Topics in algorithmic and computational number theory

算法和计算数论主题

• 批准号: 7649-2010
• 负责人: Williams, Hugh
• 金额: $ 1.75万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=474253
• 关键词: Topics; algorithmic; computational; number; theory

Over the last several decades number theory, that branch of mathematics which deals with the properties of integers, has become a very important area of study in Canada. Indeed, this is one of the most active areas of pure mathematical research in this country. My research involves the discovery of methods, and their computer implementation, to compute certain number theoretic objects. These problems include the seemingly simple problem of determining whether or not an integer is a prime, to more complex problems such as computing the class number of a number field. This latter quantity is of great importance to the corresponding number field; very roughly speaking, it can be considered as a measure of how much the integers of the number field differ in their properties from the integers with which we are all familiar: the whole numbers. My main interest is in finding very efficient ways of solving these kinds of problems.

在过去的几十年里，数论，数学的分支，它处理整数的性质，已成为一个非常重要的研究领域在加拿大。 事实上，这是一个最活跃的领域纯数学研究在这个国家。 我的研究涉及方法的发现，以及它们的计算机实现，以计算某些数论对象。 这些问题包括确定整数是否是素数的看似简单的问题，以及更复杂的问题，如计算数域的类数。 后一个量对于相应的数域非常重要;粗略地说，它可以被认为是数域的整数在性质上与我们所熟悉的整数（整数）有多大区别的度量。我的主要兴趣是寻找解决这类问题的有效方法。