I want to define an abstract function.
For example,$a=a[x]$, whose expression is unknown. It can be used for calculation and deduction later. Assume that there are sufficient conditions, so I can get the specific expression of $a=a[x]$ finally.
My question is that which Code is needed to build $a=a[x]$?
You can delay as long as you want before deciding what you want a[x] to be.
ClearAll[a, b, c, x]
a[x] (* a[x] *)
b[x_] := a[x] (* a[x] *)
b[25] (* a[25] *)
c[x_] = D[a[x], x] (* (a^\[Prime])[x] *)
c[25] (* (a^\[Prime])[25] *)
a[x_] := x*x (* finally we decide to define it! *)
b[25] (* 625 *)
c[25] (* 50 *)
To understand this better, read about DownValues.
a = a[x]in Mathematica; evaluating it would give infinite recursion. – m_goldberg Jul 15 '17 at 07:10a=a[x], check this post. – xzczd Jul 15 '17 at 08:17a[x]and it is a function. For example, if you want to know its derivative, takeD[a[x],x]and you get a representation of the derivative ofa[x]with respect tox. On the other hand, if you asked forD[a[x],y], the derivative ofa[x]with respect toy, then you get 0, as you might expect. – bill s Jul 15 '17 at 12:46