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Volume 27, Issue 3
Stable Border Bases for Ideals of Numerical Cartesian Sets

Lili Liu, Zhe Li & Shugong Zhang

Commun. Math. Res., 27 (2011), pp. 243-252.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

empirical point, numerical cartesian set, vanishing ideal, border base.

  • AMS Subject Headings

65H10, 14Q15, 13P10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-243, author = {Lili and Liu and and 18403 and and Lili Liu and Zhe and Li and and 18404 and and Zhe Li and Shugong and Zhang and and 18405 and and Shugong Zhang}, title = {Stable Border Bases for Ideals of Numerical Cartesian Sets}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {3}, pages = {243--252}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19089.html} }
TY - JOUR T1 - Stable Border Bases for Ideals of Numerical Cartesian Sets AU - Liu , Lili AU - Li , Zhe AU - Zhang , Shugong JO - Communications in Mathematical Research VL - 3 SP - 243 EP - 252 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19089.html KW - empirical point, numerical cartesian set, vanishing ideal, border base. AB -

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.

Lili Liu, Zhe Li & Shugong Zhang. (2021). Stable Border Bases for Ideals of Numerical Cartesian Sets. Communications in Mathematical Research . 27 (3). 243-252. doi:
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