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$D$-resultant for rational functions


Authors: Jaime Gutierrez, Rosario Rubio and Jie-Tai Yu
Journal: Proc. Amer. Math. Soc. 130 (2002), 2237-2246
MSC (1991): Primary 13P05; Secondary 14E05
DOI: https://doi.org/10.1090/S0002-9939-02-06331-1
Published electronically: January 23, 2002
MathSciNet review: 1896403
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Abstract: In this paper we introduce the $D$-resultant of two rational functions $f(t),g(t) \in \mathbb{K}(t)$ and show how it can be used to decide if $\mathbb{K}(f(t),g(t))=\mathbb{K}(t)$ or if $\mathbb{K}[t]\subset \mathbb{K}[f(t),g(t)]$ and to find the singularities of the parametric algebraic curve define by $X=f(t), Y=g(t)$. In the course of our work we extend a result about implicitization of polynomial parametric curves to the rational case, which has its own interest.


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Additional Information

Jaime Gutierrez
Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. Los Castros, s/n 39005 Santander, Spain
Email: jaime@matesco.unican.es

Rosario Rubio
Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. Los Castros, s/n 39005 Santander, Spain
Email: sarito@matesco.unican.es

Jie-Tai Yu
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
Email: yujt@hkusua.hku.hk

DOI: https://doi.org/10.1090/S0002-9939-02-06331-1
Keywords: Resultant, implicitization, parametric algebraic curve
Received by editor(s): May 24, 2000
Received by editor(s) in revised form: March 7, 2001
Published electronically: January 23, 2002
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2002 American Mathematical Society

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