Chenqi Mou

Chenqi Mou
Beihang University (BUAA) | BUAA · School of Mathematics and Systems Science

Doctor of Philosophy

About

23
Publications
753
Reads
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220
Citations
Introduction
Personal homepage: cmou.net

Publications

Publications (23)
Article
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...
Chapter
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...
Chapter
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...
Article
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...
Chapter
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...
Chapter
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...
Article
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...
Article
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...
Preprint
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...
Conference Paper
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...
Article
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...
Conference Paper
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
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....
Conference Paper
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...
Article
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...