A System for Symbolic Computation in Hopf Algebras

在过去的十年里，执行符号计算来解决数学、科学和工程问题的计算机程序变得非常流行和有用。然而，非交换代数符号计算系统还没有达到交换代数系统的通用性。本课题开发了一个Hopf代数符号计算系统，支持代数和Hopf代数。该项目依赖于代数学家和计算机科学家之间的多学科互动。Hopf系统使用GAP系统作为基础，在此基础上构建更高级的功能。GAP和Hopf系统一样，在互联网上免费分发。Hopf系统能够支持非交换代数及其在科学，特别是数学和物理中的应用的高级研究。

Computer programs to perform symbolic calculations to solve mathematical, scientific, and engineering problems have become popular and highly useful in the last decade. However, systems for symbolic computation in noncommutative algebras have not attained the generality of systems for commutative algebra. This project develops a system for symbolic computation in Hopf algebras, and supports algebras and Hopf algebras. The project relies on multidisciplinary interaction between algebraists and computer scientists. The Hopf system uses the GAP system as a foundation upon which to build more advanced functions. GAP is freely distributed over the Internet, as is the Hopf system. The Hopf system is able to support advanced research in noncommutative algebras and their applications to science, especially mathematics and physics.