8 citations · 44 across the 14 of their papers we have counts for
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New bounds and efficient algorithm for sparse difference resultant
Chun-Ming Yuan, Zhi-Yong Zhang
The sparse difference resultant introduced in \citep{gao-2015} is a basic concept in difference elimination theory. In this paper, we show that the sparse difference resultant of a…
Quantum Algorithm for Optimization and Polynomial System Solving over Finite Field and Application to Cryptanalysis
Yu-Ao Chen, Xiao-Shan Gao, Chun-Ming Yuan
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the object…
Toric Difference Variety
Xiao-Shan Gao, Zhang Huang, Jie Wang +1
In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational pa…
Binomial Difference Ideals
Xiao-Shan Gao, Zhang Huang, Chun-Ming Yuan
In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Groebner basis of Z[…
A Polynomial-time Algorithm to Compute Generalized Hermite Normal Form of Matrices over Z[x]
Rui-Juan Jing, Chun-Ming Yuan, Xiao-Shan Gao
In this paper, a polynomial-time algorithm is given to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Groebner basis of the Z[x]…
Sparse Difference Resultant
Wei Li, Chun-Ming Yuan, Xiao-Shan Gao
In this paper, the concept of sparse difference resultant for a Laurent transformally essential system of difference polynomials is introduced and a simple criterion for the existe…
Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials
Zhi-Yong Zhang, Chun-Ming Yuan, Xiao-Shan Gao
In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomials and in the differential indeterminate with or…
Sparse Differential Resultant for Laurent Differential Polynomials
Wei Li, Chun-Ming Yuan, Xiao-Shan Gao
In this paper, we first introduce the concept of Laurent differentially essential systems and give a criterion for Laurent differentially essential systems in terms of their suppor…