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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.

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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?

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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!

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  • $\begingroup$ Thank you for your answer! It is ok to separate items with positive and negative powers. But I still wonder why there is no such a direct command to gain coefficients for both items with positive and negative powers:) $\endgroup$ – Robin_Lyn Nov 16 '18 at 12:14
  • $\begingroup$ It is a general situation. Mma has no all functions that one can wish. In this case, we may write our own functions and use when needed. Taking my idea as a basis you might like to construct such a function. $\endgroup$ – Alexei Boulbitch Nov 16 '18 at 13:02
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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} *)
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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."

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  • $\begingroup$ It is a spelling mistake, and is trivial. The question has been updated. $\endgroup$ – Robin_Lyn Nov 16 '18 at 7:55

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