标题： 希尔伯特函数的切分理想 显示英文标题

标题： Hilbert Functions of Chopped Ideals

摘要： 从齐次理想中通过仅考虑固定次数的生成元得到一个截断理想。 我们研究截断理想与原一维理想定义相同有限点集的情况。 从截断理想计算这些点的复杂性由Hilbert函数和正则性决定。 我们对这些不变量提出猜想，并在许多情况下证明了它们。 我们表明我们的猜想对于对称张量分解具有实际相关性。 显示英文摘要

摘要： A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of computing these points from the chopped ideal is governed by the Hilbert function and regularity. We conjecture values for these invariants and prove them in many cases. We show that our conjecture is of practical relevance for symmetric tensor decomposition.