Calculating the sequence of main minors of the toeplitz band matrix

In this paper, we consider an algorithm that allows you to calculate the sequence of the main minors of the Toeplit.z band matrix associated with the Cauchy problem for a two-dimensional polynomial difference operator with constant coefficients, with an upper (lower) band width equal to one, which allows us to determine the non-degeneracy of such a matrix and, therefore, draw conclusions on the solvability of the Cauchy problem.