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poly34.h
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poly34.h
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// 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
// 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