Science China Mathematics

, Volume 55, Issue 6, pp 1293–1302 | Cite as

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

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Abstract

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 Gröbner basis. The new algorithm also provides a method for testing separating elements.

Keywords

RUR PUR zero-dimensional ideals Gröbner basis 

MSC(2010)

12Y05 13P10 13P15 33F10 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.KLMM, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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