LinApart: Optimizing the univariate partial fraction decomposition

We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for the decomposition of rational functions with fully factorized denominators. We provide an implementation in the Wolfram Mathematica language, which can lead to very significant performance gains over the built-in Apart command. Furthermore, a C language library implementing the core functionality and suitable for interfacing with other software is also provided. Both codes are made available at https://github.com/fekeshazy/LinApart.

本报告推出LinApart，一项旨在高效执行大规模符号表达式一元部分分式分解的常规程序。本方法基于对具有完全分解分母的有理函数分解的显式封闭公式的应用。我们以Wolfram Mathematica语言实现了该方案，相较于内置的Apart指令，可显著提升性能。此外，我们还提供了一款C语言库，该库实现了核心功能，并适用于与其他软件的接口。两款代码均已发布于https://github.com/fekeshazy/LinApart。