most recent 30 from http://mathoverflow.net 2013-06-18T06:27:55Z http://mathoverflow.net/feeds/question/72684 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72684/quick-algorithm-for-finding-real-solutions-for-a-system-polynomial-equations Al Tal 2011-08-11T14:28:09Z 2011-08-11T18:28:31Z

<p>Would you please recommend a computer program that could give quick answer Yes/No for the question: does there exist a real solution of a given system of polynomial equations with integer coefficients. I will need it to solve a huge list of such systems, each of them is over $\mathbb{R}^6$, has $6$ equations of degree $4$ or less. Coefficients are also quite small. Maple's Triangularize procedure for most of the cases works too long, so applying it for big list is almost impossible.</p>

http://mathoverflow.net/questions/72684/quick-algorithm-for-finding-real-solutions-for-a-system-polynomial-equations/72700#72700 muestrass 2011-08-11T16:05:41Z 2011-08-11T16:05:41Z

<p>Have you thought obtain a Groebner basis of the set of defining polynomials of your system? Maybe, it could simplify considerably the aspect of the system, and you would need a little time to calculate the real solutions of the system. For that, you could use the free software wxMaxima. If you don't have it, you can download in <a href="http://maxima.sourceforge.net/download.html" rel="nofollow">http://maxima.sourceforge.net/download.html</a>. </p> <p>I would like post this comment just as a comment and not as an answer, but I don't know how to do it.</p>