On Signature-Based Gröbner Bases Over Euclidean Rings
نویسندگان
چکیده
In this paper we present first steps in using signature-based Gröbner basis algorithms like Faugère’s F5 or GVW for computation over Euclidean rings. We present problems appearing when having to deal with coefficients and zero divisors and give practical solution techniques. A hybrid algorithm is presented trying to combine the advantages of signature-based and non-signature-based Gröbner basis computation. For some examples speedups are achieved due to faster finding good reducers with the hybrid technique.
منابع مشابه
Signature-based Criteria for Möller's Algorithm for Computing Gröbner Bases over Principal Ideal Domains
Signature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in general rings is not yet as well understood. In this paper, we present a signature-based algorithm for computing Gröbner bases over principal ideal domains (e.g. the ring of integers or the ring of univariate polynomi...
متن کاملRevisiting strong Gröbner bases over Euclidean domains
Buchberger and Kandri−Rody and Kapur defined a strong Gröbner basis for a polynomial ideal over a Euclidean domain in a way that gives rise to canonical reductions. This retains what is perhaps the most important property of Gröbner bases over fields. A difficulty is that these can be substantially harder to compute than their field counterparts. We extend their results for computing these base...
متن کاملComprehensive Gröbner bases and von Neumann regular rings
There is a close relation between comprehensive Gröbner bases and non-parametric Gröbner bases over commutative von Neumann regular rings. By this relation, Gröbner bases over a commutative von Neumann regular ring can be viewed as an alternative to comprehensive Gröbner bases. (Therefore, this Gröbner basis is called an “alternative comprehensive Gröbner basis (ACGB)”.) In the first part of th...
متن کاملReduced Gröbner Bases in Polynomial Rings over a Polynomial Ring
We define reduced Gröbner bases in polynomial rings over a polynomial ring and introduce an algorithm for computing them. There exist some algorithms for computing Gröbner bases in polynomial rings over a polynomial ring. However, we cannot obtain the reduced Gröbner bases by these algorithms. In this paper we propose a new notion of reduced Gröbner bases in polynomial rings over a polynomial r...
متن کاملGeneralized Discrete Comprehensive Gröbner Bases
We showed special types of comprehensive Gröbner bases can be defined and calculated as the applications of Gröbner bases in polynomial rings over commutative Von Neumann regular rings in [5] and [6]. We called them discrete comprehensive Gröbner bases, since there is a strict restriction on specialization of parameters, that is parameters can take values only 0 and 1. In this paper, we show th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017