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

计算代数结合了符号计算和代数中的纯研究，涉及到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性概念的重要代数对象。尽管在科学上非常常见和重要，但研究它们的结构的算法很少。该项目将为使用这些对象进行计算开发深刻的新数学理论，导致计算代数取得突破性进展，并提供强大的工具促进新的研究，包括在其他科学领域。新功能将用于解决群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.