Homalg：一个同调代数的元包
Homalg: A meta-package for homological algebra
摘要：
这项工作的中心概念是，在所谓的可计算环上的非线性表示模的范畴之间的函子，即环R，其中人们可以算法地求解R中系数的非齐次线性方程。本文介绍了一种在计算机代数系统中实现Hom、张量积、Ext、Tor等函子的方法。一旦实现了这一点，人们就可以组合和派生函子，甚至不需要任何关于这些函子的特定知识就可以完成这个过程。这些想法在环独立包homalg中实现。它的目的是扩展任何计算机代数软件实现算术的可计算环R，只要后者包含算法，以解决非齐次线性方程的系数在R。除了解释这是如何足够的，本文介绍了由homalg提供的扩展的性质。
英文摘要：
The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
