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Stable Border Bases for Ideals of Numerical Cartesian Sets

Stable Border Bases for Ideals of Numerical Cartesian Sets
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摘要 In this paper, we discuss a special class of sets of bivariate empirical points, namely, numerical cartesian sets. We find that the stable quotient bases for numerical cartesian sets are unique if they exist. Furthermore, the corresponding border bases are the unique stable border bases for the vanishing ideals of numerical cartesian sets. In this paper, we discuss a special class of sets of bivariate empirical points, namely, numerical cartesian sets. We find that the stable quotient bases for numerical cartesian sets are unique if they exist. Furthermore, the corresponding border bases are the unique stable border bases for the vanishing ideals of numerical cartesian sets.
作者 LIU LI-LI LI ZHE ZHANG SHU-GONG
机构地区 Institute of Mathematics
出处 《Communications in Mathematical Research》 CSCD 2011年第3期243-252,共10页 数学研究通讯（英文版）
基金 Partially supported by the National Grand Fundamental Research 973 Program (2004CB318000) of China
关键词 empirical point numerical cartesian set vanishing ideal border base empirical point, numerical cartesian set, vanishing ideal, border base
分类号 O11 [理学—基础数学] TP301.6 [自动化与计算机技术—计算机系统结构]
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  • 1Sauer, T., Approximate varieties, approximate ideals and dimension reductions, Numer. Algo- r./t.hms, 45(2007), 295-313.
  • 2Heldt, D., Kreuzer, M., Pokutta, S. and Poulisse, H., Approximate computation of zero- dimensional polynomial ideals, J. Sybmolic Comput., 44(2009), 1566-1591.
  • 3Abbott, J., Fassino, C. and Torrente, M., Stable border bases for ideals of points, J. Symbolic Comput., 43(2008), 883-894.
  • 4Fassino, C., Almost vanishing polynomials for sets of limited precision points, J. Symbolic Comput., 45(2010), 19-37.
  • 5Cox, D., Little, J. and O'Shea, D., Ideal, Varieties, and Algorithms, 3rd Edition, Undergraduate Texts in Mathematics, Springer, New York, 2007.
  • 6Kreuzer, M., and Robbiano, L., Computational Commutative Algebra 1, Springer, Berlin, 2008.
  • 7Crainic, N., Multivariate Birkhoff-Lagrange interpolation schemes and cartesian sets of nodes, Acta Math. Univ. Cornenia. (N.S.), LXXIII(2004), 217-221.
  • 8Dong, T., Chen, T., Zhmag, S. and Wang, X., Bivariate Lagrange interpolation on tower inter- polation sites, http://aa-xiv.org/abs/1003.2493v2.
  • 9Kreuzer, M., Poulisse, H. and Robbiano, L., From oil fields to hilbert schemes, in: L. Robbiano, J. Abbott (Eds.), Approximate Commutative Algebra, Texts and Monographs in Symbolic Computation, Springer Vienna, New York, 2009, pp.1-54.
Communications in Mathematical Research
2011年 第3期

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