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...
| Authors: | , , |
|---|---|
| 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 |
| 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. |
|---|