Test whether a given function is a valid w(z)

valid_function.py

from sympy import Symbol, sympify

def test(w):
  """Test if w is valid
  
  Argument w should be a string expression containing the symbol z.
  
  Returns True if w is real and positive, for all real and positive z, otherwise False.
  
  Example:
  >>> test('z + 1')
  True
  >>> test('z - 1')
  False
  """
  ns = dict(z=Symbol('z', real=True, positive=True))
  w = sympify(w, ns)
  return (w.is_real is True) and (w.is_positive is True)