Sympy. How to check input is numeric, sympy expression and if so if a symbol included in the expression?

Question

I want to code some function that takes 1 input. The input could be numeric (integer, float, Sympy constant like sympy.pi or expression evaluated as real number like sympy.sin(5)), or could be a sympy expression (like x**2-2*y+5.

What I need is to determine:

1. Is the input is numeric (has no symbols)?
2. If the input is expression, does a specific variable exist?

I have tried .free_symbols and it fails if the input is integer and throws exception. Also str(input).isnumeric fails if the input is sympy.sin(5).

Answer 1

There is a function in SymPy called sympify whose purpose is to turn non-SymPy objects into SymPy expressions e.g. an int becomes a SymPy Integer etc. If you sympify the input then you can use free_symbols:

In [6]: def inspect(expr):
   ...:     expr = sympify(expr)
   ...:     symbols = expr.free_symbols
   ...:     if not symbols:
   ...:         print(expr, 'has no symbols')
   ...:     else:
   ...:         print(expr, 'has these symbols:', ', '.join(map(str, symbols)))
   ...: 

In [7]: inspect(1)
1 has no symbols

In [8]: inspect(pi)
pi has no symbols

In [9]: inspect(x+y)
x + y has these symbols: y, x