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:我们提出计算在理想内插框架范围内一组有限点的消失理想的减少的 Gr\ {o}bner基础的算法。 理想内插由线性投影器定义, 其内核是多元性理想的线性投影器。 在本文中, 我们通过 Taylor 扩展将内插条件函数转换成正式的权力序列, 然后通过 Gaussian 消灭从正式的权力序列中读取减少的 Gr\ "{o}bner基础。 我们的算法具有多元性的时间复杂性。 它与单点理想内插和若干点理想内插法的 MMM 算法比较优异。