标题： 抽象单纯复形在{\tt Macaulay2} 显示英文标题

标题： Abstract simplicial complexes in {\tt Macaulay2}

摘要： {\tt 抽象单纯复形.m2}是一个为计算机代数系统{\tt Macaulay2} \cite{M2} 编写的计算机代数包。 它提供了新的基础设施来处理抽象单纯复形及相关同调构造。 其关键新特性是将每个给定的抽象单纯复形实现为一种分级列表，形式为带有整数键的哈希表。 在其他功能中，这允许直接实现相关的约化和非约化单纯链复形。 此外，它还便于构造随机单纯复形。 我们在此采用的方法建立在{\tt Macaulay2}包{\tt 复形.m2} \cite{Stillman:Smith:Complexes.m2} 的基础上。 它补充了现有的{\tt Macaulay2}单纯复形框架，该框架由包{\tt 单纯复形.m2}\cite{Smith:et:al:SimplicialComplexes.m2:jsag}实现，且与之完全不同。 显示英文摘要

摘要： {\tt AbstractSimplicialComplexes.m2} is a computer algebra package written for the computer algebra system {\tt Macaulay2} \cite{M2}. It provides new infrastructure to work with abstract simplicial complexes and related homological constructions. Its key novel feature is to implement each given abstract simplicial complex as a certain graded list in the form of a hash table with integer keys. Among other features, this allows for a direct implementation of the associated reduced and non-reduced simplicial chain complexes. Further, it facilitates construction of random simplicial complexes. The approach that we employ here builds on the {\tt Macaulay2} package {\tt Complexes.m2} \cite{Stillman:Smith:Complexes.m2}. It complements and is entirely different from the existing {\tt Macaulay2} simplicial complexes framework that is made possible by the package {\tt SimplicialComplexes.m2} \cite{Smith:et:al:SimplicialComplexes.m2:jsag}.