Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

Grobner basis Related Publications

2 Parallel-Distributed Software Implementation of Buchberger Algorithm

Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

Abstract:

Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: MPI, OpenMP, Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation

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1 Computing SAGB-Gröbner Basis of Ideals of Invariant Rings by Using Gaussian Elimination

Authors: Abdolali Basiri, Sajjad Rahmany

Abstract:

The link between Gröbner basis and linear algebra was described by Lazard [4,5] where he realized the Gr┬¿obner basis computation could be archived by applying Gaussian elimination over Macaulay-s matrix . In this paper, we indicate how same technique may be used to SAGBI- Gröbner basis computations in invariant rings.

Keywords: Reduction, Grobner basis, SAGBI- Gröbner basis, Invariant ring, permutation groups

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