高维代数簇上点的几乎均匀抽样
Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
摘要：
本文研究代数簇上点的均匀抽样问题。具体来说，我们开发了一个随机算法，给定一个小的多元多项式在一个足够大的有限域，产生一个共同的零的多项式几乎均匀随机。该算法的输出分布与公共零点集上的均匀分布之间的统计距离在域大小上是多项式小的，并且在多项式个数为常数的情况下，该算法的运行时间在多项式及其次数的描述上是多项式的.
英文摘要：
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynomials almost uniformly at random. The statistical distance between the output distribution of the algorithm and the uniform distribution on the set of common zeros is polynomially small in the field size, and the running time of the algorithm is polynomial in the description of the polynomials and their degrees provided that the number of the polynomials is a constant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
