Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
A Gro¨bner approach to involutive bases
Journal of Symbolic Computation
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
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
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A pommaret division algorithm for computing Grobner bases in boolean rings
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Detecting unnecessary reductions in an involutive basis computation
Journal of Symbolic Computation
On compatibility of discrete relations
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
On connection between constructive involutive divisions and monomial orderings
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
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In this paper, effectiveness of using four criteria in an involutive algorithm based on the Pommaret division for construction of Boolean Gröbner bases is studied. One of the results of this study is the observation that the role of the criteria in computations in Boolean rings is much less than that in computations in an ordinary ring of polynomials over the field of integers. Another conclusion of this study is that the efficiency of the second and/or third criteria is higher than that of the two others.