Group algorithms: Complexity, Theory and Practice.

群算法：复杂性、理论与实践。

• 批准号: ARC : DP0209706
• 负责人: Cheryl Praeger
• 金额: $ 18.6万
• 依托单位: The University of Western Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2002
• 资助国家: 澳大利亚
• 起止时间: 2002-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/group-algorithms-complexity-theory-practice/66787
• 关键词: Group; algorithms; Complexity; Theory; Practice.

Group algorithms: Complexity, Theory and Practice. The symmetry of a mathematical or physical system is often best described by an abstract structure called a group, and groups are commonly represented as groups of permutations or matrices. In this project we shall design and analyse a general algorithmic framework for computing with finite groups. In the context of permutation groups and matrix groups we will produce prototype implementations. The proposed framework has the potential to revolutionise algorithmic group theory as it draws together theoretical and computational models of groups.

群算法：复杂性、理论与实践。数学或物理系统的对称性通常最好用称为群的抽象结构来描述，群通常被表示为排列或矩阵的群。在这个项目中，我们将设计和分析一个用于有限群计算的通用算法框架。在置换群和矩阵群的背景下，我们将产生原型实现。提出的框架有可能彻底改变算法群体理论，因为它将群体的理论模型和计算模型结合在一起。