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Last name: ROBBIANO
First name: Lorenzo
Robbiano, Lorenzo; Abbott, John (Eds.); Series: Texts and Monographs in Symbolic Computation; Springer-Verlag Wien; ISBN 978-3-211-99313-2
Il risveglio di un matematico in un mondo inusuale induce considerazioni sui modelli matematici, sull'algebra computazionale, sulla vita. Poesie, sogni, pozzi petroliferi, palindromi, teoremi si rincorrono e si intrecciano.
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Hilbert schemes of zero-dimensional ideals in a polynomial ring can be covered with suitable affine open subschemes whose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing zero-dimensional ideals when the coefficients are inexact. And in this situation they show a clear...
The main topic of this book is that of Groebner bases and their applications. The main purpose of this book is that of bridging the current gap in the literature between theory and real computation. The book can be used by teachers and students alike as a comprehensive guide to both the theory and the practice of Computational Commutative...
Following the path trodden by several authors along the border between Algebraic Geometry and Algebraic Combinatorics, we present some new results on the combinatorial struc- ture of Borel ideals. This enables us to prove theorems on the shape of the sectional matrix of a homogeneous ideal, which is a new invariant stronger than the Hilbert function.
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Libro di testo per corsi di Istituzioni di Matematica
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In the computation of a Gr\"obner basis using Buchberger's algorithm, a key issue for improving the efficiency is to produce techniques for avoiding as many unnecessary critical pairs as possible. A good solution would be to avoid {\it all}\/ non-minimal critical pairs, and hence to process only a {\it minimal set of generators}\/ of the...
This paper generalizes the Buchberger-M\"oller algorithm to zero-dimensional schemes in both affine and projective spaces. We also introduce a new, general way of viewing the problems which can be solved by the algorithm: an approach which looks to be readily applicable in several areas. Implementation issues are also addressed, especially...
In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger's Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use...
The generic initial ideals of a given ideal are rather recent invariants. Not much is known about these objects, and it turns out to be very difficult to compute them. The main purpose of this paper is to study the behaviour of generic initial ideals with respect to the operation of taking distractions. Theorem 4.3 is our main result. It states...
We prove a theorem, which provides a formula for the computation of the Poincar\'e series of a monomial ideal in $k[X_1,\dots,X_n]$, via the computation of the Poincare' series of some monomial ideals in $k[X_1,\dots ,\widehat{X_i}, \dots,X_n]$. The complexity of our algorithm is optimal for Borel-normed ideals and an implementation in CoCoA...
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 develop new theories which allow us to devise a parallel algorithm and an efficient elimination algorithm. In many respects they improve existing...
We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for polynomial parametrizations: one algorithm, "ElimTH", has as main step the computation of an elimination...
Toric ideals are binomial ideals which represent the algebraic relations of finite sets of power-products. Their importance comes from on the fact that they show up in many problems arising from different branches of science, for instance Integer Programming and Combinatorics. Largely inspired by the fundamental book [St], we have recently...
Design of Experiments is a branch of Statistics, which has a long tradition in the use of algebraic methods. In general all this methods where developed in the case of binary experiments, with level coding either 0, 1 and -1, 1 and refer to computations in Z_2 The classical theory fully exploits the characteristics of the binary case, in...
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We address the problem of computing ideals of polynomials which vanish at a finite set of points. In particular we develop a modular Buchberger-Moeller algorithm, best suited for the computation over QQ, and study its complexity; then we describe a variant for the computation of ideals of projective points, which uses a direct approach and a...