由吴方法计算零维系统的有理单元表示  

Computing the rational univariate representations for zero-dimensional systems by Wu’s method

作　　者：曾广兴[1] 肖水晶[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《中国科学：数学》2010年第10期999-1016,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10761006);国家重点基础研究发展规划(973)(批准号:2004CB318000)资助项目

摘　　要：本文提出一个计算零维系统的有理单元表示的新算法.无需进行Grbner基运算,我们的算法仅运用了著名的吴方法.基于吴方法,我们的算法在Maple平台上被编制成一个通用程序RUR-Wu,可快速地计算出零维系统的有理单元表示.作为一个应用,本文提出了一个有效方法,用来计算某些多项式的整体最小值.此外,本文给出了几个实例,用来表明算法的效率.The purpose of this paper is to present a new algorithm for computing the rational univariate representations of zero-dimensional systems. Instead of the Gro¨bner bases calculation, our algorithm is based on the well-known Wu’s method. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to compute rational univariate representations of zero-dimensional systems. As an application of our algorithm, we give an effective method to compute the global minimums of certain polynomials. Moreover, several examples are given to illustrate the efficiency of our algorithm.

关 键 词：零维系统 有理单元表示 吴方法 多项式优化 

分 类 号：O174.14[理学—数学]