def test_is_polynomial():
k = Symbol('k', nonnegative=True, integer=True)
assert Rational(2).is_polynomial(x, y, z) == True
assert (S.Pi).is_polynomial(x, y, z) == True
assert x.is_polynomial(x) == True
assert x.is_polynomial(y) == True
assert (x**2).is_polynomial(x) == True
assert (x**2).is_polynomial(y) == True
assert (x**(-2)).is_polynomial(x) == False
assert (x**(-2)).is_polynomial(y) == True
assert (2**x).is_polynomial(x) == False
assert (2**x).is_polynomial(y) == True
assert (x**k).is_polynomial(x) == False
assert (x**k).is_polynomial(k) == False
assert (x**x).is_polynomial(x) == False
assert (k**k).is_polynomial(k) == False
assert (k**x).is_polynomial(k) == False
assert (x**(-k)).is_polynomial(x) == False
assert ((2 * x)**k).is_polynomial(x) == False
assert (x**2 + 3 * x - 8).is_polynomial(x) == True
assert (x**2 + 3 * x - 8).is_polynomial(y) == True
assert (x**2 + 3 * x - 8).is_polynomial() == True
assert sqrt(x).is_polynomial(x) == False
assert (sqrt(x)**3).is_polynomial(x) == False
assert (x**2 + 3 * x * sqrt(y) - 8).is_polynomial(x) == True
assert (x**2 + 3 * x * sqrt(y) - 8).is_polynomial(y) == False
assert ((x**2) * (y**2) + x * (y**2) + y * x +
exp(2)).is_polynomial() == True
assert ((x**2) * (y**2) + x * (y**2) + y * x +
exp(x)).is_polynomial() == False
assert ((x**2) * (y**2) + x * (y**2) + y * x + exp(2)).is_polynomial(
x, y) == True
assert ((x**2) * (y**2) + x * (y**2) + y * x + exp(x)).is_polynomial(
x, y) == False
def test_is_polynomial():
k = Symbol('k', nonnegative=True, integer=True)
assert Rational(2).is_polynomial(x, y, z) is True
assert (S.Pi).is_polynomial(x, y, z) is True
assert x.is_polynomial(x) is True
assert x.is_polynomial(y) is True
assert (x**2).is_polynomial(x) is True
assert (x**2).is_polynomial(y) is True
assert (x**(-2)).is_polynomial(x) is False
assert (x**(-2)).is_polynomial(y) is True
assert (2**x).is_polynomial(x) is False
assert (2**x).is_polynomial(y) is True
assert (x**k).is_polynomial(x) is False
assert (x**k).is_polynomial(k) is False
assert (x**x).is_polynomial(x) is False
assert (k**k).is_polynomial(k) is False
assert (k**x).is_polynomial(k) is False
assert (x**(-k)).is_polynomial(x) is False
assert ((2*x)**k).is_polynomial(x) is False
assert (x**2 + 3*x - 8).is_polynomial(x) is True
assert (x**2 + 3*x - 8).is_polynomial(y) is True
assert (x**2 + 3*x - 8).is_polynomial() is True
assert sqrt(x).is_polynomial(x) is False
assert (sqrt(x)**3).is_polynomial(x) is False
assert (x**2 + 3*x*sqrt(y) - 8).is_polynomial(x) is True
assert (x**2 + 3*x*sqrt(y) - 8).is_polynomial(y) is False
assert ((x**2)*(y**2) + x*(y**2) + y*x + exp(2)).is_polynomial() is True
assert ((x**2)*(y**2) + x*(y**2) + y*x + exp(x)).is_polynomial() is False
assert (
(x**2)*(y**2) + x*(y**2) + y*x + exp(2)).is_polynomial(x, y) is True
assert (
(x**2)*(y**2) + x*(y**2) + y*x + exp(x)).is_polynomial(x, y) is False