The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
The design of maple: A compact, portable and powerful computer algebra system
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Non-modular computation of polynomial GCD's using trial division
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
On solving systems of algebraic equations via ideal bases and elimination theory
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
Some properties of Gröbner-bases for polynomial ideals
ACM SIGSAM Bulletin
A heuristic selection strategy for lexicographic Gröner bases?
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
IEEE Transactions on Knowledge and Data Engineering
Foreword: In honour of Keith Geddes on his 60th birthday
Journal of Symbolic Computation
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An implementation in the Maple system of Buchberger's algorithm for computing Gröbner bases is described. The efficiency of the algorithm is significantly affected by choices of polynomial representations, by the use of criteria, and by the type of coefficient arithmetic used for polynomial reductions. The improvement possible through a slightly modified application of the criteria is demonstrated by presenting time and space statistics for some sample problems. A fraction-free method for polynomial reduction is presented. Timings on problems with integer and polynomial coefficients show that a fraction-free approach is recommended.