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Article: Polynomial automorphisms and gröbner reductions
Title | Polynomial automorphisms and gröbner reductions |
---|---|
Authors | |
Issue Date | 1997 |
Publisher | Academic 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? |
Abstract | LetPn=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 Identifier | http://hdl.handle.net/10722/156068 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 1.023 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Shpilrain, V | en_US |
dc.contributor.author | Yu, JT | en_US |
dc.date.accessioned | 2012-08-08T08:40:16Z | - |
dc.date.available | 2012-08-08T08:40:16Z | - |
dc.date.issued | 1997 | en_US |
dc.identifier.citation | Journal Of Algebra, 1997, v. 197 n. 2, p. 546-558 | en_US |
dc.identifier.issn | 0021-8693 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156068 | - |
dc.description.abstract | LetPn=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.language | eng | en_US |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra | en_US |
dc.relation.ispartof | Journal of Algebra | en_US |
dc.title | Polynomial automorphisms and gröbner reductions | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_US |
dc.identifier.authority | Yu, JT=rp00834 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1006/jabr.1997.7083 | en_US |
dc.identifier.scopus | eid_2-s2.0-0031573395 | en_US |
dc.identifier.hkuros | 36448 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0031573395&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 197 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 546 | en_US |
dc.identifier.epage | 558 | en_US |
dc.identifier.isi | WOS:A1997YK66400014 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Shpilrain, V=6603904879 | en_US |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |
dc.identifier.issnl | 0021-8693 | - |