Abstract. NCSOStools is a Matlab toolbox for - symbolic computation with polynomials in noncommuting variables; - constructing and solving sum of hermitian squares (with commutators) programs for polynomials in noncommuting variables. It can be used in combination with semidefinite programming software, such as SeDuMi, SDPA or SDPT3 to solve these constructed programs. This paper provides an overview of the theoretical underpinning of these sum of hermitian squares (with commutators) programs, and provides a gentle introduction to the primary features of NCSOStools.
Cafuta, Kristijan; Klep, Igor; Povh, Janez. NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials. Optim. Methods Softw. 26 (2011), no. 3, 363--380.