Some issues on the automatic computation of plane envelopes in interactive environments

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URI: http://hdl.handle.net/10902/5258
ISSN: 0378-4754
ISSN: 1872-7166
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Autoría
Botana Ferreiro, Francisco RamónAutoridad Unican; Recio Muñiz, TomásAutoridad Unican
Fecha
2014-06
Derechos
Copyright © 2014 IMACS. Published by Elsevier Ltd. All rights reserved., This is the author’s version of a work that was accepted for publication in Mathematics and Computers in Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematics and Computers in Simulation Online (2014), DOI: 10.1016/j.matcom.2014.05.011
Publicado en
Mathematics and Computers in Simulation, Online (2014)
Editorial
Elsevier
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Palabras clave
Envelope
Dynamic geometry
Automatic computation
Gröbner Cover algorithm
Resumen/Abstract
This paper addresses some concerns, and describes some proposals, on the elusive concept of envelope of an algebraic family of varieties, and on its automatic computation. We describe how to use the recently developed Gröbner Cover algorithm to study envelopes of families of algebraic curves, and we give a protocol toward its implementation in dynamic geometry environments. The proposal is illustrated through some examples. A beta version of GeoGebra is used to highlight new envelope abilities in interactive environments, and limitations of our approach are discussed, since the computations are performed in an algebraically closed field.
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