# Chenqi MouBeihang University (BUAA) | BUAA · School of Mathematics and Systems Science

Chenqi Mou

Doctor of Philosophy

## About

24

Publications

1,185

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309

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Introduction

Personal homepage: cmou.net

**Skills and Expertise**

## Publications

Publications (24)

Many biological systems are modeled mathematically as dynamic systems in the form of polynomial or rational differential equations. In this paper we apply sparse triangular decomposition to compute the equilibria of biological dynamic systems by exploiting the inherent sparsity of parameter-free systems via the chordal graph and by constructing sui...

Biological systems modeled as dynamical systems can be large in the number of variables and sparse in the interrelationship between the variables. In this paper we exploit the variable sparsity of biological dynamical systems in computing their equilibria by using sparse triangular decomposition. The variable sparsity of a biological dynamical syst...

Simple decomposition of polynomial sets computes conditionally squarefree triangular sets or systems with certain zero or ideal relationships with the polynomial sets. In this paper we study the chordality of polynomial sets occurring in the process of simple decomposition in top-down style. We first reformulate Wang’s algorithm for simple decompos...

In this paper, we first prove that when the associated graph of a polynomial set is chordal, a particular triangular set computed by a general algorithm in top-down style for computing the triangular decomposition of this polynomial set has an associated graph as a subgraph of this chordal graph. Then for Wang's method and a subresultant-based algo...

The Berlekamp–Massey and Berlekamp–Massey–Sakata algorithms compute a minimal polynomial or polynomial set of a linearly recurring sequence or multi-dimensional array. In this paper some underlying properties of and connections between these two algorithms are clarified theoretically: a unified flow chart for both algorithms is proposed to reveal t...

In this paper, the concepts of quasi-characteristic pair and quasi-characteristic decomposition are introduced. The former is a pair \((\mathcal {G}, \mathcal {C})\) of a reduced lexicographic Gröbner basis \(\mathcal {G}\) and the W-characteristic set \(\mathcal {C}\) which is regular and extracted from \(\mathcal {G}\); the latter is the decompos...

The structures of lexicographic (LEX) Gröbner bases were studied first by Lazard [4] for bivariate ideals and then extended to general zero-dimensional multivariate (radical) ideals [3, 6, 2]. Based on the structures of LEX Gröbner bases, algorithms have been proposed to compute triangular decompositions out of LEX Gröbner bases for zero-dimensiona...

In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into finitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr¨obner basis and the...

In this paper, we first prove that when the associated graph of a polynomial set is chordal, a particular triangular set computed by a general algorithm in top-down style for computing the triangular decomposition of this polynomial set has an associated graph as a subgraph of this chordal graph. Then for Wang's method and a subresultant-based algo...

In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set has a chordal associated graph. We prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-down style is a subgraph of th...

In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-do...

In this paper we focus on the algorithms and their implementations for decomposing an arbitrary polynomial set simultaneously into pairs of lexicographic Gröbner bases and normal triangular sets with inherent connections in between and associated zero relationship with the polynomial set. In particular, a method by temporarily changing the variable...

A characteristic pair is a pair (G,C) of polynomial sets in which G is a reduced lexicographic Groebner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be decomposed algorithmically into finitely many characteristic pairs with associated zero relations, which provid...

This article reports an algebraic criterion of the eigenvalue assignment, transversality condition and non-resonance condition for fold-N-S bifurcations. By means of symbolic computation methods, we propose an algorithmic approach for systematically analyzing codimension 2 bifurcations for high-dimensional discrete systems. The effectiveness of the...

Polynomial system solving over finite fields is of particular interest because of its applications in Cryptography, Coding Theory, and other areas of information science and technologies. In this thesis we study several important theoretical and computational aspects for solving polynomial systems over finite fields, in particular on the two widely...

Given a zero-dimensional ideal I in K[x1,...,xn] of degree D, the
transformation of the ordering of its Groebner basis from DRL to LEX is
a key step in polynomial system solving and turns out to be the
bottleneck of the whole solving process. Thus it is of crucial
importance to design efficient algorithms to perform the change of
ordering. The main...

This paper presents an algorithm for decomposing any positive-dimensional polynomial set into simple sets over an arbitrary finite field. The algorithm is based on some relationship established between simple sets and radical ideals, reducing the decomposition problem to the problem of computing the radicals of certain ideals. In addition to direct...

This paper is concerned with stability analysis of biological networks modeled as discrete and finite dynamical systems. We show how to use algebraic methods based on quantifier elimination, real solution classification and discriminant varieties to detect steady states and to analyze their stability and bifurcations for discrete dynamical systems....

Let I in K[x1,...,xn] be a 0-dimensional ideal of degree D where K is a field. It is well-known that obtaining efficient algorithms for change of ordering of Gröbner bases of I is crucial in polynomial system solving. Through the algorithm FGLM, this task is classically tackled by linear algebra operations in K[x1,...,n]/I. With recent progress on...

This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredient of these algorithms, we generalize the squarefree decomposition approach for univariate polynomials over a finite field to that over the field product...