计算点理想的所有边界基
Computing all border bases for ideals of points
摘要：
在本文中，我们考虑的问题，计算所有可能的阶理想，也连接到1的集合，以及相应的边界基，为消失理想的一个给定的有限集的点。在这种情况下，两种不同的方法进行了讨论：基于Buchberger-Möller算法，我们首先提出了一个新的算法来计算所有可能的阶理想和相应的边界基地的理想的点。第二种方法涉及调整Farr-Gao算法，用于找到连接到1的所有集合以及对应的边界基，用于点的理想。应该指出的是，我们的算法是术语排序自由。因此，他们可以成功地计算所有的边界基地的理想点。这两种算法都已实现，并通过一组基准测试讨论了它们的效率。
英文摘要：
In this paper we consider the problem of computing all possible order ideals and also sets connected to 1, and the corresponding border bases, for the vanishing ideal of a given finite set of points. In this context two different approaches are discussed: based on the Buchberger-Möller Algorithm, we first propose a new algorithm to compute all possible order ideals and the corresponding border bases for an ideal of points. The second approach involves adapting the Farr-Gao Algorithm for finding all sets connected to 1, as well as the corresponding border bases, for an ideal of points. It should be noted that our algorithms are term ordering free. Therefore they can compute successfully all border bases for an ideal of points. Both proposed algorithms have been implemented and their efficiency is discussed via a set of benchmarks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
