The Liouville Generator for Producing Integrable Expressions

TL;DR

This paper introduces the Liouville generator, a novel method for creating complex, integrable expressions in computer algebra, leveraging Liouville's theorem and the Risch Algorithm, to aid benchmarking and machine learning.

Contribution

The paper presents a new data generation method for integrable expressions based on Liouville's theorem, improving upon previous methods for benchmarking and machine learning applications.

Findings

Generates complex, realistic integrands

Retains advantages of previous data methods

Suitable for benchmarking and machine learning

Abstract

There has been a growing need to devise processes that can create comprehensive datasets in the world of Computer Algebra, both for accurate benchmarking and for new intersections with machine learning technology. We present here a method to generate integrands that are guaranteed to be integrable, dubbed the LIOUVILLE method. It is based on Liouville's theorem and the Parallel Risch Algorithm for symbolic integration. We show that this data generation method retains the best qualities of previous data generation methods, while overcoming some of the issues built into that prior work. The LIOUVILLE generator is able to generate sufficiently complex and realistic integrands, and could be used for benchmarking or machine learning training tasks related to symbolic integration.