def test_requires_partial():
    x, y, z, t, nu = symbols('x y z t nu')
    n = symbols('n', integer=True)

    f = x * y
    assert requires_partial(Derivative(f, x)) is True
    assert requires_partial(Derivative(f, y)) is True

    ## integrating out one of the variables
    assert requires_partial(Derivative(Integral(exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False

    ## bessel function with smooth parameter
    f = besselj(nu, x)
    assert requires_partial(Derivative(f, x)) is True
    assert requires_partial(Derivative(f, nu)) is True

    ## bessel function with integer parameter
    f = besselj(n, x)
    assert requires_partial(Derivative(f, x)) is False
    # this is not really valid (differentiating with respect to an integer)
    # but there's no reason to use the partial derivative symbol there. make
    # sure we don't throw an exception here, though
    assert requires_partial(Derivative(f, n)) is False

    ## bell polynomial
    f = bell(n, x)
    assert requires_partial(Derivative(f, x)) is False
    # again, invalid
    assert requires_partial(Derivative(f, n)) is False

    ## legendre polynomial
    f = legendre(0, x)
    assert requires_partial(Derivative(f, x)) is False

    f = legendre(n, x)
    assert requires_partial(Derivative(f, x)) is False
    # again, invalid
    assert requires_partial(Derivative(f, n)) is False

    f = x ** n
    assert requires_partial(Derivative(f, x)) is False

    assert requires_partial(Derivative(Integral((x*y) ** n * exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False

    # parametric equation
    f = (exp(t), cos(t))
    g = sum(f)
    assert requires_partial(Derivative(g, t)) is False

    f = symbols('f', cls=Function)
    assert requires_partial(Derivative(f(x), x)) is False
    assert requires_partial(Derivative(f(x), y)) is False
    assert requires_partial(Derivative(f(x, y), x)) is True
    assert requires_partial(Derivative(f(x, y), y)) is True
    assert requires_partial(Derivative(f(x, y), z)) is True
    assert requires_partial(Derivative(f(x, y), x, y)) is True

def test_latex_bessel():
    from sympy.functions.special.bessel import besselj, bessely, besseli, besselk, hankel1, hankel2, jn, yn
    from sympy.abc import z

    assert latex(besselj(n, z ** 2) ** k) == r"J^{k}_{n}\left(z^{2}\right)"
    assert latex(bessely(n, z)) == r"Y_{n}\left(z\right)"
    assert latex(besseli(n, z)) == r"I_{n}\left(z\right)"
    assert latex(besselk(n, z)) == r"K_{n}\left(z\right)"
    assert latex(hankel1(n, z ** 2) ** 2) == r"\left(H^{(1)}_{n}\left(z^{2}\right)\right)^{2}"
    assert latex(hankel2(n, z)) == r"H^{(2)}_{n}\left(z\right)"
    assert latex(jn(n, z)) == r"j_{n}\left(z\right)"
    assert latex(yn(n, z)) == r"y_{n}\left(z\right)"

def test_latex_bessel():
    from sympy.functions.special.bessel import (besselj, bessely, besseli,
            besselk, hankel1, hankel2, jn, yn)
    from sympy.abc import z
    assert latex(besselj(n, z**2)**k) == r'J^{k}_{n}\left(z^{2}\right)'
    assert latex(bessely(n, z)) == r'Y_{n}\left(z\right)'
    assert latex(besseli(n, z)) == r'I_{n}\left(z\right)'
    assert latex(besselk(n, z)) == r'K_{n}\left(z\right)'
    assert latex(hankel1(n, z**2)**2) == \
              r'\left(H^{(1)}_{n}\left(z^{2}\right)\right)^{2}'
    assert latex(hankel2(n, z)) == r'H^{(2)}_{n}\left(z\right)'
    assert latex(jn(n, z)) == r'j_{n}\left(z\right)'
    assert latex(yn(n, z)) == r'y_{n}\left(z\right)'

def test_sympy__functions__special__bessel__besselj():
    from sympy.functions.special.bessel import besselj
    assert _test_args(besselj(x, 1))