How can I enumerate the undefined functions in a SymPy expression?

Question

I have a variety of SymPy expressions involving UndefinedFunction instances: ``` f = Function('f') g = Function('g') e = f(x) / g(x) ``` How can I obtain a list of the function invocations appearing in such expressions? In this example, I'd like to get `[f(x), g(x)]`. I'm aware of `free_symbols` but it kicks back `set([x])` (as it should).

Accepted Answer

You are right that you want to use `atoms`, but be aware that all functions in SymPy subclass from `Function`, not just undefined functions. So you'll also get

```
>>> (sin(x) + f(x)).atoms(Function)
set([f(x), sin(x)])
```

So you'll want to further reduce your list to only those functions that are `UndefinedFunction`s. Note that `UndefinedFunction` is the metaclass of `f`, so do to this, you need something like

```
>>> [i for i in expr.atoms(Function) if isinstance(i.__class__, UndefinedFunction)]
[f(x)]
```

How can I enumerate the undefined functions in a SymPy expression?

Solution

Problem