A superexponential lower bound for Gro¨bner bases and church-Rosser Commutative Thue systems
Information and Control
On an installation of Buchberger's algorithm
Journal of Symbolic Computation
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Evaluation of "performance enhancements" in algebraic manipulation systems
Evaluation of "performance enhancements" in algebraic manipulation systems
Parallel Programming in C with MPI and OpenMP
Parallel Programming in C with MPI and OpenMP
Parallel Gaussian elimination for Gröbner bases computations in finite fields
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
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In 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.