如何枚举SymPy表达式中未定义的函数？

I have a variety of SymPy expressions involving UndefinedFunction instances:

我有各种涉及UndefinedFunction实例的SymPy表达式：

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)].

如何获取此类表达式中出现的函数调用列表？在这个例子中，我想得到[f（x），g（x）]。

I'm aware of free_symbols but it kicks back set([x]) (as it should).

我知道free_symbols但是它会踢回set（[x]）（就像它应该的那样）。

2 个解决方案

#1

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

你想要使用原子是正确的，但要注意SymPy中的所有函数都是来自Function的子类，而不仅仅是未定义的函数。所以你也会得到

>>> (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 UndefinedFunctions. Note that UndefinedFunction is the metaclass of f, so do to this, you need something like

因此，您需要进一步将列表缩小为仅包含UndefinedFunctions的函数。请注意，UndefinedFunction是f的元类，所以要做到这一点，你需要类似的东西

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

#2

It turns out that the atoms member method can accept a type on which to filter. So

事实证明，atoms成员方法可以接受要过滤的类型。所以

e.atoms(Function)

returns

回报

set([f(x), g(x)])

as I'd wanted. And that fancier things like

就像我想要的那样。还有更高级的东西

e.diff(x).atoms(Derivative)

are possible.

是可能的。

#1