Details:
Title  An extension of Buchberger  Author(s)  John Perry  Type  Article in Journal  Abstract  Two 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 Spolynomials) 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 worstcase scenario from m(m−1)/2 Spolynomials to m−1.  ISSN  14611570/e 
URL 
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7599336&fileId=S1461157008000193 
Language  English  Journal  LMS J. Comput. Math.  Volume  13  Pages  111129  Publisher  Cambridge University Press, Cambridge; London Mathematical Society, London  Year  2010  Edition  0  Translation 
No  Refereed 
No 
