Prevent evaluation of parameter inside function

Question

I am learning mathematica, and I am stuck at the point where I want to pass an unevaluated expression (a polynomial) to a function and work with that expression / polynomial inside the function. For simplification reason, assume the following setup, which should give me the coefficients of the polynomial:

SetAttributes[myCoef, HoldAll]
myCoef[exp_] := CoefficientList[exp, Variables[exp]]

This works fine for the following call:

p = myCoef[5*x^3 + 4*x^2 + 3]
(* Returns {3, 0, 4, 5} *)

The problem is, when I set x on the global scope:

x = 5
p = myCoef[5*x^3 + 4*x^2 + 3]
(* Returns 728 *)

How can I prevent the evaluation of 5*x^3 + 4*x^2 + 3 to 728? What would I have to change in myCoef to make it work, even if x is defined globally?

Answer 1

Of course, the simplest solution is to make sure you haven't defined the variables you're using in your polynomials, but there are other ways to go.

You could wrap the code in Module or Block :

Block[{x},
 myCoef[5*x^3 + 4*x^2 + 3]
 ]

{3, 0, 4, 5}

If you wanted to, you could build this into myCoef by adding a second argument :

myCoef[exp_, varsToBlock_List] :=
 Block[varsToBlock,
  CoefficientList[exp, Variables[exp]]
  ]

x=2;
myCoef[5*x^3 + 4*x^2 + 3, {x}]

{3, 0, 4, 5}

Note that the original form of myCoef still works for a variable that doesn't have a definition:

myCoef[5*y^3 + 4*y^2 + 3]

{3, 0, 4, 5}

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Of course, it would be nice to solve the problem without having to explicitly specify the variables which need to be held. I'm unsure how to do this, but perhaps someone else will come up with a solution.