Sparse difference resultant

Authors:
Wei Li;Chun-Ming Yuan;Xiao-Shan Gao
Affiliations:
KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, China;KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, China;KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, China
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

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Abstract

In this paper, the concept of sparse difference resultant for a Laurent transformally essential system of Laurent difference polynomials is introduced and its properties are proved. In particular, order and degree bounds for the 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 system. Also, the precise order, degree, a determinant representation, and a Poisson-type product formula for the difference resultant are given.