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A Normal Form for Matrix Multiplication Schemes

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Algebraic Informatics (CAI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13706))

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Abstract

Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for a large number of schemes a pairwise equivalence check becomes cumbersome. In this paper we propose an algorithm to compute a normal form of matrix multiplication schemes. This allows us to decide pairwise equivalence of a larger number of schemes efficiently.

M.K. was supported by the Austrian Science Fund (FWF) grant P31571-N32.

J.M. was supported by the Land Oberösterreich through the LIT-AI Lab.

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Authors and Affiliations

  1. Institute for Algebra, Johannes Kepler University, Linz, Austria

    Manuel Kauers & Jakob Moosbauer

Authors
  1. Manuel Kauers
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  2. Jakob Moosbauer
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Correspondence to Jakob Moosbauer .

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Editors and Affiliations

  1. Aristotle University of Thessaloniki, Thessaloniki, Greece

    Dimitrios Poulakis

  2. Aristotle University of Thessaloniki, Thessaloniki, Greece

    George Rahonis

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Kauers, M., Moosbauer, J. (2022). A Normal Form for Matrix Multiplication Schemes. In: Poulakis, D., Rahonis, G. (eds) Algebraic Informatics. CAI 2022. Lecture Notes in Computer Science, vol 13706. Springer, Cham. https://doi.org/10.1007/978-3-031-19685-0_11

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  • DOI: https://doi.org/10.1007/978-3-031-19685-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-19684-3

  • Online ISBN: 978-3-031-19685-0

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