#!/usr/bin/env node;
/******************************************************************************
 * 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.
 *****************************************************************************/

const A = 1.0;
const B = -6.0;
const C = 11.0;
const D = -6.0;

const main = async () => {
/******************************************************************************
 * General cubic can be changed to a depressed cubic 
 * t^3 + pt + q = 0
 * by substituting
 * x = t - B / 3A
 *****************************************************************************/

    let p = (3. * A * C - B * B) / (3. * A * A);
    let 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))
 *****************************************************************************/
    let a = 2. * Math.sqrt(-p / 3.);
    let b = (1. / 3.) * Math.acos(3. * q / 2. / p * Math.sqrt(-3. / p));

    let t1 = a * Math.cos(b);
    let t2 = a * Math.cos(b - 2. * Math.PI / 3.);
    let t3 = a * Math.cos(b - 4. * Math.PI / 3.);
    let root1 = t1 - B / (3. * A);
    let root2 = t2 - B / (3. * A);
    let root3 = t3 - B / (3. * A);
    console.log(["root #1: ", root1].join(''));
    console.log(["root #2: ", root2].join(''));
    console.log(["root #3: ", root3].join(''));
}
main().catch( e => { console.error(e) } );