Automatic deduction in (dynamic) geometry: Loci computation
| Autor: | Francisco Botana, Miguel A. Abánades |
|---|---|
| Přispěvatelé: | Universidad de Cantabria |
| Rok vydání: | 2014 |
| Předmět: |
Control and Optimization
Theoretical computer science Locus Computer science Computation Degenerate energy levels Automatic deduction Geometry Gröbner cover Sage Symbolic computation File format Computer Science Applications GeoGebra Computational Mathematics Parametric system Computational Theory and Mathematics ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Automatic deduction in geometry Geometry and Topology Algebraic number Algorithm Coding (social sciences) |
| Zdroj: | Computational Geometry, Vol. 47, Iss. 1, Pp. 75–89, (2014) UCrea Repositorio Abierto de la Universidad de Cantabria Universidad de Cantabria (UC) |
| ISSN: | 0925-7721 |
| DOI: | 10.1016/j.comgeo.2013.07.001 |
| Popis: | A symbolic tool based on open source software that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction is presented. The prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction, namely with the open source dynamic geometry system GeoGebra or using the common file format for dynamic geometry developed by the Intergeo project. Locus computation algorithms based on Automatic Deduction techniques are recalled and presented as basic for an efficient treatment of advanced methods in dynamic geometry. Moreover, an algorithm to eliminate extraneous parts in symbolically computed loci is discussed. The algorithm, based on a recent work on the Gröbner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Several examples are shown in detail. |
| Databáze: | OpenAIRE |
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