how to get coefficient list from a polynomial with negative powers

Question

Say a polynomial x^2-x^(-2), I need to extract its coefficient. I tried the command CoefficientList[x^2-x^(-2)], but no result comes out.

I am confused why it happens. How can I get the desired result {-1,0,0,0,1}?

It should be an easy question, but I do not know the suitable command. Would you please give me some tips?

Answer 1

Would it be OK for you to look separately for the list of coefficients with positive and that with negative powers? If yes, try this. Let us introduce a rule transforming, say, x^-2 into y^2:

rule = Power[x, n_] /; n < 0 -> y^-n;

Here is your polynomial:

p = x^2 - x^(-2);

Now this:

CoefficientList[p /. rule, x] /. y -> 0
CoefficientList[p /. rule, y] /. x -> 0
(* {0, 0, 1}
   {0, 0, -1}   *)

gives us the answers separately for positive and negative powers.

Have fun!

Answer 2

Could find the min exponent, then make it an explicit polynomial.

laurentCoefficientList[lpol_, x_] := With[
  {min = Exponent[lpol, x, Min]}, CoefficientList[lpol/x^min, x]]

In[56]:= laurentCoefficientList[x^2 - x^(-2), x]

(* Out[56]= {-1, 0, 0, 0, 1} *)

Answer 3

Check your spelling (upper-case L):

CoefficientList[x^2 - x^(-2), x]

From the documentation: "Terms that do not contain positive integer powers of a particular variable are included in the first element of the list for that variable."