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The problem I have is the following:

Let C be a list of coordinates, say, C = {x1, x2, ..., xn} and T be a tensor (possibly with symmetries) defined using the Array command (e.g., for a tensor with $3$ covariant components):

T = Array[ tt, { dim, dim, dim}]

where dim = n.
Now what I want is to declare that each and every component is a function of the coordinates.

Unfortunately, a command like:

T = Array[ tt[ x1, x2, ..., xn], { dim, dim, dim}]

does not work.

Any suggestions?

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Look up Function or Slot. Define tt as tt[x1[#1,#2,#3], x2[...], ...]& –  Sjoerd C. de Vries Nov 3 '13 at 23:25
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