We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal. In this paper, we translate interpolation condition functionals into formal power series via Taylor expansion, then the reduced Gr\"{o}bner basis is read from formal power series by Gaussian elimination. Our algorithm has a polynomial time complexity. It compares favorably with MMM algorithm in single point ideal interpolation and some several points ideal interpolation.

翻译：我们提出了在理想插值框架下计算有限点集零化理想约化格勒布纳基的算法。理想插值由线性投影算子定义，其核为一个多项式理想。本文通过泰勒展开将插值条件泛函转化为形式幂级数，进而利用高斯消元从形式幂级数中读取约化格勒布纳基。本算法具有多项式时间复杂度，在单点理想插值及若干多点理想插值中均优于MMM算法。