In modern mathematics there exists a l conflict since the 1930's between the classical notation of powers (Count of equal factors in a an Orderless function Times) and the TensorAlgebra notation of tensors in a pair of dual spaces of vectors and their projection functions to the coordinates.
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Vectors are the generalization of dirctinal derivatives, their duals are the directional differentials in line integrals, in short
int D f[x^1,--.], x^i ] dx^i == f[x^1,--]
Einsteins most ingenious idea was probable to get rid of the clumsy Leibniz-Euler notation with these intimidating sum and Int symbols and their appendices and reduce that central formula of calculus to
f_,k dx^k = f
where summation or integration or both over equal "dummy" (meaning local ) upper and lower indices is implied and indices after the comma are coordinate indices of partial derivatives.
For a CAS system to be taylored to the use by the worldwide community of applied mathematics in an open field of ever growing specialized model mathematics, the symmetrical use of sub- and superscripts would shrink the market to a handful of abstractly working mathematicians and physicists.
So the Ricci-Einstein-Cartan display form of calculus is packed and outsurced to a special paclet.
At least, such a packet makes sense only if sub- and superscripted entities can be declared as atomically symbols for pattern matching. Times and Power has to be replaced by non-Orderless constructs like TensorProduct in order to guarantee strict 1-1 map between basis coordinate variables and their index, sub, or superscript numbers .
With these conceptual guidelines, I suppose, Wolfram decided to implement the Superscript use to the special Einstein case of denoting the indexed derivatives of a function via sequences of the integer order of differentiations in each variable.
Derivative[2,3][f][x^2+ a, y-x ] -> f^(2,3)[x^2+ a,y-x]
There exists no extra ^ key to differentiate in input between Power, Derivative and Superscript.
Could simply by implemented, I suppose, as an escape sequence. But without an elaborated algebra on a class of such symbolized, atomized expressions, its use is restricted to pretty printing.enter code here
