The purpose of this secondment was twofold. Firstly , the secondment is an opportunity to make a connection between the secondee, Vu Trung Hieu and experts who work at Konstanz University. Secondly, the secondment is expected to solve problems concerning the topic of computing sum of squares decompositions of polynomials with rational coefficients.
Because of the pandemic, the secondee has performed the secondment remotely. The secondee joined the weekly meetings with his advisors Mohab Safey El Din (Sorbonne University), Victor Margon (LAAS), and Markus Schweighofer (Konstanz University). They discussed the problem of computing exact sum of squares decompositions of Hermitian complex trigonometric polynomials with Gaussian coefficients. Based on the discussions, they proposed a new algorithm to compute such sum of squares decompositions for polynomials that are non-negative on the unit circle. The algorithm has been implemented using the Maple computer algebra system. A complexity analysis of the algorithm has been started.
A paper is planned to be published following this secondment.