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 کامل4 Local Gröbner Fan : Polyhedral and Computational Approach
The goal of this paper is to show that the local Gröbner fan is a polyhedral fan for ideals in the ring of power series and the homogenized ring of analytic differential operators. We will also discuss about relations between the local Gröbner fan and the (global) Gröbner fan for a given ideal and algorithms of computing local Gröbner fans. In rings of differential operators, finiteness and con...
متن کاملLocal Gröbner fan
This note summarizes results concerning local Gröbner fans. Any Gröbner fan of an ideal in a power series ring, or in an analytic or formal differential operator ring, is found to be a polyhedral fan. We also compare the notions of global and local Gröbner fans, and discuss applications of our results. To cite this article: R. Bahloul, N. Takayama, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
متن کاملThe Gröbner fan and Gröbner walk for modules
This paper extends the theory of the Gröbner fan and Gröbner walk for ideals in polynomial rings to the case of submodules of free modules over a polynomial ring. The Gröbner fan for a submodule creates a correspondence between a pair consisting of a cone in the fan and a point in the support of the cone and a pair consisting of a leading monomial submodule (or equivalently, a reduced marked Gr...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2007
ISSN: 1631-073X
DOI: 10.1016/j.crma.2006.11.030