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

摘要

We describe the integration of a well known algorithm for computing and displaying plane loci based on ideal elimination using Grobner 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 Groebner bases calculations we use CoCoa, a computer algebra system with its focus on computations in commutative algebra.