def anti(a, b): q1 = motions[a] q2 = motions[b] return SE2.distance(q1, SE2.inverse(q2))
def same(a, b): q1 = motions[a] q2 = motions[b] return SE2.distance(q1, q2)
def commuting(a, b): q1 = motions[a] q2 = motions[b] return SE2.distance(SE2.multiply(q1, q2), SE2.multiply(q2, q1))