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Design and implementation of maple packages for processing offsets and conchoids

  • Juana SendraEmail author
  • David Gómez Sánchez-Pascuala
  • Valerio Morán
Article
  • 83 Downloads

Abstract

In this paper we present two packages, implemented in the computer algebra system Maple, for dealing with offsets and conchoids to algebraic curves, respectively. Help pages and procedures are described. Also in an annex, we provide a brief atlas, created with these packages, and where the offset and the conchoid of several algebraic plane curves are obtained, their rationality is analyzed, and parametrizations are computed. Practical performance of the implemented algorithms shows that the packages execute in reasonable time; we include time cost tables of the computation of the offset and conchoid curves of two rational families of curves using the implemented packages.

Keywords

Symbolic mathematical software Maple Offset variety Conchoid variety Pedal construction Rational parametrization 

Mathematics Subject Classification (2010)

97N88 65D17 68W30 14QXX 15Q05 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Juana Sendra
    • 1
    Email author
  • David Gómez Sánchez-Pascuala
    • 2
  • Valerio Morán
    • 3
  1. 1.Departamento de Matemática Aplicada a las TICUniversidad Politécnica de MadridMadridSpain
  2. 2.Research Center on Software Technologies and Multimedia SystemsUPMMadridSpain
  3. 3.ETSI Sistemas de TelecomunicaciónUniversidad Politécnica de MadridMadridSpain

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