make a quaternion calculator in python

main.py
import numpy as np

class Quaternion:
    
    def __init__(self, scalar, x, y, z):
        self.scalar = scalar
        self.vector = np.array([x, y, z])
    
    def __repr__(self):
        return f'{self.scalar} + {self.vector[0]}i + {self.vector[1]}j + {self.vector[2]}k'
    
    def __add__(self, other):
        return Quaternion(self.scalar + other.scalar, self.vector[0] + other.vector[0], self.vector[1] + other.vector[1], self.vector[2] + other.vector[2])
    
    def __sub__(self, other):
        return Quaternion(self.scalar - other.scalar, self.vector[0] - other.vector[0], self.vector[1] - other.vector[1], self.vector[2] - other.vector[2])
    
    def __mul__(self, other):
        if isinstance(other, Quaternion):
            scalar = self.scalar * other.scalar - np.dot(self.vector, other.vector)
            vector = self.scalar * other.vector + other.scalar * self.vector + np.cross(self.vector, other.vector)
            return Quaternion(scalar, vector[0], vector[1], vector[2])
        else:
            return Quaternion(other * self.scalar, other * self.vector[0], other * self.vector[1], other * self.vector[2])
    
    def __rmul__(self, other):
        return self.__mul__(other)
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main.py
q1 = Quaternion(1, 2, 3, 4)
q2 = Quaternion(5, 6, 7, 8)
print(q1 + q2)  # prints 6.0 + 8.0i + 10.0j + 12.0k
print(q1 - q2)  # prints -4.0 - 4.0i - 4.0j - 4.0k
print(q1 * q2)  # prints -60.0 + 12.0i + 30.0j + 24.0k
print(q1 * 2)   # prints 2.0 + 4.0i + 6.0j + 8.0k
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