%% qtn examples

e = qtn(1)
i = qtn(0, [1 0 0])
j = qtn(0, [0 1 0])
k = qtn(0, [0 0 1])

%% properties
isq = i*i
jsq = j*j
ksq = k*k

ij = i*j
jk = j*k
ki = k*i

ji = j*i
kj = k*j
ik = i*k

%% two random qtn's
p = randq
q = randq

%% overloaded ops
p_plus_q = p + q
p_minus_q = p - q
pq = p*q
p_slash_q = p/q
p_backslash_q = p\q

%% methods
inv_p = inv(p)
p_m1 = p^(-1)
norm_p = norm(p)
p_sq = p^2
pp = p*p

%% tests
r = pq/p
test1 = norm(p\r*p - q) 

v = randn(1,3)
r = rot(36,v)
test2 = norm(r^10 - e)