Details:
Title  MXL$_3$: an efficient algorithm for computing Gr\"obner bases of zerodimensional ideals.  Author(s)  Johannes Buchmann, Stanislav Bulygin, Daniel Cabarcas, Jintai Ding, Mohamed Saied Emam Mohamed  Type  Book, Chapter in Book, Conference Proceeding  Abstract  This paper introduces a new efficient algorithm, called MXL3, for computing Gröbner bases of zerodimensional ideals. The MXL3 is based on XL algorithm, mutant strategy, and a new sufficient condition for a set of polynomials to be a Gröbner basis. We present experimental results comparing the behavior of MXL3 to F4 on HFE and random generated instances of the MQ problem. In both cases the first implementation of the MXL3 algorithm succeeds faster and uses less memory than Magma’s implementation of F4.  Keywords  Multivariate polynomial systems, Gröbner basis, XL algorithm, Mutant, MutantXL algorithm  ISBN  9783642144226/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783642144233_7 
Language  English  Pages  87100  Publisher  Berlin: Springer  Year  2010  Edition  0  Translation 
No  Refereed 
No 
