Any expression may be used as the head of an expression. Thus,

a = 37[1, 2, 3]

is perfectly valid (although strange). Here, a[[0]] is the number 37. You may even mutate it with Set (=):

a[[0]]=33
a
(* 33[1, 2, 3] *)

Note, however, that vector operations will generally not recognize an object as a vector unless its head is List. You may recover the tail as a list by:

List@@a
(* {1, 2, 3} *)

Fred,

nPP[[0]] is equivalent to Part[nPP, 0]. There might be a way to alter the definition of the built-in Part function to do what you want. A much simpler solution would be to shift the index values by one. Store the sum in nPP[[1]] , why does it have to be at nPP[[0]]?

Hi Fred,

Not exactly, expr[[0]] evaluates to the Head of expr, which is List in your example, not "nothing".

List + List
(* 2 List *)

(a*b)[[0]] + Sqrt[2][[0]]
(* Power + Times *)

Perhaps it is something like this

vector={3,4,5};
2*vector[[0]]

which returns

2 List

when

2*vector[[1]]

returns

6

because vector subscripts start at 1 in Mathematica and the 0'th element is the Head, which is List in this case.