2012/12/13 by Wei Li, Li, Wei, Chun-Ming Yuan +3
Agricultural and Biological Sciences · Computer Science · Mathematics · #12H10 #68W30 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #I.1 #Polynomial and algebraic computation #Polysaccharides and Plant Cell Walls #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.1212.3090
openalex publication_date 2012/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 existence of sparse difference resultant is given. The concept of transformally homogenous polynomial is introduced and the sparse difference resultant is shown to be transformally homogenous. It is shown that the vanishing of the sparse difference resultant gives a necessary condition for the corresponding difference polynomial system to have non-zero solutions. The order and degree bounds for sparse difference resultant are given. Based on these bounds, an algorithm to compute the sparse difference resultant is proposed, which is single exponential in terms of the number of variables, the Jacobi number, and the size of the Laurent transformally essential system. Furthermore, the precise order and degree, a determinant representation, and a Poisson-type product formula for the difference resultant are given.