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Gauss-Lintel, an Algorithm Suite for Exploring Chord Diagrams

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Intelligent Computer Mathematics (CICM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12833))

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Abstract

Gauss diagrams, or more generally chord diagrams are a well-established tool in the study of topology of knots and of planar curves. In this paper we present a system description of Gauss-lintel, our implementation in SWI-Prolog of a suite of algorithms for exploring chord diagrams. Gauss-lintel employs a datatype which we call “lintel”, which is a list representation of an odd-even matching for the set of integers [0,...,2n–1], for efficiently generating Gauss diagrams and testing their properties, including one important property called realizability. We report on extensive experiments in generation and enumeration of various classes of Gauss diagrams, as well as on experimental testing of several published descriptions of realizability.

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Notes

  1. 1.

    A dynamic fact is a Prolog fact (atomic formula) which can be added or removed during run time. Using dynamic facts goes outside of the pure Prolog paradigm, but it is very useful for keeping information about the global state.

  2. 2.

    TaitCurves.

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Acknowledgements

This work was supported by the Leverhulme Trust Research Project Grant RPG-2019-313.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Essex, Essex, UK

    Abdullah Khan & Alexei Vernitski

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Alexei Lisitsa

Authors
  1. Abdullah Khan
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  2. Alexei Lisitsa
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  3. Alexei Vernitski
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Corresponding author

Correspondence to Alexei Lisitsa .

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Editors and Affiliations

  1. Heriot-Watt University, Edinburgh, UK

    Fairouz Kamareddine

  2. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

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Khan, A., Lisitsa, A., Vernitski, A. (2021). Gauss-Lintel, an Algorithm Suite for Exploring Chord Diagrams. In: Kamareddine, F., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2021. Lecture Notes in Computer Science(), vol 12833. Springer, Cham. https://doi.org/10.1007/978-3-030-81097-9_16

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  • DOI: https://doi.org/10.1007/978-3-030-81097-9_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81096-2

  • Online ISBN: 978-3-030-81097-9

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