Interpretation of output derivative expression

Question

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.

The output is very likely not what you want, and indicates that you did something wrong. Since you didn't say what input you actually used, I can only guess that you will find the answer to your problem here: How to write a differential operator in Mathematica. Another possible source of inspiration is: Having the derivative be an operator — Jens, Jun 12 '13 at 21:47
Another possible source to look at: How to change coordinates of a differential operator? — Jens, Jun 12 '13 at 21:50
You may also take a look at this: Using D to find a symbolic derivative — Artes, Jun 12 '13 at 23:04
Perhaps you are missing some semicolons in your input, and various terms are getting (erroneously) multiplied by each other. — bill s, Jun 13 '13 at 03:04
It means that somewhere this probably happened: D[f[r, theta, z][r, theta, z], theta] -- i.e. you applied your function to r, theta, z twice. Code would be helpful, if you need more help. — Michael E2, Jun 13 '13 at 14:20
There are several votes to close as a duplicate, but I do not find that the question asked here is answered in the duplicates. I would say it is probably too localized, since it appears from what has been given that it is probably a coding error. — Michael E2, Jun 13 '13 at 14:22
@MichaelE2 I cast the last dup vote. As I think interpretation for the expression in OP is one question, but what OP really needs/wants is how to write differential operators. But maybe we can shift/extend the question itself to a different one and reopen it? — Silvia, Jun 13 '13 at 18:25
@Silvia I think it's up to the OP to respond. The question can be edited to clarify what's being asked, and folks can vote to reopen. Or OP may be able to fix it and not need the question reopened. — Michael E2, Jun 14 '13 at 03:32

Interpretation of output derivative expression

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