def test_quaternion_construction():
q = Quaternion(x, y, z, w)
assert q + q == Quaternion(2*x, 2*y, 2*z, 2*w)
q2 = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), 2*pi/3)
assert q2 == Quaternion(Rational(1/2), Rational(1/2),
Rational(1/2), Rational(1,2))
M = Matrix([[cos(x), -sin(x), 0], [sin(x), cos(x), 0], [0, 0, 1]])
q3 = trigsimp(Quaternion.from_rotation_matrix(M))
assert q3 == Quaternion(sqrt(2)*sqrt(cos(x) + 1)/2, 0, 0, sqrt(-2*cos(x) + 2)/2)
def test_quaternion_construction():
q = Quaternion(x, y, z, w)
assert q + q == Quaternion(2*x, 2*y, 2*z, 2*w)
q2 = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3), 2*pi/3)
assert q2 == Quaternion(Rational(1, 2), Rational(1, 2),
Rational(1, 2), Rational(1, 2))
M = Matrix([[cos(x), -sin(x), 0], [sin(x), cos(x), 0], [0, 0, 1]])
q3 = trigsimp(Quaternion.from_rotation_matrix(M))
assert q3 == Quaternion(sqrt(2)*sqrt(cos(x) + 1)/2, 0, 0, sqrt(-2*cos(x) + 2)/2)
nc = Symbol('nc', commutative=False)
raises(ValueError, lambda: Quaternion(x, y, nc, w))
def test_quaternion_construction():
q = Quaternion(w, x, y, z)
assert q + q == Quaternion(2*w, 2*x, 2*y, 2*z)
q2 = Quaternion.from_axis_angle((sqrt(3)/3, sqrt(3)/3, sqrt(3)/3),
pi*Rational(2, 3))
assert q2 == Quaternion(S.Half, S.Half,
S.Half, S.Half)
M = Matrix([[cos(phi), -sin(phi), 0], [sin(phi), cos(phi), 0], [0, 0, 1]])
q3 = trigsimp(Quaternion.from_rotation_matrix(M))
assert q3 == Quaternion(sqrt(2)*sqrt(cos(phi) + 1)/2, 0, 0, sqrt(2 - 2*cos(phi))*sign(sin(phi))/2)
nc = Symbol('nc', commutative=False)
raises(ValueError, lambda: Quaternion(w, x, nc, z))
