Initial data commit

Task/Quaternion-type/Python/quaternion-type-1.py

@@ -0,0 +1,82 @@
+from collections import namedtuple
+import math
+
+class Q(namedtuple('Quaternion', 'real, i, j, k')):
+    'Quaternion type: Q(real=0.0, i=0.0, j=0.0, k=0.0)'
+
+    __slots__ = ()
+
+    def __new__(_cls, real=0.0, i=0.0, j=0.0, k=0.0):
+        'Defaults all parts of quaternion to zero'
+        return super().__new__(_cls, float(real), float(i), float(j), float(k))
+
+    def conjugate(self):
+        return Q(self.real, -self.i, -self.j, -self.k)
+
+    def _norm2(self):
+        return sum( x*x for x in self)
+
+    def norm(self):
+        return math.sqrt(self._norm2())
+
+    def reciprocal(self):
+        n2 = self._norm2()
+        return Q(*(x / n2 for x in self.conjugate()))
+
+    def __str__(self):
+        'Shorter form of Quaternion as string'
+        return 'Q(%g, %g, %g, %g)' % self
+
+    def __neg__(self):
+        return Q(-self.real, -self.i, -self.j, -self.k)
+
+    def __add__(self, other):
+        if type(other) == Q:
+            return Q( *(s+o for s,o in zip(self, other)) )
+        try:
+            f = float(other)
+        except:
+            return NotImplemented
+        return Q(self.real + f, self.i, self.j, self.k)
+
+    def __radd__(self, other):
+        return Q.__add__(self, other)
+
+    def __mul__(self, other):
+        if type(other) == Q:
+            a1,b1,c1,d1 = self
+            a2,b2,c2,d2 = other
+            return Q(
+                 a1*a2 - b1*b2 - c1*c2 - d1*d2,
+                 a1*b2 + b1*a2 + c1*d2 - d1*c2,
+                 a1*c2 - b1*d2 + c1*a2 + d1*b2,
+                 a1*d2 + b1*c2 - c1*b2 + d1*a2 )
+        try:
+            f = float(other)
+        except:
+            return NotImplemented
+        return Q(self.real * f, self.i * f, self.j * f, self.k * f)
+
+    def __rmul__(self, other):
+        return Q.__mul__(self, other)
+
+    def __truediv__(self, other):
+        if type(other) == Q:
+            return self.__mul__(other.reciprocal())
+        try:
+            f = float(other)
+        except:
+            return NotImplemented
+        return Q(self.real / f, self.i / f, self.j / f, self.k / f)
+
+    def __rtruediv__(self, other):
+        return other * self.reciprocal()
+
+    __div__, __rdiv__ = __truediv__, __rtruediv__
+
+Quaternion = Q
+
+q  = Q(1, 2, 3, 4)
+q1 = Q(2, 3, 4, 5)
+q2 = Q(3, 4, 5, 6)
+r  = 7

Task/Quaternion-type/Python/quaternion-type-2.py

@@ -0,0 +1,56 @@
+>>> q
+Quaternion(real=1.0, i=2.0, j=3.0, k=4.0)
+>>> q1
+Quaternion(real=2.0, i=3.0, j=4.0, k=5.0)
+>>> q2
+Quaternion(real=3.0, i=4.0, j=5.0, k=6.0)
+>>> r
+7
+>>> q.norm()
+5.477225575051661
+>>> q1.norm()
+7.3484692283495345
+>>> q2.norm()
+9.273618495495704
+>>> -q
+Quaternion(real=-1.0, i=-2.0, j=-3.0, k=-4.0)
+>>> q.conjugate()
+Quaternion(real=1.0, i=-2.0, j=-3.0, k=-4.0)
+>>> r + q
+Quaternion(real=8.0, i=2.0, j=3.0, k=4.0)
+>>> q + r
+Quaternion(real=8.0, i=2.0, j=3.0, k=4.0)
+>>> q1 + q2
+Quaternion(real=5.0, i=7.0, j=9.0, k=11.0)
+>>> q2 + q1
+Quaternion(real=5.0, i=7.0, j=9.0, k=11.0)
+>>> q * r
+Quaternion(real=7.0, i=14.0, j=21.0, k=28.0)
+>>> r * q
+Quaternion(real=7.0, i=14.0, j=21.0, k=28.0)
+>>> q1 * q2
+Quaternion(real=-56.0, i=16.0, j=24.0, k=26.0)
+>>> q2 * q1
+Quaternion(real=-56.0, i=18.0, j=20.0, k=28.0)
+>>> assert q1 * q2 != q2 * q1
+>>>
+>>> i, j, k = Q(0,1,0,0), Q(0,0,1,0), Q(0,0,0,1)
+>>> i*i
+Quaternion(real=-1.0, i=0.0, j=0.0, k=0.0)
+>>> j*j
+Quaternion(real=-1.0, i=0.0, j=0.0, k=0.0)
+>>> k*k
+Quaternion(real=-1.0, i=0.0, j=0.0, k=0.0)
+>>> i*j*k
+Quaternion(real=-1.0, i=0.0, j=0.0, k=0.0)
+>>> q1 / q2
+Quaternion(real=0.7906976744186047, i=0.023255813953488358, j=-2.7755575615628914e-17, k=0.046511627906976744)
+>>> q1 / q2 * q2
+Quaternion(real=2.0000000000000004, i=3.0000000000000004, j=4.000000000000001, k=5.000000000000001)
+>>> q2 * q1 / q2
+Quaternion(real=2.0, i=3.465116279069768, j=3.906976744186047, k=4.767441860465116)
+>>> q1.reciprocal() * q1
+Quaternion(real=0.9999999999999999, i=0.0, j=0.0, k=0.0)
+>>> q1 * q1.reciprocal()
+Quaternion(real=0.9999999999999999, i=0.0, j=0.0, k=0.0)
+>>>