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Zeta Types and Tannakian Symbols as a Method for Representing Mathematical Knowledge

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10383))

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Abstract

We present two closely related notions called (1) a zeta type and (2) a Tannakian symbol. These are data types for representing information about number-theoretic objects, and we argue that a database built out of zeta types and Tannakian symbols could lead to interesting discoveries, similar to what has been achieved for example by the OEIS, the LMFDB, and other existing databases of mathematical objects. We give several examples illustrating what database records would look like, and we describe a tiny prototype database which has already been used to find and automatically prove new theorems about multiplicative functions.

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Acknowledgements

Aspects of this work has been presented in various talks, including at CICM 2016, at AITP 2017 (Conference on Artificial Intelligence and Theorem Proving), at the Representation Theory 2016 Conference in Uppsala, and at seminars in Stockholm and in Leicester. We would like to acknowledge the encouragement and many helpful comments received on these occasions, and in particular we thank Michael Kohlhase, Volodymyr Mazorchuk, Frank Neumann, Florian Rabe, Andreas Strömbergsson, and Josef Urban.

(Slides from some of these talks are available on the first author’s webpage; andreasholmstrom.org. Together with the other documents mentioned, they may serve as a complement to this paper.)

Finally, we also want to thank Magnus Hellebust Haaland and Olav Hellebust Haaland for implementing the Berlekamp-Massey algorithm for us in Sage; many of the automated procedures for computing with Tannakian symbols rely on this implementation.

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Authors and Affiliations

  1. Stockholm University, Stockholm, Sweden

    Andreas Holmstrom

  2. Fagerlia vgs, Ålesund, Norway

    Andreas Holmstrom & Torstein Vik

Authors
  1. Andreas Holmstrom
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  2. Torstein Vik
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Corresponding author

Correspondence to Andreas Holmstrom .

Editor information

Editors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Herman Geuvers

  2. Coventry University, Coventry, United Kingdom

    Matthew England

  3. National University of Sciences and Technology, Islamabad, Pakistan

    Osman Hasan

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. FIZ Karlsruhe, Berlin, Germany

    Olaf Teschke

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Holmstrom, A., Vik, T. (2017). Zeta Types and Tannakian Symbols as a Method for Representing Mathematical Knowledge. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds) Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Computer Science(), vol 10383. Springer, Cham. https://doi.org/10.1007/978-3-319-62075-6_13

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  • DOI: https://doi.org/10.1007/978-3-319-62075-6_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62074-9

  • Online ISBN: 978-3-319-62075-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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