Rewriting input expressions in complex algebraic geometry provers

  • Z. KovácsEmail author
  • T. Recio
  • C. Sólyom-Gecse


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.


Automatic theorem proving Automatic theorem deduction Complex algebraic geometry Elementary geometry Dynamic geometry software GeoGebra 

Mathematics Subject Classification (2010)

14Q99 13P10 68T15 


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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. 1.The Private University College of Education of the Diocese of LinzLinzAustria
  2. 2.Universidad de CantabriaSantanderSpain
  3. 3.Johannes Kepler UniversityLinzAustria

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