# How to sum over the variable in partial derivative operator?

I need to use the partial derivative operator in Wolfram Mathematica within a summation, specifically to define the D'Alembertian operator of scalar fields. I am having trouble summing over the D operator.

This is how I have defined the function currently and this is giving me an error.

(*Defining D'alembertian of a 2nd rank tensor H*)
DALembert[H_, g_, xx_] := Block[{n, ig, det, detg, res},
n = 4; det = Det[g]; detg = Sqrt[-det]; ig = InverseMetric[g];
res = Table[1/detg Sum[\!$$\*SubscriptBox[\(\[PartialD]$$, $$k$$]$$[detg*ig[k, l]*\ \(( \*SubscriptBox[\(\[PartialD]$$, $$l$$]H[i, j])\)]\)\), {k, 1, n}, {l,
1, n}], {i, 1, n}, {j, 1, n}];
Simplify[res]]


Please help.

• You're using square brackets ([...]) after the partial derivative operator instead of parentheses ((...)). In Mathematica, expressions can only be grouped using parentheses. Square brackets are reserved for function calls – Lukas Lang Jan 9 at 14:43
• – Bob Hanlon Jan 9 at 16:57
• @LukasLang, using parentheses instead of square brackets has helped me obtain an output. Thank you! But I realize that my approach of summing over k and l is not giving me the intended result. What I intended is to take partial derivatives with respect to 3 space coordinates and 1 time coordinate. I used k and l hoping to run over these 4 coordinates, but that is not happening. Please give some suggestions on how to do this! – mv1996 Jan 9 at 18:06
• @BobHanlon I appreciate the info, since I am just beginning to use Mathematica. Thank you :) – mv1996 Jan 9 at 18:07