ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 24 Dec 2016 09:25:45 -0600A polynomial system with at least one solutionhttps://ask.sagemath.org/question/36077/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 $[1]$ 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.Fri, 23 Dec 2016 10:37:23 -0600https://ask.sagemath.org/question/36077/a-polynomial-system-with-at-least-one-solution/Comment by slelievre for <p>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.</p>
https://ask.sagemath.org/question/36077/a-polynomial-system-with-at-least-one-solution/?comment=36078#post-id-36078The answer to [Ask Sage question 11070 "Find algebraic solutions to system of polynomial equations"](https://ask.sagemath.org/question/11070/find-algebraic-solutions-to-system-of-polynomial-equations/)
might answer your question too.Fri, 23 Dec 2016 11:45:33 -0600https://ask.sagemath.org/question/36077/a-polynomial-system-with-at-least-one-solution/?comment=36078#post-id-36078Comment by petitloup for <p>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.</p>
https://ask.sagemath.org/question/36077/a-polynomial-system-with-at-least-one-solution/?comment=36082#post-id-36082Thanks for your answer. Unfortunately, the methods presented in your reference require the calculation of the complete Grobner basis.Sat, 24 Dec 2016 09:25:45 -0600https://ask.sagemath.org/question/36077/a-polynomial-system-with-at-least-one-solution/?comment=36082#post-id-36082