Implicitization using univariate resultants
type: Item
instance of: scholarly article
title: Implicitization using univariate resultants
zbMATH Open document ID: 1213.14093
published in: Journal of Systems Science and Complexity
publication date: 2011-02-25T00:00:00Z
review text: Rational curves and surfaces can either be represented implicitly by polynomial equations, or parametrically by rational parametrizations. Transforming one representation into the other is a problem near the top of the list in constructive algebraic geometry. It is also the source for a variety of symbolic algebraic and also numerical algorithms. Implicitization -- transforming a parametric representation into an implicit one -- is a problem in elimination theory; the rational relation between the space coordinates and the parameters of the variety are first transformed into polynomial ones, and then we want to have relations only between the space coordinates. Gröbner bases, resultants, and any other methods in elimination theory may be employed. In this paper the authors present a specific resultant based approach to the implicitization of a certain class of space curves and surfaces. No formal complexity analysis is given. But an experimental implementation seems to support the claim to lower computational complexity.
reviewed by: Franz Winkler
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14E08
Mathematics Subject Classification ID: 13Pxx
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 5857558
zbMATH Keywords: rational curves and surfaces
zbMATH Keywords: implicitization
zbMATH Keywords: resultants
Wikidata QID: Q57533634
author: Li-Yong Shen
author: Chunming Yuan
MaRDI profile type: Publication
full work available at URL: s11424-010-7218-6
OpenAlex ID: W2012127059
cites work: Q3714165
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DOI: 10.1007/S11424-010-7218-6
description: scientific article; zbMATH DE number 5857558