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TitleOn the Computation of Comprehensive Boolean Gröbner Bases
Author(s) Shutaro Inoue
TypeArticle in Conference Proceedings
AbstractWe show that a comprehensive Boolean Gröbner basis of an ideal <em>I</em> in a Boolean polynomial ring B $(\bar A,\bar X)$ with main variables $\bar X$ and parameters $\bar A$ can be obtained by simply computing a usual Boolean Gröbner basis of <em>I</em> regarding both $\bar X$ and $\bar A$ as variables with a certain block term order such that $\bar X \gg \bar A$. The result together with a fact that a finite Boolean ring is isomorphic to a direct product of the Galois field $\mathbb{GF}_2$ enables us to compute a comprehensive Boolean Gröbner basis by only computing corresponding Gröbner bases in a polynomial ring over $\mathbb{GF}_2$. Our implementation in a computer algebra system Risa/Asir shows that our method is extremely efficient comparing with existing computation algorithms of comprehensive Boolean Gröbner bases.
Length12
ISBN978-3-642-04102-0
URL http://dx.doi.org/10.1007/978-3-642-04103-7_13
LanguageEnglish
SeriesCASC '09
Pages130--141
PublisherSpringer-Verlag
AddressBerlin, Heidelberg
Year2009
Translation No
Refereed No
How publishedCASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
ConferencenameCASC '09, 11th International Workshop on Computer Algebra in Scientific Computing
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