Journal of Automated Reasoning

, Volume 21, Issue 3, pp 357–380 | Cite as

A New Approach for Automatic Theorem Proving in Real Geometry

  • Andreas Dolzmann
  • Thomas Sturm
  • Volker Weispfenning
Article

Abstract

We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theorems whose complex analogues fail. Moreover, the problem formulation may involve order inequalities. After specification of independent variables, nondegeneracy conditions are generated automatically. Moreover, when trying to prove conjectures that – apart from nondegeneracy conditions – do not hold in the claimed generality, missing premises are found automatically. We demonstrate the applicability of our method to nontrivial examples.

real quantifier elimination real geometry automatic theorem proving over the reals 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Andreas Dolzmann
    • 1
  • Thomas Sturm
    • 1
  • Volker Weispfenning
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauGermany

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