AI 中文总结
介绍fkcompute开源软件包，它通过三相管道计算链环的古科夫 - 马诺列斯库不变量，能计算多种纽结和链环，还用于编译首个相关公共数据库，可作为多种工具使用。
AI 中文摘要
我们介绍了fkcompute，一个用于从辫子表示计算链环的古科夫 - 马诺列斯库不变量的开源软件包。fkcompute通过一个三相管道实现了帕克的反转状态和。首先，搜索合适的辫子表示和辫子上的额外反转数据。然后，将反转和的状态空间编码为一个多面体，由相关的线性约束系统界定。最后，通过与状态相关的\(R\)矩阵相乘来构造不变量。基准测试表明，12交叉以下的素纽结以及10交叉以下且最多3个分量的素链环都能轻松计算。因此，fkcompute被用于编译第一个古科夫 - 马诺列斯库不变量的公共数据库。该软件包可作为Python库、命令行工具和Mathematica插件使用。
英文摘要
We introduce fkcompute, an open-source package for computing the Gukov--Manolescu invariant of links from a braid presentation. fkcompute implements Park's inverted state sum through a three-phase pipeline. First, a search is performed for a suitable braid presentation and for an additional inversion data on the braid. Then, the state space of the inverted sum is encoded as a polytope, bounded by the associated linear constraint system. Finally, the invariant is constructed by multiplication of R-matrices associated to the states. Benchmarks show that prime knots up to 12 crossings, and prime links up to 10 crossings and of at most 3 components, are comfortably within reach. As a result, fkcompute is used to compile the first public database of the Gukov--Manolescu invariant. The package is available as a Python library, a command-line tool, and a Mathematica paclet.
Comments17 pages, 1 figure, 1 table, GitHub repository: github.com/caltech-quantum-topology/fkcompute, database: topology.fyi
