A p-adic approach to the computation ofGröbner bases
Journal of Symbolic Computation
On lucky ideals for Gro¨bner basis computations
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Converting bases with the Gröbner walk
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Gröbner Bases and Systems Theory
Multidimensional Systems and Signal Processing
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Some properties of Gröbner-bases for polynomial ideals
ACM SIGSAM Bulletin
Computational Commutative Algebra 1
Computational Commutative Algebra 1
On the performances of parametric finite elements when geometry distortions occur
Finite Elements in Analysis and Design
Deriving Finite Sphere Packings
SIAM Journal on Discrete Mathematics
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In this paper, we give a brief overview on Gröbner bases theory, addressed to novices without prior knowledge in the field. After explaining the general strategy for solving problems via the Gröbner approach, we develop the concept of Gröbner bases by studying uniquenss of polynomial division ("reduction"). For explicitly constructing Gröbner bases, the crucial notion of S-polynomials is introduced, leading to the complete algorithmic solution of the construction problem. The algorithm is applied to examples from polynomial equation solving and algebraic relations. After a short discussion of complexity issues, we conclude the paper with some historical remarks and references.