On nD polynomial matrix factorizations

This paper presents an overview of one of the nD polynomial matrix factorization problems, namely the factorization of a given nD polynomial matrix A(z) into A(z)=A₁(z)A₂(z) such that A₁(z) and A₂(z) are both nD polynomial matrices with certain special properties. The paper covers applications of both “classical” techniques as well as the Grobner bases to this factorization problem for the 2D and nD (n>2) cases. The difference between the 2D and the nD cases is pointed out. Besides reviewing the existing results, a new result and some open problems are also presented