纯五次域的单生成性：筛法的力量
Monogenity of pure quintic fields: the power of sieving
AI总结：
本文提出一种简单算法，用于计算纯五次域中的幂积分基生成器，通过改进的筛法显著减少需考虑的小指数数量。
摘要：
我们提供了一种简单算法，用于计算纯五次域中所有幂积分基的生成器。该过程涉及通常的标准元素，如Baker的方法和LLL约简。本文的主要目的是引入一种新思想，显著减少约简步骤后需考虑的小指数数量。这种新思想允许在几分钟内测试所有剩余的小指数，使用适当筛法，结果出人意料地快速。该思想将在许多类似情况下适用。
英文摘要：
We provide a simple algorithm for calculating all generators of power integral bases in pure quintic fields. This procedure involves the usual standard elements like Baker's method, LLL-reduction. The main purpose of the paper is to introduce a new idea to considerably diminish the number of small exponents to be considered after the reduction step. This new idea allows to test all remaining small exponents within a few minutes, using an appropriate sieve method, which turns out to be surprisingly fast. This idea will be applicable in many similar cases.
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。
