2022-10-30 14:37:41 +0200 received badge ● Notable Question (source) 2021-07-31 21:02:30 +0200 received badge ● Popular Question (source) 2020-05-30 13:39:20 +0200 received badge ● Scholar (source) 2020-05-30 13:39:19 +0200 received badge ● Supporter (source) 2020-05-30 13:39:07 +0200 commented answer Equating coefficients of multivariate polynomials Thank you so much for this detailed answer, this is perfect! (Yes in this simple example there is no solution, my actual application has lots of variables and a higher degree so it would have been clumsy to show here). 2020-05-30 13:26:08 +0200 received badge ● Nice Question (source) 2020-05-30 13:01:26 +0200 received badge ● Student (source) 2020-05-30 12:50:23 +0200 asked a question Equating coefficients of multivariate polynomials Here is a simple question, and despite looking at answers to other questions I cannot find how to proceed. I would be extremely grateful for any help. We have a polynomial Pol in several variables (with rational coefficients, if it helps). Its coefficients involve some parameters. And I would like to find values of these parameter so that Pol is the zero polynomial. Here's some code that does not work but capture what I've tried to do. var('a0,a1') ; R. = QQ[] ; Pol = (a1*x+a0)*(1-x*y)-5*y*x ;  ad then I would like to solve (in the variables a0, a1) the system of coefficients equated to 0: WA = [SR(Pol).coefficient({x:0,y:0})==0, SR(Pol).coefficient({x:2,y:1})==0, SR(Pol).coefficient({x:1,y:1})==0, SR(Pol).coefficient({x:1,y:0})==0 ].solve(SR(a0),SR(a1)); WA