- symbolic computation with polynomials in noncommuting variables;
- constructing and solving sum of hermitian squares (with commutators) programs for polynomials in noncommuting variables.
The programs constructed are semidefinite programs (SDP) and are currently solved using SeDuMi (Jos Sturm’s old version is available here) or SDPT3. For a full description of the toolbox please see http://ncsostools.fis.unm.si/documentation.
Readers interested in sum of squares and optimization of polynomials in commuting variables are refered to one of the many great existing packages, such as GloptiPoly, SOSTOOLS, YALMIP, etc.
A Mathematica package for computations with noncommutative polynomials is Bill Helton’s NCAlgebra.