Computing polynomial univariate representations of zero-dimensional ideals by Grbner basis  

作　　者：MA XiaoDong SUN Yao WANG DingKang 

机构地区：[1]KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2012年第6期1293-1302,共10页中国科学：数学（英文版）

基　　金：supported by National Key Basic Research Project of China(Grant No. 2011CB302400);National Natural Science Foundation of China (Grant Nos. 10971217,60821002/F02)

摘　　要：Rational Univariate Representation （RUR） of zero-dimensional ideals is used to describe the zeros of zero-dimensional ideals and RUR has been studied extensively. In 1999, Roullier proposed an efficient algorithm to compute RUR of zero-dimensional ideals. In this paper, we will present a new algorithm to compute Polynomial Univariate Representation （PUR） of zero-dimensional ideals. The new algorithm is based on some interesting properties of Grobner basis. The new algorithm also provides a method for testing separating elements.Rational Univariate Representation(RUR) of zero-dimensional ideals is used to describe the zeros of zero-dimensional ideals and RUR has been studied extensively.In 1999,Roullier proposed an efficient algorithm to compute RUR of zero-dimensional ideals.In this paper,we will present a new algorithm to compute Polynomial Univariate Representation(PUR) of zero-dimensional ideals.The new algorithm is based on some interesting properties of Grbner basis.The new algorithm also provides a method for testing separating elements.

关 键 词：RUR PUR zero-dimensional ideals Grobner basis 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O151.21[自动化与计算机技术—计算机科学与技术]