Some improvements for the algorithm of Gröbner bases over dual valuation domain

As a special ring with zero divisors, the dual noetherian valuation domain has attracted much attention from scholars. This article aims at to improve the Buchberger's algorithm over the dual noetherian valuation domain. We present some criterions that can be applied in the algorithm for computing Gröbner bases, and the criterions may drastically reduce the number of S-polynomials in the course of the algorithm. In addition, we clearly demonstrate the improvement with an example

further results on homogeneous grobner bases under composition

The aim of the study was to investigate the immune effect of fusion protein VP4-STI.40 mouse were randomly divided into 4 groups of test bacterin group(30 μg VP4-STI+0.6 μg LTB),aluminiumhydroxide vaccine group(30 μg VP4-STI+Al(OH)3 gel),pure protein VP4

The Statistical Zero-knowledge Proof for Blum Integer Based on Discrete Logarithm

Blum integers (BL), which has extensively been used in the domain of cryptography, are integers with form p , where p and q are di#erent primes both 3 mod 4 and k 1 and k 2 are odd integers. These integers can be divided two types: 1) M = pq, 2) M = p at least one of k 1 and k 2 is greater than 1

Generalized Serre Problem over Elementary Divisor Rings

Matrix factorization has been widely investigated in the past years due to its fundamental importance in several areas of engineering. This paper investigates completion and zero prime factorization of matrices over elementary divisor rings (EDR). The Serre problem and Lin-Bose problems are generalized to EDR and are completely solved

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

In this paper, we investigate two classes of multivariate (n-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

The Smith Form of A Multivariate Polynomial Matrix Over An Arbitrary Coefficient Field

10.1080/03081087.2020.1726275Linear and Multilinear Algebra7002366-37