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RealCertify: a Maple package for certifying non-negativity

Abstract : Let $\mathbb{Q}$ (resp. $\mathbb{R}$) be the field of rational (resp. real) numbers and $X = (X_1, \ldots, X_n)$ be variables. Deciding the non-negativity of polynomials in $\mathbb{Q}[X]$ over $\mathbb{R}^n$ or over semi-algebraic domains defined by polynomial constraints in $\mathbb{Q}[X]$ is a classical algorithmic problem for symbolic computation. The Maple package \textsc{RealCertify} tackles this decision problem by computing sum of squares certificates of non-negativity for inputs where such certificates hold over the rational numbers. It can be applied to numerous problems coming from engineering sciences, program verification and cyber-physical systems. It is based on hybrid symbolic-numeric algorithms based on semi-definite programming.
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Contributor : Victor Magron <>
Submitted on : Sunday, December 16, 2018 - 5:55:38 PM
Last modification on : Tuesday, May 11, 2021 - 11:37:00 AM

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Victor Magron, Mohab Safey El Din. RealCertify: a Maple package for certifying non-negativity. ACM Communications in Computer Algebra, Association for Computing Machinery (ACM), 2018, 52 (2), pp.34-37. ⟨10.1145/3282678.3282681⟩. ⟨hal-01956812⟩



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