test_simplify.py 文件源码

def test_powsimp_polar():
    from sympy import polar_lift, exp_polar
    x, y, z = symbols('x y z')
    p, q, r = symbols('p q r', polar=True)

    assert (polar_lift(-1))**(2*x) == exp_polar(2*pi*I*x)
    assert powsimp(p**x * q**x) == (p*q)**x
    assert p**x * (1/p)**x == 1
    assert (1/p)**x == p**(-x)

    assert exp_polar(x)*exp_polar(y) == exp_polar(x)*exp_polar(y)
    assert powsimp(exp_polar(x)*exp_polar(y)) == exp_polar(x + y)
    assert powsimp(exp_polar(x)*exp_polar(y)*p**x*p**y) == \
        (p*exp_polar(1))**(x + y)
    assert powsimp(exp_polar(x)*exp_polar(y)*p**x*p**y, combine='exp') == \
        exp_polar(x + y)*p**(x + y)
    assert powsimp(
        exp_polar(x)*exp_polar(y)*exp_polar(2)*sin(x) + sin(y) + p**x*p**y) \
        == p**(x + y) + sin(x)*exp_polar(2 + x + y) + sin(y)
    assert powsimp(sin(exp_polar(x)*exp_polar(y))) == \
        sin(exp_polar(x)*exp_polar(y))
    assert powsimp(sin(exp_polar(x)*exp_polar(y)), deep=True) == \
        sin(exp_polar(x + y))