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Positive Solutions of Systems of Signed Parametric Polynomial Inequalities

MPS-Authors
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Sturm,  Thomas
Automation of Logic, MPI for Informatics, Max Planck Society;

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Fulltext (public)

arXiv:1804.09705.pdf
(Preprint), 173KB

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Citation

Hong, H., & Sturm, T. (2018). Positive Solutions of Systems of Signed Parametric Polynomial Inequalities. Retrieved from http://arxiv.org/abs/1804.09705.


Cite as: http://hdl.handle.net/21.11116/0000-0002-5F54-6
Abstract
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.