Reduction of 2-D rational functions

This paper presents a method of reducing a two-dimensional (2-D) rational function to an irreducible one. It is achieved by searching the first linearly dependent row, in order from top to bottom, of a generalized resultant. Some properties of the resultant are discussed. The result can be used to compute the greatest common divisor (g.c.d.) of two 2-D polynomials by carrying out one additional division. This procedure does not require the computation of primitive polynomials, which is required by all existing methods, and thus provides a potentially attractive method of computing g.c.d. The method can be readily extended to three-or higher-dimensional cases.