March 2014 update

Task/Quaternion-type/JavaScript/quaternion-type-1.js

@@ -0,0 +1,58 @@
+var Quaternion = (function() {
+    // The Q() function takes an array argument and changes it
+    // prototype so that it becomes a Quaternion instance.  This is
+    // scoped only for prototype member access.
+    function Q(a) {
+	a.__proto__ = proto;
+	return a;
+    }
+
+    // Actual constructor.  This constructor converts its arguments to
+    // an array, then that array to a Quaternion instance, then
+    // returns that instance.  (using "new" with this constructor is
+    // optional)
+    function Quaternion() {
+	return Q(Array.prototype.slice.call(arguments, 0, 4));
+    }
+
+    // Prototype for all Quaternions
+    const proto = {
+	// Inherits from a 4-element Array
+	__proto__ : [0,0,0,0],
+
+	// Properties -- In addition to Array[0..3] access, we
+	// also define matching a, b, c, and d properties
+	get a() this[0],
+	get b() this[1],
+	get c() this[2],
+	get d() this[3],
+
+	// Methods
+	norm : function() Math.sqrt(this.map(function(x) x*x).reduce(function(x,y) x+y)),
+	negate : function() Q(this.map(function(x) -x)),
+	conjugate : function() Q([ this[0] ].concat(this.slice(1).map(function(x) -x))),
+	add : function(x) {
+	    if ("number" === typeof x) {
+		return Q([ this[0] + x ].concat(this.slice(1)));
+	    } else {
+		return Q(this.map(function(v,i) v+x[i]));
+	    }
+	},
+	mul : function(r) {
+	    var q = this;
+	    if ("number" === typeof r) {
+		return Q(q.map(function(e) e*r));
+	    } else {
+		return Q([ q[0] * r[0] - q[1] * r[1] - q[2] * r[2] - q[3] * r[3],
+			   q[0] * r[1] + q[1] * r[0] + q[2] * r[3] - q[3] * r[2],
+			   q[0] * r[2] - q[1] * r[3] + q[2] * r[0] + q[3] * r[1],
+			   q[0] * r[3] + q[1] * r[2] - q[2] * r[1] + q[3] * r[0] ]);
+	    }
+	},
+	equals : function(q) this.every(function(v,i) v === q[i]),
+	toString : function() (this[0] + " + " + this[1] + "i + "+this[2] + "j + " + this[3] + "k").replace(/\+ -/g, '- ')
+    };
+
+    Quaternion.prototype = proto;
+    return Quaternion;
+})();

Task/Quaternion-type/JavaScript/quaternion-type-2.js

@@ -0,0 +1,18 @@
+var q = Quaternion(1,2,3,4);
+var q1 = Quaternion(2,3,4,5);
+var q2 = Quaternion(3,4,5,6);
+var r = 7;
+
+console.log("q = "+q);
+console.log("q1 = "+q1);
+console.log("q2 = "+q2);
+console.log("r = "+r);
+console.log("1. q.norm() = "+q.norm());
+console.log("2. q.negate() = "+q.negate());
+console.log("3. q.conjugate() = "+q.conjugate());
+console.log("4. q.add(r) = "+q.add(r));
+console.log("5. q1.add(q2) = "+q1.add(q2));
+console.log("6. q.mul(r) = "+q.mul(r));
+console.log("7.a. q1.mul(q2) = "+q1.mul(q2));
+console.log("7.b. q2.mul(q1) = "+q2.mul(q1));
+console.log("8. q1.mul(q2) " + (q1.mul(q2).equals(q2.mul(q1)) ? "==" : "!=") + " q2.mul(q1)");