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TitleMXL$_3$: an efficient algorithm for computing Gr\"obner bases of zero-dimensional ideals.
Author(s) Johannes Buchmann, Stanislav Bulygin, Daniel Cabarcas, Jintai Ding, Mohamed Saied Emam Mohamed
TypeBook, Chapter in Book, Conference Proceeding
AbstractThis paper introduces a new efficient algorithm, called MXL3, for computing Gröbner bases of zero-dimensional 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.
KeywordsMultivariate polynomial systems, Gröbner basis, XL algorithm, Mutant, MutantXL algorithm
ISBN978-3-642-14422-6/pbk
URL http://link.springer.com/chapter/10.1007%2F978-3-642-14423-3_7
LanguageEnglish
Pages87--100
PublisherBerlin: Springer
Year2010
Edition0
Translation No
Refereed No
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