A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Journal of Symbolic Computation
A Gröbner-based treatment of elimination theory for affine varieties
Journal of Symbolic Computation
Algebraic characterization of uniquely vertex colorable graphs
Journal of Combinatorial Theory Series B
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This tutorial will explore the theory of Gröbner bases. The first part will review classic material on monomial orders, the Buchberger Algorithm, and elimination theory. This will be followed by a discussion of the geometry of elimination, where resultants can be replaced with Gröbner bases using ideas of Schauenberg [15]. The tutorial will conclude with a sampler of topics about Gröbner bases, including graph theory [11], geometric theorem proving via comprehensive Gröbner systems [13, 14], the generic Gröbner walk [12], alternatives to the Buchberger algorithm and applications [8, 9, 10], and moduli of quiver representations via Gröbner bases [5]. (This list of topics is tentative--the tutorial may cover slightly different topics.