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A Purely Functional Computer Algebra System Embedded in Haskell

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Book cover Computer Algebra in Scientific Computing (CASC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11077))

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Abstract

We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Gröbner basis algorithms, such as Faugère’s \(F_4\) and \(F_5\), in a composable way.

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Notes

  1. 1.

    Indeed, one can use dependent types, described in the next subsection, to require such proofs. However, this is too heavy for the small outcome, and does not currently work for primitive types.

  2. 2.

    This can be achieved in object-oriented language with subtyping and Generics.

  3. 3.

    More specifically, we used the implementation in commit 70e6e7b.

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Acknowledgments

The author would like to thank my supervisor, Prof. Akira Terui, for discussions, and to anonymous reviewers for helpful comments. This research is supported by Grant-in-Aid for JSPS Research Fellow Number 17J00479, and partially by Grants-in-Aid for Scientific Research 16K05035.

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Authors and Affiliations

  1. University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

    Hiromi Ishii

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  1. Hiromi Ishii
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Correspondence to Hiromi Ishii .

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Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Ishii, H. (2018). A Purely Functional Computer Algebra System Embedded in Haskell. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2018. Lecture Notes in Computer Science(), vol 11077. Springer, Cham. https://doi.org/10.1007/978-3-319-99639-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-99639-4_20

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  • Online ISBN: 978-3-319-99639-4

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