import numpy as np
import quaternion



# Create a quaternion: 1 + 2i + 3j + 4k
q1 = np.quaternion(1, 2, 0, 0)
q2 = np.quaternion(2, 1, 0, 0)
print(f"Quaternion q1:{q1} q2:{q2}")
mq = q1 * q2
print("Quaternion mq:", mq)

q1 = np.quaternion(1, 1, 0, 0)
q2 = np.quaternion(2, 0, 1, 0)
print(f"Quaternion q1:{q1} q2:{q2}")
mq = q1 * q2
print("Quaternion mq:", mq)

q3 = np.quaternion(1,1,0,0)
q4 = 1/q3

print(f"Quaternion q3:{q3} q4:{q4}")

q5 = np.quaternion(0,1,1,0)
q6 = 1/q5

print(f"Quaternion q5:{q5} q6:{q6}")


# Rotation quaternion (example: 90-degree rotation around the z-axis)
angle = np.pi / 2  # 90 degrees in radians
rotation_q = np.quaternion(np.cos(angle / 2), 0, 0, np.sin(angle / 2))

q7 = np.quaternion(0,1,2,3)
q8 =   rotation_q * q7
q9 =   q8 * rotation_q.conj()
print(f"q7:{q7}\nq8:{q8}\nq9:{q9}")


q10 =  rotation_q * q7 * rotation_q.conj() # rotate in one line
print(f" q10 {q10} ")