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A Dynamic Symbolic Geometry Environment Based on the GroebnerCover Algorithm for the Computation of Geometric Loci and Envelopes

机译：基于GroebnerCover算法的动态符号几何环境，用于计算几何位点和包络

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摘要

An enhancement of the dynamic geometry system GeoGebra for the automatic symbolic computation of algebraic loci and envelopes is presented. Given a GeoGebra construction, the prototype, after rewriting the construction as a polynomial system in terms of variables and parameters, uses an implementation of the recent GroebnerCover algorithm to obtain the algebraic description of the sought locus/envelope as a locally closed set. The prototype shows the applicability of these techniques in general purpose dynamic geometry systems.

机译：提出了一种动态几何系统GeoGebra的增强功能，可以自动计算代数位点和包络。在给定GeoGebra构造的情况下，原型在将构造重写为变量和参数的多项式系统之后，使用最近的GroebnerCover算法的实现方式来获取所需轨迹/包络的代数描述作为局部封闭集。原型展示了这些技术在通用动态几何系统中的适用性。

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来源
《Intelligent computer mathematics》|2013年|349-353|共5页
会议地点 Bath(GB)
作者
Miguel A. Abanades; Francisco Botana;
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作者单位

CES Felipe Ⅱ, Universidad Complutense de Madrid C/ Capitan 39, 28300 Aranjuez, Spain;

Depto. de Matematica Aplicada Ⅰ, Universidad de Vigo Campus A Xunqueira, 36005 Pontevedra, Spain;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Dynamic Geometry; Locus; Envelope; GroebnerCover Algorithm; GeoGebra; Sage;

机译：动态几何；轨迹;信封; GroebnerCover算法； GeoGebra；智者;

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A Dynamic Symbolic Geometry Environment Based on the GroebnerCover Algorithm for the Computation of Geometric Loci and Envelopes

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