منابع مشابه
Noncommutative involutive bases
Gröbner Basis theory originated in the work of Buchberger [4] and is now considered to be one of the most important and useful areas of computer algebra. In 1993, Zharkov and Blinkov [13] proposed an alternative method of computing a commutative Gröbner Basis, namely the computation of an Involutive Basis. In the mid 1980’s, Mora showed [11] that Buchberger’s work could be generalised for nonco...
متن کاملImproved Computation of Involutive Bases
In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Möller et al. [21], we present a more efficient variant of Gerdt’s algorithm (than the algorithm presented in [17]) to compute minimal involutive bases. Further, by using the involutive version of Hilbert driven technique, along with the new variant of Gerdt’s algorit...
متن کاملInvolutive Bases of Polynomial Ideals
In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial the self-consistent separation of the whole set of variables into two disjoint subsets. They are cal...
متن کاملTerm-ordering free involutive bases
In this paper, we consider a monomial ideal J / P := A[x1, . . . , xn], over a commutative ring A, and we face the problem of the characterization for the familyMf (J) of all homogeneous ideals I / P such that the A-module P/I is free with basis given by the set of terms in the Gröbner escalier N(J) of J. This family is in general wider than that of the ideals having J as initial ideal w.r.t. a...
متن کاملInvolutive Algorithms for Computing Gröbner Bases
In this paper we describe an efficient involutive algorithm for constructing Gröbner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain way. In the presented algorithm a reduced Gröbner basis is the internally fixed subset of an involutive basis, and having computed the later, the former can be...
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ژورنال
عنوان ژورنال: ACM SIGSAM Bulletin
سال: 1997
ISSN: 0163-5824
DOI: 10.1145/271130.271198