Size of coefficients of lexicographical Groöbner bases: The zero-dimensional, radical and bivariate case

研究成果: 書籍の章/レポート/Proceedings会議への寄与査読

4 被引用数 (Scopus)

抄録

This work is limited to the zero-dimensional, radical, and bivariate case. A lexicographical Gröbner basis can be simply viewed as Lagrange interpolation polynomials. In the same way the Chinese remaindering theorem generalizes Lagrange interpolation, we show how a triangular decomposition is linked to a specific Gröbner basis (not the reduced one). A bound on the size of the coefficients of this specific Gröbner basis is proved using height theory, then a bound is deduced for the reduced Gröbner basis. Besides, the link revealed between the Gröbner basis and the triangular decomposition gives straightforwardly a numerical estimate to help finding a lucky prime in the context of modular methods.

本文言語英語
ホスト出版物のタイトルISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
ページ119-126
ページ数8
DOI
出版ステータス出版済み - 2009
イベント2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, 大韓民国
継続期間: 2009 7月 282009 7月 31

出版物シリーズ

名前Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

会議

会議2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
国/地域大韓民国
CitySeoul
Period09/7/2809/7/31

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