The sparse difference resultant introduced in (Li , 2015b) is a basic concept in difference elimination theory. In this paper, we show that the sparse difference resultant of a generic Laurent transformally essential system can be computed via the sparse resultant of a simple algebraic system arising from the difference system. Moreover, new order bounds of sparse difference resultant are found. Then we propose an efficient algorithm to compute sparse difference resultant which is the quotient of two determinants whose elements are the coefficients of the polynomials in the algebraic system. The complexity of the algorithm is analyzed and experimental results show the efficiency of the algorithm.

Publication:

-    Journal of Symbolic Computation, (2021)

Authors:

-    Chun-Ming Yuan (KLMM, AMSS, Chinese Academy of Sciences & School of Mathematical Sciences, University of Chinese Academy of Sciences)

-    Zhi-Yong Zhang (College of Science, Minzu University of China)