Computation of the general solution of a multivariate polynomial matrix Diophantine equation

Abstract

In this paper we propose a procedure to reduce a 2 - D square polynomial matrix of arbitrary degrees to matrix pencils of the form sX + ZY + A, using zero coprime equivalence. As a further step, we provide the necessary and sufficient condition by which pencils of specific forms, appearing as parametric families, are zero coprime equivalent to a 2 - D regular polynomial matrix. Appropriate examples are provided to illustrate the use of proven results.