On Serre Reduction of Multidimensional Systems

الملخص EN

Serre reduction of a system plays a key role in the theory of Multidimensional systems, which has a close connection with Serre reduction of polynomial matrices.

In this paper, we investigate the Serre reduction problem for two kinds of nD polynomial matrices.

Some new necessary and sufficient conditions about reducing these matrices to their Smith normal forms are obtained.

These conditions can be easily checked by existing Gröbner basis algorithms of polynomial ideals.