SymPy and dictionary variables

I need to use for SymPy operations a number of variables that depend on other parameters in the code. As I understand, a dictionary is used normally when the number of variables is not known in advance. However, SymPy does not allow to declare dictionary variables (say, d[1][1]) symbols and use them in symbolic operations like deriving expressions with respect to them. What would be a proper solution for this situation?

It's not very clear what you want to do, but is it something like this?

>>> from sympy import *
>>> from collections import defaultdict

You could also use a function (which behaves better wrt differentiation) but it would be accessed as d[1](0) instead of d[1][0]:

>>> s=numbered_symbols('x',cls=Function)
>>> d=defaultdict(lambda:next(s))
>>> (d[0](1) + 2*d[1](1)).diff(d[1](1))
2