from aquaternion import *

Q([0, 1, 2, 3])
# The four numbers correspond to the w, x, y, and z components respectively.

# Creating a quaternion with only three numbers will assign the values to the x, y, and z (imaginary) components,
# and leave w with the default value of 0
Q([1, 2, 3])

q1 = Q([-7, 2, 9])
q2 = Q([4, -1, -5])

print(q1 + q2)
print(q1 * q2)
print(Q([0, 3, 4]).norm)

q = Q([1, 2, 3])

# This coordinate system is rotated tau/3 radians around the Q([1, 1, 1]) axis, compared to the standard i, j, k unit vectors.
new_unit_vectors = UnitVectors([qj, qk, qi])

# This will be equal to Q([3, 1, 2])
q_prime = q.morphed(*new_unit_vectors)

# This will create an unmorphed q_prime, and will be equal to q, Q([1, 2, 3])
original_q = q_prime.unmorphed(*new_unit_vectors)