Gröbner bases
David A. Cox · 2007
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.