Connecting the 3D DGS Calques3D with the CAS Maple

Eugenio Roanes-Lozano, Nicolas van Labeke and Eugenio Roanes-Macías

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 80, issue 6, 1153-1176

Abstract: Many (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).

Keywords: 3D Dynamic Geometry Systems; Computer Algebra Systems; Mechanical theorem proving in geometry; Gröbner bases; Wu’s method (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2010:i:6:p:1153-1176

DOI: 10.1016/j.matcom.2009.09.008

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