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Computing Boolean Gröbner bases within linear algebra. (English) Zbl 1187.13023
Suzuki, Masakazu (ed.) et al., The joint conference of ASCM 2009 and MACIS 2009. 9th international conference on Asian symposium on computer mathematics and 3rd international conference on mathematical aspects of computer and information sciences, Fukuoka, Japan, December 14–17, 2009. Selected papers. Fukuoka: Kyushu University, Faculty of Mathematics. COE Lecture Note 22, 201-204 (2009).
Introduction: In these years, many application of boolean Gröbner bases have been studied. Thus more effective algorithms to compute them are demanded. For a such purpose, in this article, we propose a way to compute within linear algebra.
Computation of Gröbner bases by use of linear algebra has been studied, and an explicit algorithm to compute Gröbner bases within linear algebra was shown. So we can calculate boolean Gröbner bases by modifying them.
On the other hand, these methods have a problem of wasting computer memory. In this article, we show a method to compute boolean Gröbner bases which does not require additional memory allocation during the computation.
For the entire collection see [Zbl 1181.68015].
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)