Task: Quaternion type




Go: package main

import (
    "fmt"
    "math"
)

type qtn struct {
    r, i, j, k float64
}

var (
    q  = &qtn{1, 2, 3, 4}
    q1 = &qtn{2, 3, 4, 5}
    q2 = &qtn{3, 4, 5, 6}

    r  float64 = 7
)

func main() {
    fmt.Println("Inputs")
    fmt.Println("q:", q)
    fmt.Println("q1:", q1)
    fmt.Println("q2:", q2)
    fmt.Println("r:", r)

    var qr qtn
    fmt.Println("\nFunctions")
    fmt.Println("q.norm():", q.norm())
    fmt.Println("neg(q):", qr.neg(q))
    fmt.Println("conj(q):", qr.conj(q))
    fmt.Println("addF(q, r):", qr.addF(q, r))
    fmt.Println("addQ(q1, q2):", qr.addQ(q1, q2))
    fmt.Println("mulF(q, r):", qr.mulF(q, r))
    fmt.Println("mulQ(q1, q2):", qr.mulQ(q1, q2))
    fmt.Println("mulQ(q2, q1):", qr.mulQ(q2, q1))
}

func (q *qtn) String() string {
    return fmt.Sprintf("(%g, %g, %g, %g)", q.r, q.i, q.j, q.k)
}

func (q *qtn) norm() float64 {
    return math.Sqrt(q.r*q.r + q.i*q.i + q.j*q.j + q.k*q.k)
}

func (z *qtn) neg(q *qtn) *qtn {
    z.r, z.i, z.j, z.k = -q.r, -q.i, -q.j, -q.k
    return z
}

func (z *qtn) conj(q *qtn) *qtn {
    z.r, z.i, z.j, z.k = q.r, -q.i, -q.j, -q.k
    return z
}

func (z *qtn) addF(q *qtn, r float64) *qtn {
    z.r, z.i, z.j, z.k = q.r+r, q.i, q.j, q.k
    return z
}

func (z *qtn) addQ(q1, q2 *qtn) *qtn {
    z.r, z.i, z.j, z.k = q1.r+q2.r, q1.i+q2.i, q1.j+q2.j, q1.k+q2.k
    return z
}

func (z *qtn) mulF(q *qtn, r float64) *qtn {
    z.r, z.i, z.j, z.k = q.r*r, q.i*r, q.j*r, q.k*r
    return z
}

func (z *qtn) mulQ(q1, q2 *qtn) *qtn {
    z.r, z.i, z.j, z.k =
        q1.r*q2.r-q1.i*q2.i-q1.j*q2.j-q1.k*q2.k,
        q1.r*q2.i+q1.i*q2.r+q1.j*q2.k-q1.k*q2.j,
        q1.r*q2.j-q1.i*q2.k+q1.j*q2.r+q1.k*q2.i,
        q1.r*q2.k+q1.i*q2.j-q1.j*q2.i+q1.k*q2.r
    return z
}




Python: 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