FGLM for Hermite and Popov Normal Forms of Ore Polynomial Matrices
Sprache des Vortragstitels:
Applications of Computer Algebra 2010
Sprache des Tagungstitel:
We are working with matrices over a ring $K[D,?,?]$ of Ore polynomials over a skew field $K$. Extending a result of Kojima et al for usual polynomials it is shown that in this setting the Hermite and Popov normal forms correspond to Gröbner bases with respect to certain orders. The FGLM algorithm is adapted to this setting and used for converting Popov forms into Hermite forms and vice versa. The approach works for arbitrary, i.e., not necessarily square matrices where we establish termination criteria to deal with infinitely dimensional factor spaces.