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CoefficientList
CoefficientList[
poly
,
var
] gives a list of coefficients of powers of var in poly, starting with power 0.
CoefficientList[
poly
,
,
, ... 
] gives an array of coefficients of the  .
Example: CoefficientList[x^2 + 2 x y - y,
x, y
] .
The dimensions of the array returned by CoefficientList are determined by the values of the Exponent[
poly
,
].
Terms that do not contain positive integer powers of a particular variable are included in the first element of the list for that variable.
CoefficientList always returns a full rectangular array. Combinations of powers that do not appear in poly give zeros in the array.
CoefficientList works whether or not poly is explicitly given in expanded form.
See the Mathematica book: Section 3.3.2.
See also: Series, SeriesCoefficient, Collect, FactorList.
Further Examples
This gives the coefficients in the polynomial first in the variable x.
In[1]:= 
Out[1]= 
On the other hand this gives the coefficients in the polynomial first in the variable y.
In[2]:= 
Out[2]= 
We can also get the list of coefficients over the integers modulo 3 and 4.
In[3]:= 
Out[3]= 
CoefficientList can handle powers of variables in the second argument as long as the first argument is a polynomial in those powers.
In[4]:= 
Out[4]= 
The coefficients of a polynomial in two variables are given as an array.
In[5]:= 
Out[5]= 
Here are the coefficients of some polynomials in three variables.
In[6]:= 
Out[6]//MatrixForm= 
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