Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering
نویسندگان
چکیده
منابع مشابه
Computation of Difference Gröbner Bases
This paper is an updated and extended version of our note [1] (cf. also [2]). To compute difference Gröbner bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet-like division. The algorithm has been implemented in Maple in the form of the package LDA (Linear Difference Algebra) and we describe the main features of the pa...
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This paper introduces a new efficient algorithm, called MXL3, for computing Gröbner bases of zero-dimensional ideals. The MXL3 is based on XL algorithm, mutant strategy, and a new sufficient condition for a set of polynomials to be a Gröbner basis. We present experimental results comparing the behavior of MXL3 to F4 on HFE and random generated instances of the MQ problem. In both cases the firs...
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It is well known that in the computation of Gröbner bases an arbitrarily small perturbation in the coefficients of polynomials may lead to a completely different staircase even if the roots of the polynomials change continuously. This phenomenon is called pseudo singularity in this paper. We show how such phenomenon may be detected and even “repaired” by adding a new variable and a binomial rel...
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The principal result described in this report is the design and implementation of a parallel version of Buchberger's algorithm. Its correctness is stated and some experimental results are given. The first parts are devoted to a partial review of Grobner bases, of Buchberger's algorithm which computes them, and of some of their applications.
متن کاملExponential space computation of Gröbner bases Klaus Kühnle
Given a polynomial ideal and a term order, there is a unique reduced Grr obner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of nding this normal form for any given polynomial, without prior computation of the Grr obner basis. This is done by transforming a representation of the normal form...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1993
ISSN: 0747-7171
DOI: 10.1006/jsco.1993.1051