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

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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/

Bibliographical note

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-031-69070-9_4

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

This document is the author’s post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

Funding

The authors would like to thank James H. Davenport for helpful discussion on the Parallel Risch algorithm. Matthew England is supported by EPSRC Project EP/T015748/1, Pushing Back the Doubly-Exponential Wall of Cylindrical Algebraic Decomposition (the DEWCAD Project). Rashid Barket is supported by a scholarship provided by Maplesoft and Coventry University.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/T015748/1
Maplesoft
Coventry University

Keywords

Computer algebra
Symbolic computation
Symbolic integration
Data generation
Machine learning

Access to Document

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

England2024AAMAccepted author manuscript, 10.9 MB

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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