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TitleConnecting the 3D DGS Calques3D with the CAS Maple
Author(s) Nicolas van Labeke, Eugenio Roanes-Lozano, Eugenio Roanes-Macías
TypeArticle in Journal
AbstractMany (2D) Dynamic Geometry Systems (DGSs) are able to export numeric coordinates and equations with numeric coefficients to Computer Algebra Systems (CASs). Moreover, different approaches and systems that link (2D) DGSs with CASs, so that symbolic coordinates and equations with symbolic coefficients can be exported from the DGS to the CAS, already exist. Although the 3D DGS Calques3D can export numeric coordinates and equations with numeric coefficients to Maple and Mathematica, it cannot export symbolic coordinates and equations with symbolic coefficients. A connection between the 3D DGS Calques3D and the CAS Maple, that can handle symbolic coordinates and equations with symbolic coefficients, is presented here. Its main interest is to provide a convenient time-saving way to explore problems and directly obtain both algebraic and numeric data when dealing with a 3D extension of “ruler and compass geometry”. This link has not only educational purposes but mathematical ones, like mechanical theorem proving in geometry, geometric discovery (hypotheses completion), geometric loci finding… As far as we know, there is no comparable “symbolic” link in the 3D case, except the prototype 3D-LD (restricted to determining algebraic surfaces as geometric loci).
Keywords3D Dynamic Geometry Systems, Computer Algebra Systems, Mechanical theorem proving in geometry, Gröbner bases, Wu’s method
URL http://www.sciencedirect.com/science/article/pii/S0378475409002961
JournalMathematics and Computers in Simulation
Pages1153 - 1176
NoteFifth IMACS Seminar on Monte Carlo MethodsApplications of Computer Algebra 2007 (ACA 2007) special session on Nonstandard Applications of Computer AlgebraComputational Biomechanics and Biology, a collection of papers presented at the 1st IMACS Internation
Translation No
Refereed No