def test_periodic_argument(): p = Symbol('p', positive=True) assert unbranched_argument(2 + I) == periodic_argument(2 + I, oo) assert unbranched_argument(1 + x) == periodic_argument(1 + x, oo) assert N_equals(unbranched_argument((1 + I)**2), pi/2) assert N_equals(unbranched_argument((1 - I)**2), -pi/2) assert N_equals(periodic_argument((1 + I)**2, 3*pi), pi/2) assert N_equals(periodic_argument((1 - I)**2, 3*pi), -pi/2) assert unbranched_argument(principal_branch(x, pi)) == \ periodic_argument(x, pi) assert unbranched_argument(polar_lift(2 + I)) == unbranched_argument(2 + I) assert periodic_argument(polar_lift(2 + I), 2*pi) == \ periodic_argument(2 + I, 2*pi) assert periodic_argument(polar_lift(2 + I), 3*pi) == \ periodic_argument(2 + I, 3*pi) assert periodic_argument(polar_lift(2 + I), pi) == \ periodic_argument(polar_lift(2 + I), pi) assert unbranched_argument(polar_lift(1 + I)) == pi/4 assert periodic_argument(2*p, p) == periodic_argument(p, p) assert periodic_argument(pi*p, p) == periodic_argument(p, p) assert Abs(polar_lift(1 + I)) == Abs(1 + I) assert periodic_argument(x, pi).is_real is True assert periodic_argument(x, oo, evaluate=False).is_real is None