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Design and implementation of maple packages for processing offsets and conchoids

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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.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada a las TIC, Universidad Politécnica de Madrid, Madrid, Spain

    Juana Sendra

  2. Research Center on Software Technologies and Multimedia Systems, UPM, Madrid, Spain

    David Gómez Sánchez-Pascuala

  3. ETSI Sistemas de Telecomunicación, Universidad Politécnica de Madrid, Madrid, Spain

    Valerio Morán

Authors
  1. Juana Sendra
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  2. David Gómez Sánchez-Pascuala
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  3. Valerio Morán
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Correspondence to Juana Sendra.

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Sendra, J., Sánchez-Pascuala, D.G. & Morán, V. Design and implementation of maple packages for processing offsets and conchoids. Ann Math Artif Intell 80, 47–64 (2017). https://doi.org/10.1007/s10472-016-9504-z

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  • DOI: https://doi.org/10.1007/s10472-016-9504-z

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