The sparse difference resultant introduced in Li et al. (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.

Li等人引入了稀疏差异结果。（2015b）是差异消除理论中的一个基本概念。在本文中，我们表明，可以通过由差分系统产生的简单代数系统的稀疏结果来计算通用Laurent变换本质系统的稀疏结果。此外，发现了新的稀疏差分结果的界。然后，我们提出了一种有效的算法来计算稀疏差分结果，该结果是两个行列式的商，两个行列式的元素是代数系统中多项式的系数。分析了算法的复杂性，实验结果表明了算法的有效性。