Details:
Title  Minimal Gröbner bases and the predictable leading monomial property  Author(s)  M. Kuijper, Kristina Schindelar  Type  Article in Journal  Abstract  We focus on Gröbner bases for modules of univariate polynomial vectors over a ring. We identify a useful property, the “predictable leading monomial (PLM) property” that is shared by minimal Gröbner bases of modules in F [ x ] q , no matter what positional term order is used. The PLM property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property (= row reducedness), a terminology introduced by Forney in the 70’s. Because of the presence of zero divisors, minimal Gröbner bases over a finite ring of the type Z p r (where p is a prime integer and r is an integer > 1 ) do not necessarily have the PLM property. In this paper we show how to derive, from an ordered minimal Gröbner basis, a socalled “minimal Gröbner pbasis” that does have a PLM property. We demonstrate that minimal Gröbner pbases lend themselves particularly well to derive minimal realization parametrizations over Z p r . Applications are in coding and sequences over Z p r .  Keywords  Finite ring, Polynomial vector modulue, Positional term order, Minimal Gröbner basis, Shortest linear recurrence relation, Parametrization  ISSN  00243795 
URL 
http://www.sciencedirect.com/science/article/pii/S0024379510004386 
Language  English  Journal  Linear Algebra and its Applications  Volume  434  Number  1  Pages  104  116  Year  2011  Edition  0  Translation 
No  Refereed 
No 
