MathGroup Archive 2007

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I'm having a little trouble understanding how CoefficientList works
for multivarate polynomials.  In the Mathematica book, there is this
t = (1 + x)^3 (1 - y - x)^2

1 + x - 2x^2 - 2x^3 + x^4 + x^5 - 2y - 4xy + 4x^3y + 2x^4y + y^2 +
3xy^2 + 3x^2y^2 + x^3y^2
{{1, -2, 1}, {1, -4, 3}, {-2, 0, 3}, {-2, 4, 1}, {1, 2, 0}, {1, 0, 0}}

I am confused as to what each entry of the output of the
CoefficientList corresponds to.  The Handbook says:
For multivariate polynomials, CoefficientList gives an array of the
coefficients for each power of each variable.

So what exactly do the entries of the first item, {1,-2,1}, correspond
to?  Is it the 0 order terms? Why three entries then?  Is
corresponding to the 1, the x, and the -2y?  What is the order of each
of these lists?  Maybe I'm just being dense, but it isn't immediately
obvious to me how this is structured, and the Handbook is extremely
terse in its description.

Any help would be greatly appreciated.


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