AI 中文总结
本文介绍开源Wolfram语言 paclet SimplicialHomology，用于在Mathematica中构建抽象单纯复形并计算其在整数、有理数和有限域上的同调群，还支持Betti数计算等功能，给出示例说明其性能。
AI 中文摘要
单纯同调计算对代数拓扑和计算几何至关重要。尽管已有多个成熟软件系统支持单纯复形相关操作，但Wolfram语言生态系统中此类计算的支持目前有限。本文介绍SimplicialHomology，这是一个开源Wolfram语言 paclet，用于构建抽象单纯复形并计算其在整数、有理数和有限域上的同调群。此外，该包还支持计算Betti数、自同构群，以及连接、星、链等其他构造。文中给出多个示例以说明该包及其性能。
英文摘要
Computations in simplicial homology are crucial for algebraic topology and computational geometry in general. Although several mature software systems provide facilities for working with simplicial complexes, there is currently limited support for such computations within the Wolfram language ecosystem. This paper presents SimplicialHomology, an open-source Wolfram language paclet for constructing abstract simplicial complexes and computing their homology groups over the integers, rational numbers, and finite fields. Furthermore, the package supports many other functionalities such as calculating Betti numbers, automorphism groups, and other constructions such as joins, stars, links, etc. Several examples are presented to illustrate the package and its performance.
Comments7 pages, only 1 figure and only 1 table, 13 references
