Assign variables automatically to a function

Question

Lets consider that I've this function:

fn = a*x^2 + b*x + c;

The idea here is to assign automatically the variables a, b, c and x to a function so it becomes something like that:

fn[x_,a_,b_,c_] := a*x^2 + b*x + c

In order to do this I've tried to extract the varibles from fn using Variables:

Sort@Variables@fn

{a, b, c, x}

Then in order to apply it to the function fn I do the following:

fn1@Variables@fn /. List -> Sequence

fn1[a, b, c, x]

Questions:

• Is it possible to add the Blanks to the former expression in order to have fn1[a_,b_,c_,x_]?

One of my fail attempt to do this was to use Blank@#&/@Sort@Variables@fn but it's obviously not working.

• One other point is that if you consider that you've found a way to automaticly have fn1[a_,b_,c_,x_], how to assign the value of fn to fn1[a_,b_,c_,x_] without having the fn1[a_,b_,c_,x_] is protected message?

Answer 1

The following works:

fn = a*x^2 + b*x + c;
Clear[fn1];
autofunc[fn_] := 
 ToString[
   fn1[
    ToExpression /@ 
      Apply[StringJoin, 
       With[{var = ToString /@ Sort@Variables@fn}, 
        Transpose@Append[{var}, Table["_", {Length@var}]]], 2] /. 
     List -> Sequence]] <> ":= " <> ToString[fn, InputForm]

autofunc[fn]
ToExpression@autofunc[fn]
fn1[1, 2, 3, 4]

"fn1[a_, b_, c_, x_]:= c + b*x + a*x^2"

27

(I didn't say it was pretty..)

You have to evaluate it to see the number of variables in the new function (which is displayed as a "string"). Also Clear[fn1] is important in this case. With a bit more playing around I'm sure I could work out a way to automate the naming of the new function.

As others have said this may not be the best way to go about this...