RealCertify: a Maple package for certifying non-negativity

05/06/2018

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by   Victor Magron, et al.

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Let Q (resp. R) be the field of rational (resp. real) numbers and X = (X_1, ..., X_n) be variables. Deciding the non-negativity of polynomials in Q[X] over R^n or over semi-algebraic domains defined by polynomial constraints in Q[X] is a classical algorithmic problem for symbolic computation. The Maple package 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.