Data update

Task/Quaternion-type/Dart/quaternion-type.dart

@@ -0,0 +1,63 @@
+import 'dart:math' as math;
+
+class Quaternion {
+  final double a, b, c, d;
+
+  Quaternion(this.a, this.b, this.c, this.d);
+
+  Quaternion operator +(Object other) {
+    if (other is Quaternion) {
+      return Quaternion(a + other.a, b + other.b, c + other.c, d + other.d);
+    } else if (other is double) {
+      return Quaternion(a + other, b, c, d);
+    }
+    throw ArgumentError('Invalid type for addition: ${other.runtimeType}');
+  }
+
+  Quaternion operator *(Object other) {
+    if (other is Quaternion) {
+      return Quaternion(
+        a * other.a - b * other.b - c * other.c - d * other.d,
+        a * other.b + b * other.a + c * other.d - d * other.c,
+        a * other.c - b * other.d + c * other.a + d * other.b,
+        a * other.d + b * other.c - c * other.b + d * other.a,
+      );
+    } else if (other is double) {
+      return Quaternion(a * other, b * other, c * other, d * other);
+    }
+    throw ArgumentError('Invalid type for multiplication: ${other.runtimeType}');
+  }
+
+  Quaternion operator -() => Quaternion(-a, -b, -c, -d);
+
+  Quaternion conj() => Quaternion(a, -b, -c, -d);
+
+  double norm() => math.sqrt(a * a + b * b + c * c + d * d);
+
+  @override
+  String toString() => '($a, $b, $c, $d)';
+}
+
+void main() {
+  var q  = Quaternion(1.0, 2.0, 3.0, 4.0);
+  var q1 = Quaternion(2.0, 3.0, 4.0, 5.0);
+  var q2 = Quaternion(3.0, 4.0, 5.0, 6.0);
+  var r  = 7.0;
+  print("q  = $q");
+  print("q1 = $q1");
+  print("q2 = $q2");
+  print("r  = $r\n");
+  print("norm(q) = ${q.norm().toStringAsFixed(6)}");
+  print("-q      = ${-q}");
+  print("conj(q) = ${q.conj()}\n");
+  print("r  + q  = ${q + r}");
+  print("q  + r  = ${q + r}");
+  print("q1 + q2 = ${q1 + q2}\n");
+  print("r  * q  = ${q * r}");
+  print("q  * r  = ${q * r}");
+  var q3 = q1 * q2;
+  var q4 = q2 * q1;
+  print("q1 * q2 = $q3");
+  print("q2 * q1 = $q4\n");
+  print("q1 * q2 != q2 * q1 = ${q3 != q4}");
+}

Task/Quaternion-type/EasyLang/quaternion-type.easy

@@ -0,0 +1,61 @@
+func qnorm q[] .
+   for i to 4
+      s += q[i] * q[i]
+   .
+   return sqrt s
+.
+func[] qneg q[] .
+   for i to 4
+      q[i] = -q[i]
+   .
+   return q[]
+.
+func[] qconj q[] .
+   for i = 2 to 4
+      q[i] = -q[i]
+   .
+   return q[]
+.
+func[] qaddreal q[] r .
+   q[1] += r
+   return q[]
+.
+func[] qadd q[] q2[] .
+   for i to 4
+      q[i] += q2[i]
+   .
+   return q[]
+.
+func[] qmulreal q[] r .
+   for i to 4
+      q[i] *= r
+   .
+   return q[]
+.
+func[] qmul q1[] q2[] .
+   res[] &= q1[1] * q2[1] - q1[2] * q2[2] - q1[3] * q2[3] - q1[4] * q2[4]
+   res[] &= q1[1] * q2[2] + q1[2] * q2[1] + q1[3] * q2[4] - q1[4] * q2[3]
+   res[] &= q1[1] * q2[3] - q1[2] * q2[4] + q1[3] * q2[1] + q1[4] * q2[2]
+   res[] &= q1[1] * q2[4] + q1[2] * q2[3] - q1[3] * q2[2] + q1[4] * q2[1]
+   return res[]
+.
+q[] = [ 1 2 3 4 ]
+q1[] = [ 2 3 4 5 ]
+q2[] = [ 3 4 5 6 ]
+r = 7
+#
+print "q = " & q[]
+print "q1 = " & q1[]
+print "q2 = " & q2[]
+print "r = " & r
+print "norm(q) = " & qnorm q[]
+print "neg(q) = " & qneg q[]
+print "conjugate(q) = " & qconj q[]
+print "q+r = " & qaddreal q[] r
+print "q1+q2 = " & qadd q1[] q2[]
+print "qr = " & qmulreal q[] r
+print "q1q2 = " & qmul q1[] q2[]
+print "q2q1 = " & qmul q2[] q1[]
+if q1[] <> q2[]
+   print "q1 != q2"
+.