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.

翻译：我们研究了零维理想的特定Gröbner基与理想插值条件泛函之间的关系。理想插值由线性幂等投影算子定义，其核为多项式理想。本文提出"逆向"完全约化基的概念，并基于该概念给出在任意相容序下计算理想投影子核的约化Gröbner基的快速算法。作为应用，我们证明了仿射簇已知时，可获取关于约化Gröbner基的可用信息。