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Rewriting input expressions in complex algebraic geometry provers

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Abstract

We present an algorithm to help converting expressions having non-negative quantities (like distances) in Euclidean geometry theorems to be usable in a complex algebraic geometry prover. The algorithm helps in refining the output of an existing prover, therefore it supports immediate deployment in high level prover systems. We prove that the algorithm may take doubly exponential time to produce the output in polynomial form, but in many cases it is still computable and useful.

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Acknowledgments

The MEP formula was suggested by Bernard Parisse, inventor of Giac.

We are thankful to Predrag Janičić, Julien Narboux, Francisco Botana and the anonymous reviewers for their suggestions to improve the text of this paper.

First and second authors are partially supported by the grant MTM2017-88796-P from the Spanish MINECO (Ministerio de Economía y Competitividad) and the ERDF (European Regional Development Fund). Second author was partially supported by the grant MTM2014-54141-P.

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Authors and Affiliations

  1. The Private University College of Education of the Diocese of Linz, Salesianumweg 3, 4020, Linz, Austria

    Z. Kovács

  2. Universidad de Cantabria, Avenida de los Castros, s/n, 39071, Santander, Spain

    T. Recio

  3. Johannes Kepler University, Altenberger Straße 54, 4040, Linz, Austria

    C. Sólyom-Gecse

Authors
  1. Z. Kovács
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  2. T. Recio
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  3. C. Sólyom-Gecse
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Correspondence to Z. Kovács.

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Kovács, Z., Recio, T. & Sólyom-Gecse, C. Rewriting input expressions in complex algebraic geometry provers. Ann Math Artif Intell 85, 73–87 (2019). https://doi.org/10.1007/s10472-018-9590-1

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  • DOI: https://doi.org/10.1007/s10472-018-9590-1

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