Details:
Title  A new incremental algorithm for computing Groebner bases  Author(s)  Shuhong Gao, Yinhua Guan, Frank Volny  Type  Article in Conference Proceedings  Abstract  In this paper, we present a new algorithm for computing Gröbner bases. Our algorithm is incremental in the same fashion as F5 and F5C. At a typical step, one is given a Gröbner basis G for an ideal I and any polynomial g, and it is desired to compute a Gröbner basis for the new ideal <I, g>, obtained from I by joining g. Let (I: g) denote the colon ideal of I divided by g. Our algorithm computes Gröbner bases for <I, g> and (I: g) simultaneously. In previous algorithms, Spolynomials that reduce to zero are useless, in fact, F5 tries to avoid such reductions as much as possible. In our algorithm, however, these "useless" Spolynomials give elements in (I: g) and are useful in speeding up the subsequent computations. Computer experiments on some benchmark examples indicate that our algorithm is much more efficient (two to ten times faster) than F5 and F5C.  Keywords  Buchberger's algorithm, F5 algorithm, Grobner basis, colon ideal  ISBN  9781450301503 
URL 
http://www.ces.clemson.edu/~fvolny/pub/ISSAC2010.pdf 
Language  English  Journal  Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation  Series  ISSAC '10  Number  7  Pages  1319  Publisher  ACM  Address  New York, NY, USA  Year  2010  Translation 
No  Refereed 
Yes  Conferencename  ISSAC '10 International Symposium on Symbolic and Algebraic Computation 
