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The superscript notation $f^n$ for the coordinate functions is very strange -- I think it is likely to be confused with the $n$th derivative or the $n$th power. --Jjg 02:14, 3 August 2012 (CEST)

The derivative would be $f^{(n)}$. The power is indeed a problem. But "very strange" is an overstatement. I saw such notation many times, since the tensor notation stipulates upper and lower indices (contravariant and covariant...). Maybe in such cases we should add a note like "(upper index, not a power)". --Boris Tsirelson 07:41, 3 August 2012 (CEST)
Indeed the notation I have chosen is the tensor one: for instance the divergence of a vector field would then be $\partial_{x_i} X^i$, using Einstein's convention on repeated indices. I am aware of the possible confusions: the line "where $(f^1, \ldots, f^m)$ are the coordinate functions of $f$" should make things sufficiently clear though.Camillo 08:06, 3 August 2012 (CEST)
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