Computational Commutative Algebra 1

By Martin Kreuzer, L. Robbiano. 2000

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Characterizations of Border Bases (2005, methodology): “To characterize border bases in analogy with conditions C1) { C4) of [ 4, Section 2.2 ] we dene the rewrite relation associated to G. Let f 2 P be a polynomial such that t 2 Supp(f) is a multiple of a border term t = t0bi .”
On computing Belyi maps (2013, background): “[97] Martin Kreuzer and Lorenzo Robbiano, Computational commutative algebra 1, SpringerVerlag, New York, 2000.”
Integral closure of ideals, rings, and modules (2006, background): “But A is a polynomial ring over a field, and there are algorithms for factoring in polynomial rings (see the book [316] by von zur Gathen and Gerhard; or the tutorial on page 38 of [174]).”
Gröbner Bases and Determinantal Ideals (2003, neutral): “f Gro¨bner bases, monomial orders, initial ideals and initial algebras. For further information on the theory of Gro¨bner bases we refer the reader to the books by Eisenbud [33], Kreuzer and Robbiano [56], Sturmfels [67] and Vasconcelos [71]. For the so-called Sagbi bases and initial algebras one sh”
The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry (2004, background): “The books [Greuel and Pfister 2002] and [Kreuzer and Robbiano 2000], and for projective geometry, the forthcoming book of Decker and Schreyer [Decker and Schreyer ≥ 2003] will be very helpful.”