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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 was marked as an exact duplicate of an existing 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