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
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
def test_unpolarify():
p = exp_polar(7*I) + 1
u = exp(7*I) + 1
assert unpolarify(1) == 1
assert unpolarify(p) == u
assert unpolarify(p**2) == u**2
assert unpolarify(p**x) == p**x
assert unpolarify(p*x) == u*x
assert unpolarify(p + x) == u + x
assert unpolarify(sqrt(sin(p))) == sqrt(sin(u))
# Test reduction to principal branch 2*pi.
t = principal_branch(x, 2*pi)
assert unpolarify(t) == x
assert unpolarify(sqrt(t)) == sqrt(t)
# Test exponents_only.
assert unpolarify(p**p, exponents_only=True) == p**u
assert unpolarify(uppergamma(x, p**p)) == uppergamma(x, p**u)
# Test functions.
assert unpolarify(sin(p)) == sin(u)
assert unpolarify(tanh(p)) == tanh(u)
assert unpolarify(gamma(p)) == gamma(u)
assert unpolarify(erf(p)) == erf(u)
assert unpolarify(uppergamma(x, p)) == uppergamma(x, p)
assert unpolarify(uppergamma(sin(p), sin(p + exp_polar(0)))) == \
uppergamma(sin(u), sin(u + 1))
assert unpolarify(uppergamma(polar_lift(0), 2*exp_polar(0))) == \
uppergamma(0, 2)
assert unpolarify(Eq(p, 0)) == Eq(u, 0)
assert unpolarify(Ne(p, 0)) == Ne(u, 0)
assert unpolarify(polar_lift(x) > 0) == (x > 0)
# Test bools
assert unpolarify(True) is True
def test_unpolarify():
p = exp_polar(7*I) + 1
u = exp(7*I) + 1
assert unpolarify(1) == 1
assert unpolarify(p) == u
assert unpolarify(p**2) == u**2
assert unpolarify(p**x) == p**x
assert unpolarify(p*x) == u*x
assert unpolarify(p + x) == u + x
assert unpolarify(sqrt(sin(p))) == sqrt(sin(u))
# Test reduction to principal branch 2*pi.
t = principal_branch(x, 2*pi)
assert unpolarify(t) == x
assert unpolarify(sqrt(t)) == sqrt(t)
# Test exponents_only.
assert unpolarify(p**p, exponents_only=True) == p**u
assert unpolarify(uppergamma(x, p**p)) == uppergamma(x, p**u)
# Test functions.
assert unpolarify(sin(p)) == sin(u)
assert unpolarify(tanh(p)) == tanh(u)
assert unpolarify(gamma(p)) == gamma(u)
assert unpolarify(erf(p)) == erf(u)
assert unpolarify(uppergamma(x, p)) == uppergamma(x, p)
assert unpolarify(uppergamma(sin(p), sin(p + exp_polar(0)))) == \
uppergamma(sin(u), sin(u + 1))
assert unpolarify(uppergamma(polar_lift(0), 2*exp_polar(0))) == \
uppergamma(0, 2)
assert unpolarify(Eq(p, 0)) == Eq(u, 0)
assert unpolarify(Ne(p, 0)) == Ne(u, 0)
assert unpolarify(polar_lift(x) > 0) == (x > 0)
# Test bools
assert unpolarify(True) is True
def test_principal_branch():
p = Symbol('p', positive=True)
neg = Symbol('x', negative=True)
assert principal_branch(polar_lift(x), p) == principal_branch(x, p)
assert principal_branch(polar_lift(2 + I), p) == principal_branch(2 + I, p)
assert principal_branch(2*x, p) == 2*principal_branch(x, p)
assert principal_branch(1, pi) == exp_polar(0)
assert principal_branch(-1, 2*pi) == exp_polar(I*pi)
assert principal_branch(-1, pi) == exp_polar(0)
assert principal_branch(exp_polar(3*pi*I)*x, 2*pi) == \
principal_branch(exp_polar(I*pi)*x, 2*pi)
assert principal_branch(neg*exp_polar(pi*I), 2*pi) == neg*exp_polar(-I*pi)
assert N_equals(principal_branch((1 + I)**2, 2*pi), 2*I)
assert N_equals(principal_branch((1 + I)**2, 3*pi), 2*I)
assert N_equals(principal_branch((1 + I)**2, 1*pi), 2*I)
# test argument sanitization
assert isinstance(principal_branch(x, I), principal_branch)
assert isinstance(principal_branch(x, -4), principal_branch)
assert isinstance(principal_branch(x, -oo), principal_branch)
assert isinstance(principal_branch(x, zoo), principal_branch)
assert (principal_branch((4 + I)**2, 2*pi).evalf() ==
principal_branch((4 + I)**2, 2*pi))
def test_principal_branch_fail():
# TODO XXX why does abs(x)._eval_evalf() not fall back to global evalf?
assert N_equals(principal_branch((1 + I)**2, pi/2), 0)
def test_principal_branch():
p = Symbol('p', positive=True)
neg = Symbol('x', negative=True)
assert principal_branch(polar_lift(x), p) == principal_branch(x, p)
assert principal_branch(polar_lift(2 + I), p) == principal_branch(2 + I, p)
assert principal_branch(2*x, p) == 2*principal_branch(x, p)
assert principal_branch(1, pi) == exp_polar(0)
assert principal_branch(-1, 2*pi) == exp_polar(I*pi)
assert principal_branch(-1, pi) == exp_polar(0)
assert principal_branch(exp_polar(3*pi*I)*x, 2*pi) == \
principal_branch(exp_polar(I*pi)*x, 2*pi)
assert principal_branch(neg*exp_polar(pi*I), 2*pi) == neg*exp_polar(-I*pi)
assert N_equals(principal_branch((1 + I)**2, 2*pi), 2*I)
assert N_equals(principal_branch((1 + I)**2, 3*pi), 2*I)
assert N_equals(principal_branch((1 + I)**2, 1*pi), 2*I)
# test argument sanitization
assert isinstance(principal_branch(x, I), principal_branch)
assert isinstance(principal_branch(x, -4), principal_branch)
assert isinstance(principal_branch(x, -oo), principal_branch)
assert isinstance(principal_branch(x, zoo), principal_branch)
assert (principal_branch((4 + I)**2, 2*pi).evalf() ==
principal_branch((4 + I)**2, 2*pi))
def test_principal_branch_fail():
# TODO XXX why does abs(x)._eval_evalf() not fall back to global evalf?
assert N_equals(principal_branch((1 + I)**2, pi/2), 0)
