5 citations · 8 across the 5 of their papers we have counts for
5 papers
Differential Chow Form for Projective Differential Variety
Wei Li, Xiao-Shan Gao
In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential vari…
Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation
Jin-San Cheng, Xiao-Shan Gao, Leilei Guo
In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represente…
Multiplicity Preserving Triangular Set Decomposition of Two Polynomials
Jin-San Cheng, Xiao-Shan Gao
In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the pol…
Efficient Characteristic Set Algorithms for Equation Solving in Finite Fields and Applications in Cryptanalysis
Xiao-Shan Gao, Zhenyu Huang
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and…
On Functional Decomposition of Multivariate Polynomials with Differentiation and Homogenization
Shangwei Zhao, Ruyong Feng, Xiao-Shan Gao
In this paper, we give a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which…