Composition tree algorithms for large matrix groups

大型矩阵组的组合树算法

• 批准号: DP160104626
• 负责人: Prof John Cannon
• 金额: $ 21.41万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160104626
• 关键词: Composition; tree; algorithms; large; matrix

This project aims to develop new algorithms for analysing groups. A group is a rather simple mathematical structure – an example is the set of all integers considering only the operations of addition and subtraction. Since the symmetries of an object form a group, groups are ubiquitous throughout mathematics and elsewhere in science. Because it is frequently necessary to determine a group's properties, there is great interest in finding efficient algorithms for analysing groups. A matrix group is a common type of group whose elements are square matrices. This project plans to employ a novel approach to designing algorithms for analysing large matrix groups, a task which is currently impossible using existing algorithms.

这个项目旨在开发分析群体的新算法。群是一种相当简单的数学结构——一个例子是只考虑加减运算的所有整数的集合。由于一个物体的对称性形成了一个群，所以群在数学和其他科学领域中无处不在。由于经常需要确定组的属性，因此寻找分析组的有效算法非常有兴趣。矩阵群是一种常见的群，它的元素是方阵。该项目计划采用一种新颖的方法来设计算法来分析大型矩阵群，这是目前使用现有算法无法完成的任务。