منابع مشابه
Computing Border Bases without using a Term Ordering
Border bases, a generalization of Gröbner bases, have actively been researched during recent years due to their applicability to industrial problems. In [6] Kehrein and Kreuzer formulated the so called Border Basis Algorithm, an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In this paper we extend the original Border Basis Algorithm in ...
متن کاملSubideal border bases
In modeling physical systems, it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases, provide some basic properties and generalize a suitable variant of the Buchberger-Möller algorithm as well as the AVI-algorithm of [5] to the subideal settin...
متن کاملDeformations of Border Bases
Border bases have recently attracted a lot of attention. Here we study the problem of generalizing one of the main tools of Gröbner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the deformation to the degree form ideal works only under additional hypotheses, we introduce border basis sch...
متن کاملToric Border Bases
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining “toric” roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more efficient approach which works directly with the variables and their inverse. We show that the commutation relations and the inversion relations characterize tori...
متن کاملModule Border Bases
In this paper, we generalize the notion of border bases of zerodimensional polynomial ideals to the module setting. To this end, we introduce order modules as a generalization of order ideals and module border bases of submodules with finite codimension in a free module as a generalization of border bases of zero-dimensional ideals in the first part of this paper. In particular, we extend the d...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.07.006