Quaternion Comparison?

Question

Is quaternion comparison possible? I'm writing a Java class of Quaternions and I want to implement the Comparable interface to use the Collections.sort(List<Quaternion>) facility. I'm not expert at math, I really don't understand the things I read about Quaternions. So, can anyone tell me can I override the compareTo method for Quaternions and how?

My class declarition:

public class Quaternion implements Serializable, Comparable<Quaternion> {

    private double s; // scalar part
    private double i, j, k; // vectorel part


    public Quaternion() {
        super();
    }

    public Quaternion(double s, double i, double j, double k) {
        super();
        this.s = s;
        this.i = i;
        this.j = j;
        this.k = k;
    }

Answer 1

You can implement compareTo, by comparing its fields. However, you need to determine what you want the order to be like. AFAIK, there is no standard definition of what comes before or after for complex numbers let alone a quaternion.