LinApart2: efficient parallel partial fraction decomposition algorithm for denominators with polynomials of general degree

TL;DR

LinApart2 is an improved algorithm for univariate partial fraction decomposition that efficiently handles denominators of any degree without explicit factorization, offering significant speed and memory advantages over existing methods.

Contribution

It introduces a parallelizable algorithm capable of decomposing polynomials of arbitrary degree without explicit factorization, enhancing efficiency and scalability.

Findings

Substantial speedups over Mathematica's Apart

Reduced memory usage in benchmarks

Able to handle previously intractable problems

Abstract

We present LinApart2, a major update to the LinApart algorithm for univariate partial fraction decomposition. Unlike its predecessor, LinApart2 can handle denominators of arbitrary polynomial degree without explicit factorization, while retaining the efficiency and parallelizability of the Laurent series method. Benchmarks show substantial speedups in both runtime and memory usage compared to Mathematica's built-in routine Apart and to the Euclidean algorithm, enabling computations that were previously intractable.