Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
Fast Search for the Janet Divisor
Programming and Computing Software
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Effectiveness of involutive criteria in computation of polynomial Janet bases
Programming and Computing Software
On selection of nonmultiplicative prolongations in computation of Janet bases
Programming and Computing Software
On compatibility of discrete relations
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
On computation of Boolean involutive bases
Programming and Computing Software
Programming and Computing Software
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In this paper, an involutive algorithm for computation of Gröbner bases for polynomial ideals in a ring of polynomials in many variables over the finite field $$ \mathbb{F}_2 $$ with the values of variables belonging of $$ \mathbb{F}_2 $$ is considered. The algorithm uses Janet division and is specialized for a graded reverse lexicographical order of monomials. We compare efficiency of this algorithm and its implementation in C++ with that of the Buchberger algorithm, as well as with the algorithms of computation of Gröbner bases that are built in the computer algebra systems Singular and CoCoA and in the FGb library for Maple. For the sake of comparison, we took widely used examples of computation of Gröbner bases over 驴 and adapted them for $$ \mathbb{F}_2 $$ . Polynomial systems over $$ \mathbb{F}_2 $$ with the values of variables in $$ \mathbb{F}_2 $$ are of interest, in particular, for modeling quantum computation and a number of cryptanalysis problems.