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 Title On the Computation of Comprehensive Boolean Gröbner Bases Author(s) Shutaro Inoue Type Article in Conference Proceedings Abstract We show that a comprehensive Boolean Gröbner basis of an ideal I 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 I 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. Length 12 ISBN 978-3-642-04102-0 URL http://dx.doi.org/10.1007/978-3-642-04103-7_13 Language English Series CASC '09 Pages 130--141 Publisher Springer-Verlag Address Berlin, Heidelberg Year 2009 Translation No Refereed No How published CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing Conferencename CASC '09, 11th International Workshop on Computer Algebra in Scientific Computing
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