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Sendra, J.Author

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June 9, 2019
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Rational parametrization of conchoids to algebraic curves

Publicated to: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING. 21 (4): 285-308 - 2010-07-01 21(4), DOI: 10.1007/s00200-010-0126-0

Authors:

Sendra, J; Sendra, JR
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Affiliations

Univ Politecn Madrid, Dept Matemat Aplicada, IT Telecomunicac, EUIT Telecomunicac - Author

Abstract

We study the rationality of each of the components of the conchoid to an irreducible algebraic affine plane curve, excluding the trivial cases of the lines through the focus and the circle centered at the focus and radius the distance involved in the conchoid. We prove that conchoids having all their components rational can only be generated by rational curves. Moreover, we show that reducible conchoids to rational curves have always their two components rational. In addition, we prove that the rationality of the conchoid component, to a rational curve, does depend on the base curve and on the focus but not on the distance. As a consequence, we provide an algorithm that analyzes the rationality of all the components of the conchoid and, in the affirmative case, parametrizes them. The algorithm only uses a proper parametrization of the base curve and the focus and, hence, does not require the previous computation of the conchoid. As a corollary, we show that the conchoid to the irreducible conics, with conchoid-focus on the conic, are rational and we give parametrizations. In particular we parametrize the Lima double dagger ons of Pascal. We also parametrize the conchoids of Nicomedes. Finally, we show how to find the foci from where the conchoid is rational or with two rational components.
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Keywords

Conchoid curveRational parametrization

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, and although the journal is classified in the quartile Q4 (Agencia WoS (JCR)), its regional focus and specialization in Computer Science, Interdisciplinary Applications, give it significant recognition in a specific niche of scientific knowledge at an international level.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-27:

  • Google Scholar: 30
  • WoS: 4
  • Scopus: 10
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Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/9457/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 482
  • Downloads: 519
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Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (SENDRA PONS, JUANA) and Last Author (Sendra, J. R.).

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Awards linked to the item

Both authors supported by the Spanish Ministerio de Educacion e Innovacion under the Project MTM2008-04699-C03-01.
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