CoefficientList

*To*: mathgroup at smc.vnet.net*Subject*: [mg74479] CoefficientList*From*: "Luke" <hazelnusse at gmail.com>*Date*: Fri, 23 Mar 2007 18:56:53 -0500 (EST)

I'm having a little trouble understanding how CoefficientList works for multivarate polynomials. In the Mathematica book, there is this example: t = (1 + x)^3 (1 - y - x)^2 Expand[t] 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 CoefficientList[t,{x,y}] {{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. Thanks, ~Luke