Using regular expressions to replace constants by functions

Question

I have an expression of the form:

expression = A1*x + A2*x^2 + ...

and I would like to replace A1 by F1[y], A2 by F2[y], etc.

Regular expressions would seem to be the thing to use, but since the above is not a string, I'm not sure how to do this. Would like the solution to be something simple like

expression /. A* :> F*[y]

but of course this doesn't work.

How do I accomplish the above?

Answer 1

You can use SymbolName to convert symbols to their string names, and then process those strings:

ReplaceAll[
    A1*x + A2*x^2 + A3*x^3,
    s_Symbol :> Module[{n = SymbolName[s]},
        Symbol[StringReplace[n, "A"->"F"]][y] /; StringMatchQ[n, "A"~~DigitCharacter..]
    ]
]

x F1[y] + x^2 F2[y] + x^3 F3[y]

Answer 2

Here is an approach based on string manipulation:

expression = A1 x + A2 x^2 + A3 x^3;

ToString@InputForm@expression;
StringReplace[%, "A" ~~ n : DigitCharacter :> "F" ~~ n ~~ "[y]"];
ToExpression@%

(* x F1[y] + x^2 F2[y] + x^3 F3[y] *)