A polynomial system with at least one solution

asked 2016-12-23 17:37:23 +0200

petitloup gravatar image

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 $[1]$ 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.

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slelievre gravatar imageslelievre ( 2016-12-23 18:45:33 +0200 )edit

Thanks for your answer. Unfortunately, the methods presented in your reference require the calculation of the complete Grobner basis.

petitloup gravatar imagepetitloup ( 2016-12-24 16:25:45 +0200 )edit