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 a Octics by a double value.
Octic &	operator/= (const double &)
	Scale a Octics by a double value.
Sextic	Second () const
	Computes the second derivative of a Octic.
constexpr double	operator() (const double &) const
	Evaluates the Octic. More...
constexpr double	Derivative (const double &) const
	Computes the derivative of the sextic. More...

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 &, const Octic &)
	Overloaded.
Octic	operator- (const Octic &, const Octic &)
	Overloaded.
Octic	operator* (const Octic &, const double &)
	Overloaded.
Octic	operator* (const double &, const Octic &)
	Overloaded.
Octic	operator/ (const Octic &, const double &)
	Overloaded.
Octic	operator* (const Quartic &, const Quartic &)
	Multiply two quartics. More...
std::ostream &	operator<< (std::ostream &, const Octic &)
	Overloaded output-stream operator. More...

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()

constexpr 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()()

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

inlineconstexpr

Evaluates the Octic.

Parameters

x	Argument value of the function.

Friends And Related Function Documentation

operator*

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

friend

Multiply two quartics.

Parameters

u,v	Argument quartics.

operator<<

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

friend

Overloaded output-stream operator.

Parameters

s	Stream.
p	The Octic.