Question

I want to write a

 Module Arg[f_,n_] 

that takes a function f (having <=n arguments) and a natural number n and outputs the n-th argument of the function f.

As an example, suppose that f is defined by

f[a_,b_]=a^2+b^2. 

Then,

Arg[f[s,t],1] 

should be s;

while

Arg[f[u,v],2] 

should be v.

My question is whether this is possible. If so, what should I write in the place of “???” below?

Arg[f_,n_] := Module[{}, ??? ]

Note that I don’t want to specify a_ and b_ in the definition of Arg like

 Arg[f_,a_,b_,n_]

EDIT: “Arg” is just my name for the module not the internal function Arg of Mathematica.

Answer 1

Perhaps

SetAttributes[arg, HoldFirst];
arg[f_[x___], n_] := {x}[[n]]

f[a_, b_] := a^2 + b^2.
arg[f[arg[f[s, t], 1], t], 1]
arg[f[s, t], 2]

(*
 -> s
 -> t
*)

arg[ArcTan[f[Cos@Sin@x, x], t], 1]

(*
->  x^2. + Cos[Sin[x]]^2
*)