SOS.m2: A Macaulay2 package for computing sum of squares decompositions of polynomials with rational coefficients. In recent years semideffinite programming (SDP) has become the standard technique for computing sum of squares (SOS) decompositions of nonnegative polynomials. Due to the nature of the underlying methods, the solutions are computed numerically, and thus are never exact. In this paper we present a software package for Macaulay 2, which aims at computing an exact SOS decomposition from a numerical solution.
Keywords for this software
References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes: Certifying solutions to overdetermined and singular polynomial systems over (\mathbbQ) (2018)
- Dou , Xiaojie; Cheng , Jin-San: A heuristic method for certifying isolated zeros of polynomial systems (2018)
- Ahmadi, Amir Ali; Parrilo, Pablo A.: A convex polynomial that is not sos-convex (2012)
- Kaltofen, Erich L.; Li, Bin; Yang, Zhengfeng; Zhi, Lihong: Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients (2012)
- Hillar, Christopher J.: Sums of squares over totally real fields are rational sums of squares (2009)
- Kaltofen, Erich; Li, Bin; Yang, Zhengfeng; Zhi, Lihong: Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars (2008)
- Klep, Igor; Schweighofer, Markus: Sums of Hermitian squares and the BMV conjecture (2008)
- Peyrl, Helfried; Parrilo, Pablo A.: Computing sum of squares decompositions with rational coefficients (2008)