public static double[] Cubic(double A, double B, double C, double D)
{
if (A == 0)
return Quadratic(B, C, D);
double B_over_A = B / A;
double F, G, H;
F = ((3*C / A) - (System.Math.Pow(B_over_A, 2.0))) / 3;
G = ((2 * System.Math.Pow(B_over_A, 3.0)) - (9 * C * B_over_A / A) + (27 * D / A)) / 27;
double G_over_2 = -G / 2.0;
double G_over_2_sqrd = G_over_2 * G_over_2;
H = G_over_2_sqrd + (System.Math.Pow(F / 3.0, 3.0));
// Only one root is real.
if (H > 0)
{
double sqrt_H = System.Math.Sqrt(H);
double R, S, T, U;
R = G_over_2 + sqrt_H;
if (R < 0)
S = -System.Math.Pow(-R, 1.0 / 3.0);
else
S = System.Math.Pow(R, 1.0 / 3.0);
T = G_over_2 - sqrt_H;
if (T < 0)
U = -System.Math.Pow(-T, 1.0 / 3.0);
else
U = System.Math.Pow(T, 1.0 / 3.0);
double X = S + U - B_over_A / 3.0;
return new double[] { X };
}
// All 3 roots are real and equal.
else if (F == G && G == H && H == 0)
{
double D_A = D / A;
double X;
if (D_A < 0)
X = System.Math.Pow(-D_A, 1.0 / 3.0);
else
X = -System.Math.Pow(D_A, 1.0 / 3.0);
return new double[] { X };
}
// All 3 roots are real.
double I, J, K, L, M, N, P;
I = System.Math.Sqrt(G_over_2_sqrd - H);
J = System.Math.Pow(I, 1.0 / 3.0);
K = System.Math.Acos(-(G / (2 * I))) / 3.0;
L = -J;
M = System.Math.Cos(K);
N = System.Math.Sqrt(3) * System.Math.Sin(K);
P = -B_over_A / 3.0;
double X1, X2, X3;
X1 = 2*J*System.Math.Cos(K) + P;
X2 = L*(M + N) + P;
X3 = L*(M - N) + P;
var result = new double[] { X1, X2, X3 };
Array.Sort(result);
return result;
}
