I am trying to write Mathematica file to find Div, Grad, Laplacian, etc. in coordinates given by a metric tensor w.r.t Euclidean coordinates.
In test my file, I am first trying it on cylindrical coordinates $(r,\theta,z)$. Here $f$ is defined as a scalar valued function dependent on these coordinates.
I am running into the following problem. In one of the steps, I get terms like the following:
$2f^{(0,1,0)}\lbrack r,\theta,z\rbrack^{(0,1,0)}\lbrack r,\theta,z\rbrack$
$2f^{(0,1,0)}\lbrack r,\theta,z\rbrack\lbrack r,\theta,z\rbrack$
How do I interpret these? Are they different or do they mean the same thing? I know that the superscripts refer to derivative with respect to the coordinate that is non-zero.
