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.
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.