March 2014 update

Task/Quaternion-type/AutoHotkey/quaternion-type.ahk

@@ -0,0 +1,72 @@
+q  := [1, 2, 3, 4]
+q1 := [2, 3, 4, 5]
+q2 := [3, 4, 5, 6]
+r := 7
+
+MsgBox, % "q = " PrintQ(q)
+	. "`nq1 = " PrintQ(q1)
+	. "`nq2 = " PrintQ(q2)
+	. "`nr = " r
+	. "`nNorm(q) = " Norm(q)
+	. "`nNegative(q) = " PrintQ(Negative(q))
+	. "`nConjugate(q) = " PrintQ(Conjugate(q))
+	. "`nq + r = " PrintQ(AddR(q, r))
+	. "`nq1 + q2 = " PrintQ(AddQ(q1, q2))
+	. "`nq2 + q1 = " PrintQ(AddQ(q2, q1))
+	. "`nqr = " PrintQ(MulR(q, r))
+	. "`nq1q2 = " PrintQ(MulQ(q1, q2))
+	. "`nq2q1 = " PrintQ(MulQ(q2, q1))
+
+Norm(q) {
+	return sqrt(q[1]**2 + q[2]**2 + q[3]**2 + q[4]**2)
+}
+
+Negative(q) {
+	a := []
+	for k, v in q
+		a[A_Index] := v * -1
+	return a
+}
+
+Conjugate(q) {
+	a := []
+	for k, v in q
+		a[A_Index] := v * (A_Index = 1 ? 1 : -1)
+	return a
+}
+
+AddR(q, r) {
+	a := []
+	for k, v in q
+		a[A_Index] := v + (A_Index = 1 ? r : 0)
+	return a
+}
+
+AddQ(q1, q2) {
+	a := []
+	for k, v in q1
+		a[A_Index] := v + q2[A_Index]
+	return a
+}
+
+MulR(q, r) {
+	a := []
+	for k, v in q
+		a[A_Index] := v * r
+	return a
+}
+
+MulQ(q, u) {
+	a := []
+	, a[1] := q[1]*u[1] - q[2]*u[2] - q[3]*u[3] - q[4]*u[4]
+	, a[2] := q[1]*u[2] + q[2]*u[1] + q[3]*u[4] - q[4]*u[3]
+	, a[3] := q[1]*u[3] - q[2]*u[4] + q[3]*u[1] + q[4]*u[2]
+	, a[4] := q[1]*u[4] + q[2]*u[3] - q[3]*u[2] + q[4]*u[1]
+	return a
+}
+
+PrintQ(q, b="(") {
+	for k, v in q
+		b .= v (A_Index = q.MaxIndex() ? ")" : ", ")
+	return b
+}

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)");

Task/Quaternion-type/Octave/quaternion-type-1.octave

@@ -0,0 +1 @@
+pkg install -forge quaternion

Task/Quaternion-type/Octave/quaternion-type-2.octave

@@ -0,0 +1,24 @@
+> q = quaternion (1, 2, 3, 4)
+q = 1 + 2i + 3j + 4k
+>  q1 = quaternion (2, 3, 4, 5)
+q1 = 2 + 3i + 4j + 5k
+> q2 = quaternion (3, 4, 5, 6)
+q2 = 3 + 4i + 5j + 6k
+> r = 7
+r =  7
+> norm(q)
+ans =  5.4772
+> -q
+ans = -1 - 2i - 3j - 4k
+> conj(q)
+ans = 1 - 2i - 3j - 4k
+> q + r
+ans = 8 + 2i + 3j + 4k
+> q1 + q2
+ans = 5 + 7i + 9j + 11k
+> q * r
+ans = 7 + 14i + 21j + 28k
+> q1 * q2
+ans = -56 + 16i + 24j + 26k
+> q1 == q2
+ans = 0