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

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 algorit...

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Veröffentlicht in:Science China. Mathematics 2012-06, Vol.55 (6), p.1293-1302
Hauptverfasser: Ma, XiaoDong, Sun, Yao, Wang, DingKang
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1674-7283
1006-9283
1869-1862
DOI:10.1007/s11425-012-4404-0