File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Polynomial automorphisms and gröbner reductions

TitlePolynomial automorphisms and gröbner reductions
Authors
Issue Date1997
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 1997, v. 197 n. 2, p. 546-558 How to Cite?
AbstractLetPn=K[x1,...,xn] be the polynomial algebra over a fieldKof characteristic 0. We show that applying an automorphism to a given polynomialp∈Pnis mimicked by Gröbner transformations of a basis of the ideal ofPngenerated by partial derivatives of this polynomial. In the case ofP2, this yields a miraculously simple algorithm for deciding whether or not a given polynomial fromP2is part of a basis. Another application is an algorithm which, given a polynomialp∈P2that is part of a basis, finds a sequence of elementary automorphisms that reducesptox1. We also speculate on how our method may be used for constructing a possible counterexample to the Jacobian conjecture in higher dimensions. © 1997 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/156068
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorShpilrain, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:16Z-
dc.date.available2012-08-08T08:40:16Z-
dc.date.issued1997en_US
dc.identifier.citationJournal Of Algebra, 1997, v. 197 n. 2, p. 546-558en_US
dc.identifier.issn0021-8693en_US
dc.identifier.urihttp://hdl.handle.net/10722/156068-
dc.description.abstractLetPn=K[x1,...,xn] be the polynomial algebra over a fieldKof characteristic 0. We show that applying an automorphism to a given polynomialp∈Pnis mimicked by Gröbner transformations of a basis of the ideal ofPngenerated by partial derivatives of this polynomial. In the case ofP2, this yields a miraculously simple algorithm for deciding whether or not a given polynomial fromP2is part of a basis. Another application is an algorithm which, given a polynomialp∈P2that is part of a basis, finds a sequence of elementary automorphisms that reducesptox1. We also speculate on how our method may be used for constructing a possible counterexample to the Jacobian conjecture in higher dimensions. © 1997 Academic Press.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_US
dc.relation.ispartofJournal of Algebraen_US
dc.titlePolynomial automorphisms and gröbner reductionsen_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.doi10.1006/jabr.1997.7083en_US
dc.identifier.scopuseid_2-s2.0-0031573395en_US
dc.identifier.hkuros36448-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0031573395&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume197en_US
dc.identifier.issue2en_US
dc.identifier.spage546en_US
dc.identifier.epage558en_US
dc.identifier.isiWOS:A1997YK66400014-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridShpilrain, V=6603904879en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats