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**public sources and our publisher partners.**This is a book about Grbner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements. It is going to help you bridge the gap… Expand

To every ideal I in the polynomial ring A:=k[X"1,..., X"n] new invariants are attached, such as the Grobner Fan F(I), the Grobner region G(I) and the set ATO(I) of the almost term-orderings of I,… Expand

We address the problem of computing ideals of polynomials which vanish at a finite set of points. In particular we develop a modular Buchberger?Moller algorithm, best suited for the computation over… Expand

Toric ideals are binomial ideals which represent the algebraic relations of sets of power products. They appear in many problems arising from different branches of mathematics. In this paper, we… Expand

It is well known that various notions of distinguished bases of ideals, such as standard and Grobner bases, and algorithms for constructing them, play a central role in solving algorithmic problems… Expand

A set of s points in P d is called a Cayley-Bacharach scheme (CB-scheme), if every subset of s − 1 points has the same Hilbert function. We investigate the consequences of this «weak uniformity.» The… Expand

CoCoA is a special-purpose system for doing Computations in Commutative Algebra. It runs on all common platforms.CoCoA's particular strengths include ideal/module operations (such as Gröbner bases,… Expand

In this paper redescribe some experimentti findings on selection strategies for Gr6bner basis computation with the Buchberger algorithm. In particular, the results suggest that the “sugar flavor” of… Expand