poly34.h

Go to the documentation of this file.

// poly34.h : solution of cubic and quartic equation
// (c) Khashin S.I. http://math.ivanovo.ac.ru/dalgebra/Khashin/index.html
// khash2 (at) gmail.com
 
#ifndef POLY34_INCLUDED
#define POLY34_INCLUDED
 
namespace poly34
{
    // x - array of size 2
    // return 2: 2 real roots x[0], x[1]
    // return 0: pair of complex roots: x[0]±i*x[1]
    int SolveP2(double *x, double a, double b);         // solve equation x^2 + a*x + b = 0
 
    // x - array of size 3
    // return 3: 3 real roots x[0], x[1], x[2]
    // return 1: 1 real root x[0] and pair of complex roots: x[1]±i*x[2]
    int SolveP3(double *x, double a, double b, double c);           // solve cubic equation x^3 + a*x^2 + b*x + c = 0
 
    // x - array of size 4
    // return 4: 4 real roots x[0], x[1], x[2], x[3], possible multiple roots
    // return 2: 2 real roots x[0], x[1] and complex x[2]±i*x[3], 
    // return 0: two pair of complex roots: x[0]±i*x[1],  x[2]±i*x[3], 
    int SolveP4(double *x,double a,double b,double c,double d); // solve equation x^4 + a*x^3 + b*x^2 + c*x + d = 0 by Dekart-Euler method
 
    // x - array of size 5
    // return 5: 5 real roots x[0], x[1], x[2], x[3], x[4], possible multiple roots
    // return 3: 3 real roots x[0], x[1], x[2] and complex x[3]±i*x[4], 
    // return 1: 1 real root x[0] and two pair of complex roots: x[1]±i*x[2],  x[3]±i*x[4], 
    int SolveP5(double *x, double a, double b, double c, double d, double e);   // solve equation x^5 + a*x^4 + b*x^3 + c*x^2 + d*x + e = 0
 
    //-----------------------------------------------------------------------------
    // And some additional functions for internal use.
    // Your may remove this definitions from here
    int SolveP4Bi(double *x, double b, double d);               // solve equation x^4 + b*x^2 + d = 0
    int SolveP4De(double *x, double b, double c, double d); // solve equation x^4 + b*x^2 + c*x + d = 0
    void CSqrt( double x, double y, double &a, double &b);      // returns as a+i*s,  sqrt(x+i*y)
    double N4Step(double x, double a,double b,double c,double d);// one Newton step for x^4 + a*x^3 + b*x^2 + c *x + d
    double SolveP5_1(double a,double b,double c,double d,double e); // return real root of x^5 + a*x^4 + b*x^3 + c*x^2 + d*x + e = 0
}
#endif // POLY34_INCLUDED