如何判断 SymPy 是否识别 sympify() 解析的函数？

import sympy as sp
from sympy.core.function import AppliedUndef, Function

# 将字符串表达式转换为 SymPy 对象
expr = sp.sympify("sin(x) + foo(y)")

# 获取表达式中所有的函数
all_functions = expr.atoms(Function)
print(f"All functions: {all_functions}")

# 获取表达式中未定义的函数
undefined_functions = expr.atoms(AppliedUndef)
print(f"Undefined functions: {undefined_functions}")

# 获取表达式中已定义的函数
defined_functions = all_functions - undefined_functions
print(f"Defined functions: {defined_functions}")

All functions: {foo(y), sin(x)}
Undefined functions: {foo(y)}
Defined functions: {sin(x)}

import sympy as sp
from sympy.core.function import AppliedUndef, Function

def is_sympy_defined(func):
  """
  检查一个函数是否为 SymPy 定义的函数。
  """
  return not isinstance(func.func, AppliedUndef)

def is_sympy_undefined(func):
  """
  检查一个函数是否为 SymPy 未定义的函数。
  """
  return isinstance(func.func, AppliedUndef)

# 示例用法
expr = sp.sympify("sin(x) + foo(y)")
eq = sp.Eq(sp.sympify('z'), expr)

sympy_defined_funcs = [func for func in eq.atoms(sp.Function) if is_sympy_defined(func)]
sympy_undefined_funcs = [func for func in eq.atoms(sp.Function) if is_sympy_undefined(func)]

print(f"SymPy defined functions: {sympy_defined_funcs}")
print(f"SymPy undefined functions: {sympy_undefined_funcs}")

SymPy defined functions: [sin(x)]
SymPy undefined functions: [foo(y)]