We study the relationship between certain Groebner bases for zero dimensional ideals, and the interpolation condition functionals of ideal interpolation. Ideal interpolation is defined by a linear idempotent projector whose kernel is a polynomial ideal. In this paper, we propose the notion of "reverse" complete reduced basis. Based on the notion, we present a fast algorithm to compute the reduced Groebner basis for the kernel of ideal projector under an arbitrary compatible ordering. As an application, we show that knowing the affine variety makes available information concerning the reduced Groebner basis.

中文翻译：

---

理想插值的 Groebner 基结构

我们研究了零维理想的某些 Groebner 基与理想插值的插值条件泛函之间的关系。理想插值由线性幂等投影器定义，其内核是多项式理想。在本文中，我们提出了“反向”完全约简基的概念。基于这个概念，我们提出了一种快速算法来计算任意兼容排序下理想投影仪内核的约简格罗布纳基。作为一个应用，我们表明知道仿射变体可以提供有关约化 Groebner 基的信息。