Title  A new efficient algorithm for computing Gröbner basis (F 4 ) 
Author(s)  JeanCharles Faugère 
Type  Article in Journal 
Abstract  This paper introduces a new efficient algorithm for computing Gröbner bases. To avoid as much intermediate computation as possible, the algorithm computes successive truncated Gröbner bases and it replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous reduction of several polynomials. This powerful reduction mechanism is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods. Current techniques in linear algebra used in Computer Algebra are reviewed together with other methods coming from the numerical field. Some previously untractable problems (Cyclic 9) are presented as well as an empirical comparison of a first implementation of this algorithm with other well known programs. This comparison pays careful attention to methodology issues. All the benchmarks and CPU times used in this paper are frequently updated and available on a Web page. Even though the new algorithm does not improve the worst case complexity it is several times faster than previous implementations both for integers and modulo p computations. 
Length  28 
Copyright  Elsevier Science B.V. 
File 

URL 
dx.doi.org/10.1016/S00224049(99)000055 
Language  English 
Journal  Journal of Pure and Applied Algebra 
Volume  139 
Number  13 
Pages  6188 
Publisher  Elsevier Scienc B.V. 
Year  1999 
Month  June 
Edition  0 
Translation 
No 
Refereed 
No 