A polynomial system with at least one solution
Hello, using Sage, I consider a system $S$ of multivariate polynomials. I cannot obtain a Grobner basis of the previous system; no matter, I only want to know when $S$ has at least one solution. Does there exist in Sage a command that does the job. Of course, the command must give an answer without calculating the whole of the Grobner basis. Remark. When $S$ has no solutions, the process is faster and, in general, we obtain $$ as a Grobner basis. Thus, when Sage does not succeed in concluding, there is a high probability that there is at least one solution; unfortunately, this is not a proof. Thanks in advance.