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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.

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marked as duplicate by Jens, Artes, m_goldberg, Sjoerd C. de Vries, Silvia Jun 13 '13 at 18:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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 3:04
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