# Question:How to extract all coefficients of a multivariate polynomial?

August 22 2014
Maple 17
0

I have a polynomial p in two variables x and y, and I want to extract all the coefficients of p. For example, let p:=x^3+2*x*y^2-2*y^2+x, and I want to obtain the coefficient vector [1,0,0,1,0,2,0,0,-2,0], where 1,0,0,1,0,2,0,0,-2,0 are respectively the coefficients of x^3, x^2, x^2*y,x,x*y,x*y^2,y^0,y,y^2,y^3. In general, let

p(x,y)=sum(sum(c_*{i, j}*x^(n-i)*y^j, j = 0 .. i), i = 0 .. n)

=c_{0,0}x^n

+c_{1,0}x^{n-1}+c_{1,1}x^{n-1}y

+c_{2.0}x^{n-2}+c_{2,1}x^{n-2}y+c_{2,2}x^{n-2}y^2

+\dots

+c_{n,0}+c_{n,1}y+c_{n,2}y^2+\dots+c_{n,n}y^{n}.

It is possible that some coefficients c_{i,j} are equal to 0. How to obtain the coefficient vector [c_{i,j},i=0..n,j=0..i] of p(x,y)?

Thanks a lot.

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