quaternions.py

from sympy.algebras.quaternion import Quaternion
from sympy import latex, Matrix, symbols

i, j, k = symbols('i j k')

def display(q):
    return sum([
        x*y
        for x, y in [(q.a, 1),
                     (q.b, i),
                     (q.c, j),
                     (q.d, k)]
    ])
t = [Quaternion(1,0,0,0), Quaternion(-1,0,0,0),
     Quaternion(0,1,0,0), Quaternion(0,-1,0,0),
     Quaternion(0,0,1,0), Quaternion(0,0,-1,0),
     Quaternion(0,0,0,1), Quaternion(0,0,0,-1)]

m = [[display(b)] + [display(b*a) for a in t] for b in t]
m = [[None] + [display(i) for i in t]] + m
print(latex(Matrix(m)).replace(r'\\', '\\\\\n'))