/******************************************************************************
 * This program computes the roots of cubic equations
 * of the form Ax^3 + Bx^2 + Cx + D = 0
 * 
 * Copyright © 2020 Richard Lesh.  All rights reserved.
 *****************************************************************************/

import org.pureprogrammer.Utils;

public class CubicRoots {

    static final double A = 1.0;
    static final double B = -6.0;
    static final double C = 11.0;
    static final double D = -6.0;

    public static void main(String[] args) {
/******************************************************************************
 * General cubic can be changed to a depressed cubic 
 * t^3 + pt + q = 0
 * by substituting
 * x = t - B / 3A
 *****************************************************************************/

        double p = (3. * A * C - B * B) / (3. * A * A);
        double q = (2. * B * B * B - 9. * A * B * C + 27. * A * A * D) / (27. * A * A * A);

/******************************************************************************
 * Roots of the depressed cubic are...
 * tk = a cos(b - 2πk/3) for k = 0, 1, 2
 * with a = 2 sqrt(-p/3)
 * b = (1/3) arccos(3q/2p * sqrt(-3/p))
 *****************************************************************************/
        double a = 2. * Math.sqrt(-p / 3.);
        double b = (1. / 3.) * Math.acos(3. * q / 2. / p * Math.sqrt(-3. / p));

        double t1 = a * Math.cos(b);
        double t2 = a * Math.cos(b - 2. * Math.PI / 3.);
        double t3 = a * Math.cos(b - 4. * Math.PI / 3.);
        double root1 = t1 - B / (3. * A);
        double root2 = t2 - B / (3. * A);
        double root3 = t3 - B / (3. * A);
        System.out.println(Utils.join("", "root #1: ", root1));
        System.out.println(Utils.join("", "root #2: ", root2));
        System.out.println(Utils.join("", "root #3: ", root3));
    }
}