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Automated Reasoning in Reduction Rings Using the Theorema System

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Computer Algebra in Scientific Computing (CASC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9301))

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Abstract

In this paper, we present the computer-supported theory exploration, including both formalization and verification, of a theory in commutative algebra, namely the theory of reduction rings. Reduction rings, introduced by Bruno Buchberger in 1984, are commutative rings with unit which extend classical Gröbner bases theory from polynomial rings over fields to a far more general setting.

We review some of the most important notions and concepts in the theory and motivate why reduction rings are a natural candidate for being explored with the assistance of a software system, which, in our case, is the Theorema system. We also sketch the special prover designed and implemented for the purpose of semi-automated, interactive verification of the theory, and outline the structure of the formalization.

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References

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Author information

Authors and Affiliations

  1. Doctoral College “Computational Mathematics” and RISC, Johannes Kepler University, Linz, Austria

    Alexander Maletzky

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  1. Alexander Maletzky
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Correspondence to Alexander Maletzky .

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Editors and Affiliations

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

    Vladimir P. Gerdt

  2. Institute for Mathematics, Universität Kassel, Kassel, Germany

    Wolfram Koepf

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

    Werner M. Seiler

  4. Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Maletzky, A. (2015). Automated Reasoning in Reduction Rings Using the Theorema System. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_23

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  • DOI: https://doi.org/10.1007/978-3-319-24021-3_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24020-6

  • Online ISBN: 978-3-319-24021-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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