id: 05627931
dt: a
an: 05627931
au: Inoue, Shutaro
ti: On the computation of comprehensive Boolean Gröbner bases.
so: Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing.
    11th international workshop, CASC 2009, Kobe, Japan, September 13‒17,
    2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04102-0/pbk).
    Lecture Notes in Computer Science 5743, 130-141 (2009).
py: 2009
pu: Berlin: Springer
la: EN
cc: 
ut: 
ci: 
li: doi:10.1007/978-3-642-04103-7_13
ab: Summary: We show that a comprehensive Boolean Gröbner basis of an ideal
    $I$ in a Boolean polynomial ring $\bold{B}(\bar A,\bar X)$ 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.
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