Computing with matrix groups and Lie algebras: new concepts and applications

计算代数结合了符号计算和纯代数研究，关注的是解决具有代数结构的数学问题的算法设计。矩阵群和李代数是描述自然对称概念的重要代数对象。尽管它们在科学中非常常见和重要，但研究它们结构的算法却很缺乏。该项目将为使用这些对象进行计算开发深入的新数学理论，从而在计算代数方面取得突破性进展，并为包括其他科学在内的新研究提供强大的工具。新的功能将用于解决群理论和李理论中的两个分类问题。

Computational algebra combines symbolic computation and pure research in algebra, and is concerned with the design of algorithms for solving mathematical problems endowed with algebraic structure. Matrix groups and Lie algebras are prominent algebraic objects describing the natural concept of symmetry. Despite being very common and important in science, there is a paucity of algorithms to study their structure. This project will develop deep new mathematical theories for computing with these objects, leading to ground-breaking advances in computational algebra, and providing powerful tools facilitating new research, including in other sciences. The new functionality will be used to solve two classification problems in group and Lie theory.