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TitleAn extension of Buchberger
Author(s) John Perry
TypeArticle in Journal
AbstractTwo fundamental questions in the theory of Gröbner bases are decision (‘Is a basis G of a polynomial ideal a Gröbner basis?’) and transformation (‘If it is not, how do we transform it into a Gröbner basis?’) This paper considers the first question. It is well known that G is a Gröbner basis if and only if a certain set of polynomials (the S-polynomials) satisfy a certain property. In general there are m(m−1)/2 of these, where m is the number of polynomials in G, but criteria due to Buchberger and others often allow one to consider a smaller number. This paper presents two original results. The first is a new characterization theorem for Gröbner bases that makes use of a new criterion that extends Buchberger’s criteria. The second is the identification of a class of polynomial systems G for which the new criterion has dramatic impact, reducing the worst-case scenario from m(m−1)/2 S-polynomials to m−1.
URL http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7599336&fileId=S1461157008000193
JournalLMS J. Comput. Math.
PublisherCambridge University Press, Cambridge; London Mathematical Society, London
Translation No
Refereed No