-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 | References | Similar Articles | Additional Information

Abstract: In this paper we introduce the -resultant of two rational functions and show how it can be used to decide if or if and to find the singularities of the parametric algebraic curve define by . 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