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Article: Recognizing and parametrizing curves isomorphic to a line

TitleRecognizing and parametrizing curves isomorphic to a line
Authors
Lam, CMShpilrain, VYu, JT
KeywordsAutomorphisms
Complexity
Parametrization
Plane Curves
Polynomial Algebras
Issue Date2007
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jsc
Citation
Journal Of Symbolic Computation, 2007, v. 42 n. 7, p. 751-756 How to Cite?
DOI: http://dx.doi.org/10.1016/j.jsc.2007.04.002
AbstractSome time ago, Shpilrain and Yu reported an algorithm for deciding whether or not a polynomial p ∈ K [x, y] is a coordinate, or, equivalently, whether or not a plane curve p (x, y) = 0 is isomorphic to a line. Here K is any constructible field of characteristic 0. In this paper, we show that their algorithm requires O (n2) field operations, where n is the degree of a given polynomial. We also show how their algorithm can be used to find a polynomial parametrization of a plane curve p (x, y) = 0 which is isomorphic to a line. This requires O (n2 log2 n) field operations. © 2007 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156192
ISSN
0747-7171
2021 Impact Factor: 0.970
2020 SCImago Journal Rankings: 0.598
ISI Accession Number ID
WOS:000248867600004
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorLam, CMen_US
dc.contributor.authorShpilrain, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:47Z-
dc.date.available2012-08-08T08:40:47Z-
dc.date.issued2007en_US
dc.identifier.citationJournal Of Symbolic Computation, 2007, v. 42 n. 7, p. 751-756en_US
dc.identifier.issn0747-7171en_US
dc.identifier.urihttp://hdl.handle.net/10722/156192-
dc.description.abstractSome time ago, Shpilrain and Yu reported an algorithm for deciding whether or not a polynomial p ∈ K [x, y] is a coordinate, or, equivalently, whether or not a plane curve p (x, y) = 0 is isomorphic to a line. Here K is any constructible field of characteristic 0. In this paper, we show that their algorithm requires O (n2) field operations, where n is the degree of a given polynomial. We also show how their algorithm can be used to find a polynomial parametrization of a plane curve p (x, y) = 0 which is isomorphic to a line. This requires O (n2 log2 n) field operations. © 2007 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jscen_US
dc.relation.ispartofJournal of Symbolic Computationen_US
dc.subjectAutomorphismsen_US
dc.subjectComplexityen_US
dc.subjectParametrizationen_US
dc.subjectPlane Curvesen_US
dc.subjectPolynomial Algebrasen_US
dc.titleRecognizing and parametrizing curves isomorphic to a lineen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.jsc.2007.04.002en_US
dc.identifier.scopuseid_2-s2.0-34250684158en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-34250684158&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume42en_US
dc.identifier.issue7en_US
dc.identifier.spage751en_US
dc.identifier.epage756en_US
dc.identifier.isiWOS:000248867600004-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridLam, CM=7402989820en_US
dc.identifier.scopusauthoridShpilrain, V=6603904879en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US
dc.identifier.issnl0747-7171-

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