A bridge between dynamic geometry and computer algebra

Roanes–Lozano, Eugenio; Roanes-Macı́as, Eugenio; Villar-Mena, M.

doi:10.1016/s0895-7177(03)00115-8

Cited by 40 publications

(17 citation statements)

References 3 publications

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“…It adopts our philosophy of software reuse [31,34] and also processes Calques3D output and use the resulting data as input to 3D-LD, that calls the CASs CoCoA and Mathematica for performing algebraic computations externally. Nevertheless this system was a prototype exclusively oriented to determining algebraic surfaces as geometric loci.…”

Section: D Dgss -Cass Connection Preliminariesmentioning

confidence: 99%

Connecting the 3D DGS Calques3D with the CAS Maple

Roanes–Lozano

Labeke

Roanes-Macı́as

2010

Mathematics and Computers in Simulation

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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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Section: D Dgss -Cass Connection Preliminariesmentioning

confidence: 99%

Connecting the 3D DGS Calques3D with the CAS Maple

Roanes–Lozano

Labeke

Roanes-Macı́as

2010

Mathematics and Computers in Simulation

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“…It concluded aiming for a deeper interleaving of dynamic geometry and automated discovery paradigms. Such a wish was partialy fulfilled by linking The Geometer's Sketchpad with a Maple library for parametric description of constructions in [13] using Wu's method, and with Groebner bases in GDI [14,15], a DG prototype using Mathematica and CoCoA [16] as back-end symbolic engines.…”

Section: Introductionmentioning

confidence: 99%

On the Parametric Representation of Dynamic Geometry Constructions

Botana

2011

Computational Science and Its Applications - ICCSA 2011

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Abstract. This paper describes an ongoing implementation of an open source library dealing with parametric representation of dynamic geometry constructions. We show how some current issues in standard dynamic geometry environments, such as computing envelopes of lines which are not primitive objects known by the geometric system, can be efficiently solved using the correspondence between geometry and algebra. We also propose enriching the tool (or macro) mechanism, available in some environments, with our parametric approach. Finally, some problems arising from the algebraic method considered are also studied.

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“…Two ways have been devised for dealing with this cooperation. Some systems incorporate their own code for coping with algebraic techniques in geometry ( [14,8,9],...), while other systems emphasize on reusing software ( [2,15,17],...). Both strategies have been partially successful on solving some of the three main points in dynamic geometry, that is, the continuity-determinism dilemma, the proof and discovery abilities, and the complete determination of loci (see [6] for an extensive study of the subject).…”

Section: Introductionmentioning

confidence: 99%

Computing Locus Equations for Standard Dynamic Geometry Environments

Botana

Abánades²,

Escribano

2007

Computational Science – ICCS 2007

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Abstract. GLI (Geometric Locus Identifier), an open web-based tool to determine equations of geometric loci specified using Cabri Geometry and The Geometer's Sketchpad, is described. A geometric construction of a locus is uploaded to a Java Servlet server, where two computer algebra systems, CoCoA and Mathematica, following the Groebner basis method, compute the locus equation and its graph. Moreover, an OpenMath description of the geometric construction is given. GLI can be efficiently used in mathematics education, as a supplement of the locus functions of the standard dynamic geometry systems. The system is located at

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A bridge between dynamic geometry and computer algebra

Cited by 40 publications

References 3 publications

Connecting the 3D DGS Calques3D with the CAS Maple

Connecting the 3D DGS Calques3D with the CAS Maple

On the Parametric Representation of Dynamic Geometry Constructions

Computing Locus Equations for Standard Dynamic Geometry Environments

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