带符号参数多项式不等式组的正解
Positive Solutions of Systems of Signed Parametric Polynomial Inequalities
摘要：
我们考虑实数上的严格多元多项式不等式组。所有多项式系数都是实数范围内的参数，其中每个系数都指定其符号。我们感兴趣的是，我们的系统的正实解的存在性的所有选择的系数受我们的符号条件。我们给出了此类解存在性的判定程序。在积极的情况下，我们的程序产生一个参数的正解作为一个有理函数的系数。我们的框架允许重新制定启发式亚热带方法的非参数系统的多项式不等式，最近已被用于定性生物网络分析，独立，在可满足性模理论求解。我们应用我们的结果来描述这些方法的不完全性。
英文摘要：
We consider systems of strict multivariate polynomial inequalities over the reals. All polynomial coefficients are parameters ranging over the reals, where for each coefficient we prescribe its sign. We are interested in the existence of positive real solutions of our system for all choices of coefficients subject to our sign conditions. We give a decision procedure for the existence of such solutions. In the positive case our procedure yields a parametric positive solution as a rational function in the coefficients. Our framework allows to reformulate heuristic subtropical approaches for non-parametric systems of polynomial inequalities that have been recently used in qualitative biological network analysis and, independently, in satisfiability modulo theory solving. We apply our results to characterize the incompleteness of those methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
