Automatic calculation of plane loci using gröbner bases and integration into a dynamic geometry system

Authors:
Michael Gerhäuser;Alfred Wassermann
Affiliations:
Department of Mathematics, University of Bayreuth, Bayreuth, Germany;Department of Mathematics, University of Bayreuth, Bayreuth, Germany
Venue:
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Year:
2010

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Abstract

We describe the integration of a well known algorithm for computing and displaying plane loci based on ideal elimination using Gröbner bases in the dynamic geometry software JSXGraph. With our approach it is not only possible to determine loci depending on other loci but it is also possible to extend JSXGraph to deal with loci depending on arbitrary plane algebraic curves. For Gröbner bases calculations we use CoCoa, a computer algebra system with its focus on computations in commutative algebra.