Unexpected behaviour of sympy.lambdify with trigonometric functions

Question

Given an expression, we can convert it into a function using sympy.lambdify. Similarly, given a function, we can convert it into an expression by evaluating it at symbol x. We would naturally expect that these two operations are inverses of each other. And, this expected behaviour is displayed when I use polynomial expressions. For example,

import sympy as sym
x = sym.symbols('x')
expr = 5*x**2 + 2*x + 3
f = sym.lambdify([x],expr)
f_expr = f(x)
print(expr == f_expr) 

gives True as its output.

On the other hand, the following code does not run

import sympy as sym 
x = sym.symbols('x')
expr = sym.sin(x)
f = sym.lambdify([x],expr)
f_expr = f(x)
print(expr == f_expr)

and throws the error "TypeError: loop of ufunc does not support argument 0 of type Symbol which has no callable sin method". Could you please explain why this is happening? My guess would be that sym.sin(x) does not return an "expression" analogous to 5x**2 + 2x + 3. But, I would like to understand it a bit better. Thanks in advance.

Answer 1

For a non-numeric object the lambdify code tries to do x.sin() with making sure the sin function is from library sympy not numpy to avoid confusions.

you can try :

import sympy as sym 
from sympy import sin

x = sym.symbols('x')
expr = sin(x)

# f = sym.lambdify(x,expr)
f = lambda x:sin(x)
f_expr = f(x)

print(expr == f_expr)