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Realcertify: a maple package for certifying non-negativity

Authors:

Victor Magron,

Mohab Safey El DinAuthors Info & Claims

ACM Communications in Computer Algebra, Volume 52, Issue 2

Pages 34 - 37

https://doi.org/10.1145/3282678.3282681

Published: 01 October 2018 Publication History

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Abstract

Let Q (resp. R) be the field of rational (resp. real) numbers and X = (X₁, ..., X_n) be variables. Deciding the non-negativity of polynomials in Q[X] over Rⁿ 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.

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Cited By

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Devadze GMagron VStreif S(2025)Computer-Assisted Proofs for Lyapunov Stability via Sums of Squares Certificates and Constructive AnalysisJournal of Automated Reasoning10.1007/s10817-024-09717-269:1Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s10817-024-09717-2
Devadze GMunser LStreif S(2023)Extraction of a computer-certified SMT solver for nonlinear theories2023 European Control Conference (ECC)10.23919/ECC57647.2023.10178209(1-6)Online publication date: 13-Jun-2023
https://doi.org/10.23919/ECC57647.2023.10178209
Koprowski PMagron VVaccon T(2023)Pourchet’s theorem in action: decomposing univariate nonnegative polynomials as sums of five squaresProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597072(425-433)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597072
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cover image ACM Communications in Computer Algebra

ACM Communications in Computer Algebra Volume 52, Issue 2

June 2018

18 pages

ISSN:1932-2232

EISSN:1932-2240

DOI:10.1145/3282678

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Association for Computing Machinery

New York, NY, United States

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Published: 01 October 2018

Published in SIGSAM-CCA Volume 52, Issue 2

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Devadze GMagron VStreif S(2025)Computer-Assisted Proofs for Lyapunov Stability via Sums of Squares Certificates and Constructive AnalysisJournal of Automated Reasoning10.1007/s10817-024-09717-269:1Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s10817-024-09717-2
Devadze GMunser LStreif S(2023)Extraction of a computer-certified SMT solver for nonlinear theories2023 European Control Conference (ECC)10.23919/ECC57647.2023.10178209(1-6)Online publication date: 13-Jun-2023
https://doi.org/10.23919/ECC57647.2023.10178209
Koprowski PMagron VVaccon T(2023)Pourchet’s theorem in action: decomposing univariate nonnegative polynomials as sums of five squaresProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597072(425-433)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597072
Magron VDin MVu T(2023)Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational CoefficientsSIAM Journal on Optimization10.1137/21M143624533:1(63-88)Online publication date: 24-Jan-2023
https://doi.org/10.1137/21M1436245
Davis MPapp D(2022)Dual Certificates and Efficient Rational Sum-of-Squares Decompositions for Polynomial Optimization over Compact SetsSIAM Journal on Optimization10.1137/21M142257432:4(2461-2492)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1137/21M1422574
Schlosser CKorda M(2021)Converging outer approximations to global attractors using semidefinite programmingAutomatica10.1016/j.automatica.2021.109900134(109900)Online publication date: Dec-2021
https://doi.org/10.1016/j.automatica.2021.109900

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Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities

Certain classes of polynomial expansions and multiplication formulas

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