F5C: A variant of Faugère’s F5 algorithm with reduced Gröbner bases
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چکیده
منابع مشابه
F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
Faugère's F5 algorithm computes a Gröbner basis incrementally, by computing a sequence of (non-reduced) Gröbner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Gröbner basis with its reduced Gröbner basis. As a result, F5C considers fewer polynomials and performs substantially fewer polynomial reductions, so that it terminates more quickly. We also provi...
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In this paper we contribute with one main result to the interesting problem initiated by Hong (1998, J. Symb. Comput. 25, 643–663) on the behaviour of Gröbner bases under composition of polynomials. Polynomial composition is the operation of replacing the variables of a polynomial with other polynomials. The main question of this paper is: When does composition commute with reduced Gröbner base...
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We study the complexity of Gröbner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. We give a bound on the number of polynomials of degree d in a Gröbner basis computed by Faugère’s F5 algorithm ([Fau02]) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials ...
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Article history: Received 2 June 2013 Accepted 15 July 2013 Available online xxxx
متن کاملA Variant of the Gröbner Basis Algorithm for Computing Hilbert Bases
Gröbner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field given as a matrix kernel. AMS Subject Classification: 13P10, 94B05
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2010
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2010.06.019