A sum-of-squares package for Macaulay 2.
SumsOfSquares.m2 is a Macaulay2 package for computing sum-of-squares (SOS) decompositions of multivariate polynomials with rational coefficients. The algorithm uses an interior point method to solve the underlying semidefinite program and attempts to compute an exact rational decomposition from the numerical solution.
Authors: Diego Cifuentes (MIT), Thomas Kahle (OvGU Magdeburg), Pablo A. Parrilo (MIT), Helfried Peyrl (Reactive Robotics).
Special thanks: Nidhi Kaihnsa, Anton Leykin.
[1] H. Peyrl and P. A. Parrilo. "Computing sum of squares decompositions with rational coefficients", Theoretical Computer Science 409.2 (2008):269-281.
[2] D. Cifuentes, T. Kahle and P. A. Parrilo. "Sums of squares in Macaulay2", arXiv:1812.05475, 2018.