def test_issue_8368(): assert integrate(exp(-s*x)*cosh(x), (x, 0, oo)) == \ Piecewise( ( pi*Piecewise( ( -s/(pi*(-s**2 + 1)), Abs(s**2) < 1), ( 1/(pi*s*(1 - 1/s**2)), Abs(s**(-2)) < 1), ( meijerg( ((S(1)/2,), (0, 0)), ((0, S(1)/2), (0,)), polar_lift(s)**2), True) ), And( Abs(periodic_argument(polar_lift(s)**2, oo)) < pi, cos(Abs(periodic_argument(polar_lift(s)**2, oo))/2)*sqrt(Abs(s**2)) - 1 > 0, Ne(s**2, 1)) ), ( Integral(exp(-s*x)*cosh(x), (x, 0, oo)), True)) assert integrate(exp(-s*x)*sinh(x), (x, 0, oo)) == \ Piecewise( ( -1/(s + 1)/2 - 1/(-s + 1)/2, And( Ne(1/s, 1), Abs(periodic_argument(s, oo)) < pi/2, Abs(periodic_argument(s, oo)) <= pi/2, cos(Abs(periodic_argument(s, oo)))*Abs(s) - 1 > 0)), ( Integral(exp(-s*x)*sinh(x), (x, 0, oo)), True))
def test_sympy__functions__elementary__complexes__periodic_argument(): from sympy.functions.elementary.complexes import periodic_argument assert _test_args(periodic_argument(x, y))
def test_periodic_argument(): from sympy.functions.elementary.complexes import (periodic_argument, polar_lift, principal_branch, unbranched_argument) x = Symbol('x') 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)