theorem.js/src/includes/functions/math/algebra/findRoots.js

A Math library for computation in JavaScript

findRoots(f) {
    let exp = [];
    if (f.type == "polynomial") {
        switch (f.values.length - 1) {
            case 1: {
                exp.push(`${new BigNumber(f.values[1]).isNegative() ? '' : '-'}${f.values[1]} / ${f.values[0]}`)
                break;
			}
            case 2: {
				const delta = new BigNumber(f.values[1]).pow(2).minus(new BigNumber(4).times(f.values[0]).times(f.values[2])).toNumber()
				if (delta > 0) {
					exp.push(`(${new BigNumber(f.values[1]).isNegative() ? '' : '-'}${new BigNumber(f.values[1]).abs()} + Math.sqrt(${delta})) / ${new BigNumber(f.values[0]).times(2)}`)
	                exp.push(`(${new BigNumber(f.values[1]).isNegative() ? '' : '-'}${new BigNumber(f.values[1]).abs()} - Math.sqrt(${delta})) / ${new BigNumber(f.values[0]).times(2)}`)
				}
                break;
			}
            case 3: {
                let a = new BigNumber(f.values[0]).toNumber()
                let b = new BigNumber(f.values[1]).toNumber()
                let c = new BigNumber(f.values[2]).toNumber()
                let d = new BigNumber(f.values[3]).toNumber()

                // Convert to depressed cubic t^3+pt+q = 0 (subst x = t - b/3a)
                var p = (3 * a * c - b * b) / (3 * a * a);
                var q = (2 * b * b * b - 9 * a * b * c + 27 * a * a * d) / (27 * a * a * a);
                var roots;

                if (Math.abs(p) < 1e-8) { // p = 0 -> t^3 = -q -> t = -q^1/3
                    roots = [Math.cbrt(-q)];
                } else if (Math.abs(q) < 1e-8) { // q = 0 -> t^3 + pt = 0 -> t(t^2+p)=0
                    roots = [0].concat(p < 0 ? [Math.sqrt(-p), -Math.sqrt(-p)] : []);
                } else {
                    var D = q * q / 4 + p * p * p / 27;

					var u; // no-redeclare
                    if (Math.abs(D) < 1e-8) { // D = 0 -> two roots
                        roots = [-1.5 * q / p, 3 * q / p];
                    } else if (D > 0) { // Only one real root
                        u = Math.cbrt(-q / 2 - Math.sqrt(D));
                        roots = [u - p / (3 * u)];
                    } else { // D < 0, three roots, but needs to use complex numbers/trigonometric solution
                        u = 2 * Math.sqrt(-p / 3);
                        var t = Math.acos(3 * q / p / u) / 3; // D < 0 implies p < 0 and acos argument in [-1..1]
                        var k = 2 * Math.PI / 3;
                        roots = [u * Math.cos(t), u * Math.cos(t - k), u * Math.cos(t - 2 * k)];
                    }
                }

                // Convert back from depressed cubic
                for (var i = 0; i < roots.length; i++)
                    roots[i] -= b / (3 * a);
                exp = roots;
                break;
			}
            default: {
                exp = [this.numeralSolve(f, 0)[0]]
			}
        }
    } else {
        exp = [this.numeralSolve(f, 0)[0]]
    }
    return exp
}