Formalization and Implementation of Algebraic Methods in Geometry

Filip Marić
(Faculty of Mathematics, University of Belgrade, Serbia)
Ivan Petrović
(Faculty of Mathematics, University of Belgrade, Serbia)
Danijela Petrović
(Faculty of Mathematics, University of Belgrade, Serbia)
Predrag Janičić
(Faculty of Mathematics, University of Belgrade, Serbia)

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.

In Pedro Quaresma and Ralph-Johan Back: Proceedings First Workshop on CTP Components for Educational Software (THedu'11), Wrocław, Poland, 31th July 2011, Electronic Proceedings in Theoretical Computer Science 79, pp. 63–81.
Published: 21st February 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.79.4 bibtex PDF
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