List of algorithm problems in term of ideals

Question

I am new in algorithm and studied about some problems in algorithm related to graph theory. These problems we can transform to some polynomials and if for each set of polynomials related to a problem we have a solution then it means the problem has a question. For example we can transform the problem of MAx-Clique to the following set of polynomials

$P=\{x_i^2-x_i, x\in [n]\}\cup \{x_ix_j, (i,j)\notin E\}$

I want to know there is any list of problems like this? If you know any paper or book such that there lots of problems like the above one which can transform it to set of polynomials please let me know and have it.