I have two sets of coordinates, and two partial derivatives which can act on these coordinates. These should work in a way such that:

$$
\partial_{x^{\mu}} x^{\nu} = \delta_{\mu}^{\nu} = \partial_{a*{\nu}} a\*{\mu}.
$$

How would I go about implementing this in Cadabra? I've tried defining partial derivatives of corresponding coordinates directly, I've tried using notation like DX and DA to differentiate between the two and then using LaTeXform to make it more tidy but I inadvertently run into a stop of some sort.

Any and all help will be greatly appreciated!