Automatic Calculation of Plane Loci Using Gröbner Bases and Integration into a Dynamic Geometry System

  • Michael Gerhäuser
  • Alfred Wassermann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6877)


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.


dynamic geometry system gröbner bases automatic discovery of plane loci 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michael Gerhäuser
    • 1
  • Alfred Wassermann
    • 1
  1. 1.Department of MathematicsUniversity of BayreuthBayreuthGermany

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