Constructive Representation Theory and its Applications

构造表征理论及其应用

• 批准号: DP0772368
• 负责人: Prof John Cannon
• 金额: $ 22.27万
• 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: 2007
• 资助国家: 澳大利亚
• 起止时间: 2007-01-17 至 2010-01-16
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0772368
• 关键词: Constructive; Representation; Theory; its; Applications

The algorithms developed will make it possible to determine the different ways (representations) in which a group of symmetries may be  realised as transformations of some space. Such knowledge is required in many areas including differential equations, digital signal processing, engineering ('strut-and-cable' constructions), the design of telephone networks, crystallography and quantum information processing. The high-performance tools for linear algebra developed will also find application in cryptography and coding theory. This work represents the latest stage in a long-term project to discover practical algorithms for elucidating the properties of complex algebraic structures - an area where Australia is a world-leader.

所开发的算法将使人们有可能确定不同的方式（表示），其中一组对称性可以实现为一些空间的变换。这些知识在许多领域都需要，包括微分方程，数字信号处理，工程（“支柱和电缆”结构），电话网络设计，晶体学和量子信息处理。开发的高性能线性代数工具也将在密码学和编码理论中得到应用。这项工作代表了一个长期项目的最新阶段，该项目旨在发现用于阐明复杂代数结构属性的实用算法-澳大利亚在这一领域处于世界领先地位。