
int	Solve (double *) const
	Solve the octic equation over a given interval.
Septic	Prime () const
	Computes the first derivative of a Octic.
Sextic	Second () const
	Computes the second derivative of a Octic.
Quintic	Third () const
	Computes the third derivative of a Octic.
constexpr double	operator() (const double &) const
	Evaluates the Octic.
constexpr double	Derivative (const double &) const
	Computes the derivative of the sextic.

Static Public Attributes
static double	epsilon = 1.0e-10
	Epsilon value used to check discriminant terms in the root finding process.

Protected Attributes
double	c [9] = { 0.0 }
	Array of coefficients.

Friends
Octic	operator+ (const Octic &u, const Octic &v)
	Overloaded.
Octic	operator- (const Octic &v, const Octic &u)
	Overloaded.
Octic	operator* (const Octic &u, const double &e)
	Overloaded.
Octic	operator* (const double &a, const Octic &p)
	Overloaded.
Octic	operator/ (const Octic &p, const double &a)
	Overloaded.
Octic	operator* (const Quartic &u, const Quartic &v)
	Multiply two quartics.
Octic	operator* (const Sextic &s, const Quadric &q)
	Multiply a sextic by a quadric.
std::ostream &	operator<< (std::ostream &s, const Octic &p)
	Overloaded output-stream operator.

Detailed Description

Octic polynomials.

Constructors should provide the coefficients in descending order. Example of how to code the octic 19x⁸-x+1:

Octic p(19.0,0.0,0.0,0.0,0.0,0.0,-1.0,1.0);

Member Function Documentation

Derivative()

double Octic::Derivative ( const double & x ) const

inlineconstexpr

Computes the derivative of the sextic.

This function is more efficient than using Prime() and then evaluating the derivative for a given input value.

Parameters

x

Real.

operator()()

double Octic::operator() ( const double & x ) const

inlineconstexpr

Evaluates the Octic.

Parameters

x	Argument value of the function.

Solve()

int Octic::Solve

(

double *

roots

)

const

Solve the octic equation over a given interval.

Parameters

roots

Roots.

Friends And Related Symbol Documentation

operator* [1/2]

Octic operator* ( const Quartic & u, const Quartic & v )

friend

Multiply two quartics.

Parameters

u,v	Argument quartics.

operator* [2/2]

Octic operator* ( const Sextic & s, const Quadric & q )

friend

Multiply a sextic by a quadric.

Parameters

s	Sextic.
q	Quadric.

operator<<

std::ostream & operator<< ( std::ostream & s, const Octic & p )

friend

Overloaded output-stream operator.

Parameters

s	Stream.
p	The Octic.