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TitleParallel reduction of matrices in Gr\"obner bases computations.
Author(s) Neumann Severin
TypeBook, Chapter in Book, Conference Proceeding
AbstractIn this paper we provide an parallelization for the reduction of matrices for Gröbner basis computations advancing the ideas of using the special structure of the reduction matrix [4]. First we decompose the matrix reduction in three steps allowing us to get a high parallelization for the reduction of the bigger part of the polynomials. In detail we do not need an analysis of the matrix to identify pivot columns, since they are obvious by construction and we give a rule set for the order of the reduction steps which optimizes the matrix transformation with respect to the parallelization. Finally we provide benchmarks for an implementation of our algorithm. This implementation is available as open source.
URL http://link.springer.com/chapter/10.1007%2F978-3-642-32973-9_22
PublisherBerlin: Springer
Translation No
Refereed No