Moisés Bermejo Morán

Our motivation is to exploit the partial commutation structure between the variables in non-commutative polynomial optimisation problems to boost the performance. We provide an efficient normal form for free words in partially commuting letters based on the maximal cliques of the non-commutation graph between the letters. We adapt several non-commutative computations to the partially commuting setting exploiting this additional structure. In particular, we provide an algorithm to compute Grobner bases for polynomial ideals in partially commuting variables that overcomes some difficulties appearing in the non-commutative cases: sometimes infinite Grobner basis can be avoided using the normal form based on these cliques.