The Liouville Generator for Producing Integrable Expressions

Rashid Barket; Matthew England; Juergen Gerhard

doi:10.1007/978-3-031-69070-9_4

The Liouville Generator for Producing Integrable Expressions

Rashid Barket, Matthew England, Juergen Gerhard

Research Centre for Computational Science and Mathematical Modelling

Maplesoft

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

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.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing
Subtitle of host publication	26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings
Editors	François Boulier, Chenqi Mou, Timur M. Sadykov, Evgenii V. Vorozhtsov
Publisher	Springer
Chapter	4
Pages	47-62
Number of pages	16
Volume	14938
Edition	1
ISBN (Electronic)	978-3-031-69070-9
ISBN (Print)	978-3-031-69069-3
DOIs	https://doi.org/10.1007/978-3-031-69070-9_4
Publication status	Published - 21 Aug 2024
Event	26th International Computer Algebra in Scientific Computing - Rennes, France Duration: 2 Sept 2024 → 6 Sept 2024 https://casc-conference.org/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	26th International Computer Algebra in Scientific Computing
Abbreviated title	CASC 2024
Country/Territory	France
City	Rennes
Period	2/09/24 → 6/09/24
Internet address	https://casc-conference.org/

Keywords

Computer algebra
Symbolic computation
Symbolic integration
Data generation
Machine learning

Access to Document

10.1007/978-3-031-69070-9_4

Cite this

Barket, R., England, M., & Gerhard, J. (2024). The Liouville Generator for Producing Integrable Expressions. In F. Boulier, C. Mou, T. M. Sadykov, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing: 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings (1 ed., Vol. 14938, pp. 47-62). (Lecture Notes in Computer Science). Springer . https://doi.org/10.1007/978-3-031-69070-9_4

The Liouville Generator for Producing Integrable Expressions. / Barket, Rashid ; England, Matthew; Gerhard, Juergen.
Computer Algebra in Scientific Computing: 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings. ed. / François Boulier; Chenqi Mou; Timur M. Sadykov; Evgenii V. Vorozhtsov. Vol. 14938 1. ed. Springer , 2024. p. 47-62 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

Barket, R , England, M & Gerhard, J 2024, The Liouville Generator for Producing Integrable Expressions. in F Boulier, C Mou, TM Sadykov & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing: 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings. 1 edn, vol. 14938, Lecture Notes in Computer Science, Springer , pp. 47-62, 26th International Computer Algebra in Scientific Computing, Rennes, France, 2/09/24. https://doi.org/10.1007/978-3-031-69070-9_4

Barket R , England M, Gerhard J. The Liouville Generator for Producing Integrable Expressions. In Boulier F, Mou C, Sadykov TM, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing: 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings. 1 ed. Vol. 14938. Springer . 2024. p. 47-62. (Lecture Notes in Computer Science). Epub 2024 Aug 20. doi: 10.1007/978-3-031-69070-9_4

Barket, Rashid ; England, Matthew ; Gerhard, Juergen. / The Liouville Generator for Producing Integrable Expressions. Computer Algebra in Scientific Computing: 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings. editor / François Boulier ; Chenqi Mou ; Timur M. Sadykov ; Evgenii V. Vorozhtsov. Vol. 14938 1. ed. Springer , 2024. pp. 47-62 (Lecture Notes in Computer Science).

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The Liouville Generator for Producing Integrable Expressions

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