Connecting the 3D DGS Calques3D with the CAS Maple

Roanes-Lozano, Eugenio; Van Labeke, Nicolas and Roanes-Macías, Eugenio (2010). Connecting the 3D DGS Calques3D with the CAS Maple. Mathematics and Computers in Simulation, 80(6) pp. 1153–1176.

DOI: https://doi.org/10.1016/j.matcom.2009.09.008

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).

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About

  • Item ORO ID
  • 34566
  • Item Type
  • Journal Item
  • ISSN
  • 0378-4754
  • Extra Information
  • Fifth IMACS Seminar on Monte Carlo Methods, Edited by Michael Mascagni.
    Applications of Computer Algebra 2007 (ACA 2007) special session on Nonstandard Applications of Computer Algebra.

    Computational Biomechanics and Biology, a collection of papers presented at the 1st IMACS International Conference on the Computational Biomechanics and Biology ICCBB 2007. Edited by Eugenio Roanes-Lozano, Michael J. Wester and Stanly Steinberg.
  • Keywords
  • 3D Dynamic Geometry Systems; Computer Algebra Systems; Gröbner bases; mechanical theorem proving in geometry; Wu's method
  • Academic Unit or School
  • Institute of Educational Technology (IET)
  • Copyright Holders
  • © 2009 IMACS
  • Related URLs
  • Depositing User
  • Nicolas Van Labeke
CORE (COnnecting REpositories)

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