make a quaternion calculator that can divide in python

main.py
q = w + xi + yj + zk
21 chars
2 lines

main.py
q3 = q1 * q2^-1
16 chars
2 lines

main.py
import math

class Quaternion:
    def __init__(self, w=0, x=0, y=0, z=0):
        self.w = w
        self.x = x
        self.y = y
        self.z = z
        
    def __repr__(self):
        return f"{self.w} + {self.x}i + {self.y}j + {self.z}k"
    
    def __mul__(self, other):
        if isinstance(other, Quaternion):
            w = self.w*other.w - self.x*other.x - self.y*other.y - self.z*other.z
            x = self.w*other.x + self.x*other.w + self.y*other.z - self.z*other.y
            y = self.w*other.y - self.x*other.z + self.y*other.w + self.z*other.x
            z = self.w*other.z + self.x*other.y - self.y*other.x + self.z*other.w
            return Quaternion(w, x, y, z)
        else:
            return NotImplemented
        
    def __truediv__(self, other):
        if isinstance(other, Quaternion):
            return self*(other.inverse())
        else:
            return NotImplemented
        
    def inverse(self):
        norm_squared = self.w**2 + self.x**2 + self.y**2 + self.z**2
        if norm_squared != 0:
            return Quaternion(self.w/norm_squared, -self.x/norm_squared, -self.y/norm_squared, -self.z/norm_squared)
        else:
            raise ZeroDivisionError("Cannot invert a quaternion with zero norm")
1260 chars
35 lines

main.py
q1 * q2 = (w1w2 - x1x2 - y1y2 - z1z2) + (w1x2 + x1w2 + y1z2 - z1y2)i + (w1y2 - x1z2 + y1w2 + z1x2)j + (w1z2 + x1y2 - y1x2 + z1w2)k
131 chars
2 lines

main.py
q3 = q1 * q2^-1
16 chars
2 lines

main.py
q^-1 = (w/norm_squared) - (x/norm_squared)i - (y/norm_squared)j - (z/norm_squared)k
84 chars
2 lines