Sparse Differential Resultant for Laurent Differential Polynomials

被引：10

作者：

Li, Wei ^{[1
]}

Yuan, Chun-Ming ^{[1
]}

Gao, Xiao-Shan ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2015年 / 15卷 / 02期

关键词：

Sparse differential resultant; Jacobi number; Poisson product formula; Differential toric variety; BKK bound; Single exponential algorithm; CHOW FORM; COMPUTATIONAL-COMPLEXITY; ALGORITHMS; EQUATIONS; GEOMETRY; ELIMINATION; ORDER;

D O I：

10.1007/s10208-015-9249-9

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we first introduce the concept of Laurent differentially essential systems and give a criterion for a Laurent differential polynomial system to be Laurent differentially essential in terms of its support matrix. Then, the sparse differential resultant for a Laurent differentially essential system is defined, and its basic properties are proved. In particular, order and degree bounds for the sparse differential resultant are given. Based on these bounds, an algorithm to compute the sparse differential resultant is proposed, which is single exponential in terms of the Jacobi number and the size of the system.

引用

页码：451 / 517

页数：67

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