On the relation between the MXL family of algorithms and Gröbner basis algorithms
نویسندگان
چکیده
منابع مشابه
On the relation between the MXL family of algorithms and Gröbner basis algorithms
The computation of Gröbner bases remains one of the most powerful methods for tackling the Polynomial System Solving (PoSSo) problem. The most efficient known algorithms reduce the Gröbner basis computation to Gaussian eliminations on several matrices. However, several degrees of freedom are available to generate these matrices. It is well known that the particular strategies used can drastical...
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We clarify a relation between the XL algorithm and known Gröbner basis algorithms. The XL algorithm was proposed to be a more efficient algorithm to solve a system of algebraic equations under a special condition, without calculating a whole Gröbner basis. But in our result, it is shown that to solve a system of algebraic equations with a special condition under which the XL algorithm works is ...
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15 صفحه اولOn the Relation Between the Mutant Strategy and the Normal Selection Strategy in Gröbner Basis Algorithms
The computation of Gröbner bases remains one of the most powerful methods for tackling the Polynomial System Solving (PoSSo) problem. The most efficient known algorithms reduce the Gröbner basis computation to Gaussian eliminations on several matrices. However, several degrees of freedom are available to generate these matrices. It is well known that the particular strategies used can drastical...
متن کاملComparison Between XL and Gröbner Basis Algorithms
This paper compares the XL algorithm with known Gröbner basis algorithms. We show that to solve a system of algebraic equations via the XL algorithm is equivalent to calculate the reduced Gröbner basis of the ideal associated with the system. Moreover we show that the XL algorithm is also a Gröbner basis algorithm which can be represented as a redundant variant of a Gröbner basis algorithm F4. ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2012
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2012.01.002