Year: 2018
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Magron, Victor, Din, Mohab Safey El
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2800516317