The algorithm for the construction of a Gröbner basis from an arbitrary ideal basis. Buchberger's algorithm relies on the concepts
of 
-polynomial
and polynomial reduction modulo a set of polynomials, the latter being the most computationally
intensive part of the algorithm.
Buchberger's Algorithm
See also
Gröbner Basis, Knuth-Bendix Completion AlgorithmExplore with Wolfram|Alpha
References
Becker, T. and Weispfenning, V. Gröbner Bases: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, pp. 213-214, 1993.Buchberger, B. "Theoretical Basis for the Reduction of Polynomials to Canonical Forms." SIGSAM Bull. 39, 19-24, Aug. 1976.Cox, D.; Little, J.; and O'Shea, D. Ideals, Varieties, and Algorithms: An Introduction to Algebraic Geometry and Commutative Algebra, 2nd ed. New York: Springer-Verlag, 1996.Giovini, A.; Mora, T.; Niesi, G.; Robbiano, L.; and Traverso, C. "One Sugar Cube, Please?, or Selection Strategies in the Buchberger Algorithm." Proceedings of the International Symposium on Symbolic and Algebraic Computation. pp. 49-54, June 1991.Referenced on Wolfram|Alpha
Buchberger's AlgorithmCite this as:
Weisstein, Eric W. "Buchberger's Algorithm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BuchbergersAlgorithm.html