Jinwang Liu

The Lin-Bose Problem

This brief studies prime factorization problems of a multivariate polynomial matrix. We mainly investigate the Lin-Bose problem proposed by Lin and Bose in the multidimensional system theory context. A simple proof to the Lin-Bose problem is presented in a much easier way to understand. As a by-product, we obtain some properties on modules generated by all the rows of a matrix.

GVW ALGORITHM OVER PRINCIPAL IDEAL DOMAINS

GVW algorithm was given by Gao, Wang, and Volny in computing a Gröbner bases for ideal in a polynomial ring, which is much faster and more simple than F5. In this paper, the authors generalize GVW algorithm and present an algorithm to compute a Gröbner bases for ideal when the coefficient ring is a principal ideal domain.

The Gröbner h-bases under composition

Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. H.Hong has resolved following problem: when does polynomial composition commute with Gröbner basis computation? The main question of this paper is: when does polynomial composition commute with Gröbner h-bases computation? And we obtain some interesting results. These have some natural application in the computation of Gröbner bases of composed polynomials which often appear in real life problems.

Minor Prime Factorization for -D Polynomial Matrices over Arbitrary Coefficient Field

In this paper, we investigate two classes of multivariate ( -D) polynomial matrices whose coefficient field is arbitrary and the greatest common divisor of maximal order minors satisfy certain condition. Two tractable criterions are presented for the existence of minor prime factorization, which can be realized by programming and complexity computations. On the theory and application, we shall obtain some new and interesting results, giving some constructive computational methods for carrying out the minor prime factorization.

Quillen–Suslin theory for the special linear group

ABSTRACT We prove that for any valuation ring R of Krull dimension ≤1 or any commutative local ring R with Krull dimension 0 and n≥3, the special linear group SLn(R[x]) coincides with the group of elementary matrices En(R[x]), and for an arbitrary arithmetical ring R of Krull dimension ≤1 and n≥3, the group . These give partial solutions to two conjectures of Yengui.

On the equivalence of multivariate polynomial matrices

The equivalence of system is an important concept in multidimensional (

Some criteria for Gröbner bases and their applications

n

A new signature-based algorithms for computing Gröbner bases

nD) system, which is closely related to equivalence of multivariate polynomial matrices. This paper mainly investigates the equivalence of some