117,469 research outputs found
Carta geomorfologica del territorio compreso tra il M. Antola e il Lago del Brugneto (Alta Val Trebbia, Appennino ligure).
No full textFaccini F., Perasso L., Robbiano A., Brandolini P. (2009) – Geomorfologia applicata alla pianificazione del territorio ed alla difesa del suolo in un tipico ambiente montano ligure. Memorie della Società Geografica Italiana, 211-22
Families of estimable terms
No full textIn this paper we present a full solution to an open problem in Design of Experiments, a branch of Statistics, which can equally be seen as a problem in Algebraic Geometry. Given a complete set O of estimable terms, we are able to find all the fractions F of a full factorial design, such that Ō is a basis of P/I(F) as a K-vector space. This fact can be rephrased as a result in the theory of zero-dimensional schemes
Familes of Ideals in Statistics
No full textIn this paper we use Grobner basis theory and some methods of Algebraic Geometry to solve a relevant problem in Statistics, more specifically in the Design of Experiments. Namely suppose we are given a Full Factorial Design D and a complete polynomial model P, whose support is contained in the order ideal of monomials defined by D. We show how to construct families of ideals defining Fractions F of D which are minimally identified by P
Saturations of subalgebras, SAGBI bases, and U-invariants
No full textGiven a polynomial ring P over a field K, an element g∈P, and a K-subalgebra S of P, we deal with the problem of saturating S with respect to g, i.e. computing Satg(S)=S[g,g−1]∩P. In the general case we describe a procedure/algorithm to compute a set of generators for Satg(S) which terminates if and only if it is finitely generated. Then we consider the more interesting case when S is graded. In particular, if S is graded by a positive matrix W and g is an indeterminate, we show that if we choose a term ordering σ of g-DegRev type compatible with W, then the two operations of computing a σ-SAGBI basis of S and saturating S with respect to g commute. This fact opens the doors to nice algorithms for the computation of Satg(S). In particular, under special assumptions on the grading one can use the truncation of a σ-SAGBI basis and get the desired result. Notably, this technique can be applied to the problem of directly computing some U-invariants, classically called semi-invariants, even in the case that K is not the field of complex numbers
Computing inhomogeneous Groebner bases
No full textis 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 as a main tool the procedure of a self-saturating Buchberger's Algorithm. Another strictly related topic is treated later when a mathematical foundation is given to the sugar trick which is nowadays widely used in most of the implementations of Buchberger's Algorithm. A special emphasis is also given to the case of a single grading, and subsequently some timings and indicators showing the practical merits of our approach
Environmental geologic features on the anti-aircraft tunnels in the Genoan municipality (Italy)
No full textMinimal Sets of Critical Pairs
No full textIn the computation of a Grobner basis using Buchberger's algorithm, a key issue for improving the efficiency is to produce good techniques for avoiding as many unnecessary critical pairs as possible. A good solution would be to avoid all non-minimal critical pairs, and hence to process only a minimal set of generators of the module generated by the critical pairs. In this paper we show how to obtain that desired solution while retaining the same efficiency as with the classical implementation. As a consequence, we get a new Optimized Buchberger Algorithm
Efficiently computing minimal Sets of Critical Pairs
No full textIn the computation of a Gröbner 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 all non-minimal critical pairs, and hence to process only a minimal set of generators of the module generated by the critical syzygies. In this paper we show how to obtain that desired solution in the homogeneous case while retaining the same efficiency as with the classical implementation. As a consequence, we get a new optimized Buchberger algorith
Computing Toric Ideals
No full textToric 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 algorithms for the computation of toric ideals
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