理想插值的Groebner基结构
Groebner basis structure of ideal interpolation
AI总结：
本文研究理想插值中零维理想Groebner基与插值条件泛函的关系，提出逆向完全约化基概念，并给出任意相容序下快速计算理想投影算子核的约化Groebner基的算法。
摘要：
我们研究零维理想的某些Groebner基与理想插值的插值条件泛函之间的关系。理想插值由一个线性幂等投影算子定义，其核是一个多项式理想。本文提出“逆向”完全约化基的概念。基于该概念，我们给出一种快速算法，用于在任意相容序下计算理想投影算子核的约化Groebner基。作为一个应用，我们表明，已知仿射簇即可获得关于约化Groebner基的信息。
英文摘要：
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.
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