Computing Gröbner fans
نویسندگان
چکیده
منابع مشابه
Computing Gröbner fans
This paper presents algorithms for computing the Gröbner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Gröbner bases of the ideal. Our algorithms are based on a uniform definition of the Gröbner fan that applies to both homogeneous and non-homogeneous ideals and a proof that this object is a polyhedral complex. We show that the cells of a Gröbner fan ...
متن کاملGröbner fans of x-homogeneous ideals in R〚t〛[x]
We generalise the notion of Gröbner fan to ideals in RJtK[x1, . . . , xn] for certain classes of coefficient rings R and give a constructive proof that the Gröbner fan is a rational polyhedral fan. For this we introduce the notion of initially reduced standard bases and show how these can be computed in finite time. We deduce algorithms for computing the Gröbner fan, implemented in the computer...
متن کاملComputing inhomogeneous Gröbner bases
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 a technique described in Section 2: the main tool ...
متن کاملComputing Grr Obner Fans of Toric Ideals
The monomial initial ideals of a graded polynomial ideal are in bijection with the vertices of a convex polytope known as the state polytope of the ideal. The Grr obner fan of the ideal is the normal fan of its state polytope. In this paper we present a software system called TiGERS (Toric Grr obner bases Enumeration by Reverse Search) for computing the Grr obner fan of a toric ideal by enumera...
متن کاملFGb: A Library for Computing Gröbner Bases
FGb is a high-performance, portable, C library for computing Gröbner bases over the integers and over finite fields. FGb provides high quality implementations of state-of-the-art algorithms (F4 and F5) for computing Gröbner bases. Currently, it is one of the best implementation of these algorithms, in terms of both speed and robustness. For instance, FGb has been used to break several cryptosys...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-07-01986-2