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Memorias de investigación
Artículos en revistas:
Rational parametrization of conchoids to algebraic curves
Año:2010
Áreas de investigación
  • Algebra
Datos
Descripción
We study the conchoid to an algebraic affine plane curve C from the perspective of algebraic geometry, analyzing their main algebraic properties. Beside C, the notion of conchoid involves a point A in the affine plane (the focus) and a nonzero field element d (the distance).We introduce the formal definition of conchoid by means of incidence diagrams.We prove that the conchoid is a 1-dimensional algebraic set having atmost two irreducible components. Moreover, with the exception of circles centered at the focus A and taking d as its radius, all components of the corresponding conchoid have dimension 1. In addition, we introduce the notions of special and simple components of a conchoid. Furthermore we state that, with the exception of lines passing through A, the conchoid always has at least one simple component and that, for almost every distance, all the components of the conchoid are simple. We state that, in the reducible case, simple conchoid components are birationally equivalent to C, and we show how special components can be used to decide whether a given algebraic curve is the conchoid of another curve.
Internacional
Si
JCR del ISI
Si
Título de la revista
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
ISSN
0938-1279
Factor de impacto JCR
0,525
Información de impacto
Volumen
21
DOI
10.1007/s00200-010-0126-0
Número de revista
Desde la página
285
Hasta la página
308
Mes
MAYO
Ranking
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Participantes
  • Autor: Juana Sendra Pons (UPM)
  • Autor: J. Rafael Sendra Pons (Universidad de Alcalá de Henares)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Departamento: Matemática Aplicada a la Ingeniería Técnica de Telecomunicación
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