Electronic Proceedings in Theoretical Computer Science (Feb 2012)

Formalization and Implementation of Algebraic Methods in Geometry

  • Filip Marić,
  • Ivan Petrović,
  • Danijela Petrović,
  • Predrag Janičić

DOI
https://doi.org/10.4204/EPTCS.79.4
Journal volume & issue
Vol. 79, no. Proc. THedu 2011
pp. 63 – 81

Abstract

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We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java implementation of the algebraic methods. The project should fill-in some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools) and should enable new applications of theorem proving in education.