𝐷-resultant for rational functions

Gutierrez, Jaime; Rubio, Rosario; Yu, Jie-Tai

doi:10.1090/S0002-9939-02-06331-1

$D$-resultant for rational functions
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by Jaime Gutierrez, Rosario Rubio and Jie-Tai Yu PDF

Proc. Amer. Math. Soc. 130 (2002), 2237-2246 Request permission

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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