Implicitization of 3D rational surfaces using iterated univariate resultants and avoiding extraneous factors

This paper presents an interpretation for the extraneous factors appearing in the computation of iterated resultants with respect to a variable for three multivariate polynomials defined from the rational parametrization of a surface. We introduce a method for deriving the implicit equation of a sur...

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Bibliographic Details
Authors: Pérez Díaz, Sonia|||0000-0002-0174-5325, Magdalena Benedicto, J. Rafael, Fernández de Sevilla Vellón, María de los Ángeles|||0000-0002-0630-1141
Format: article
Publication Date:2026
Country:España
Institution:Universidad de Alcalá (UAH)
Repository:e_Buah Biblioteca Digital Universidad de Alcalá
Language:English
OAI Identifier:oai:ebuah.uah.es:10017/68223
Online Access:http://hdl.handle.net/10017/68223
https://dx.doi.org/10.1007/s13398-025-01806-0
Access Level:Open access
Keyword:Resultants
Multivariate polynomials
Rational parametrization
Implicit surface representation
Extraneous factors
Elimination theory
Matemáticas
Mathematics
Description
Summary:This paper presents an interpretation for the extraneous factors appearing in the computation of iterated resultants with respect to a variable for three multivariate polynomials defined from the rational parametrization of a surface. We introduce a method for deriving the implicit equation of a surface using only two univariate resultants, whose polynomials match the degree of the parametrization. Our results provide a new approach to extracting the implicit representation of rational surfaces.