Conversion between Hermite and Popov normal forms using an FGLM-like approach

We are working with matrices over a ring K[@; ; #] of Ore polynomialsover a skew eld K. Extending a result of [18] for usual polynomialsit is shown that in this setting the Hermite and Popov normal forms correspondto Gr bner bases with respect to certain orders. The FGLM algorithmis adapted to this setting and used for converting Popov forms into Hermiteforms and vice versa. The approach works for arbitrary, that is, not necessarilysquare matrices where we establish termination criteria to deal with innitelydimensional factor spaces.