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TitleOn the computation of comprehensive Boolean Gr\"obner bases.
Author(s) Shutaro Inoue
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe show that a comprehensive Boolean Gröbner basis of an ideal I in a Boolean polynomial ring B (A¯,X¯) with main variables X¯ and parameters A¯ can be obtained by simply computing a usual Boolean Gröbner basis of I regarding both X¯ and A¯ as variables with a certain block term order such that X¯≫A¯. The result together with a fact that a finite Boolean ring is isomorphic to a direct product of the Galois field 𝔾𝔽2 enables us to compute a comprehensive Boolean Gröbner basis by only computing corresponding Gröbner bases in a polynomial ring over 𝔾𝔽2. 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.
URL http://link.springer.com/chapter/10.1007%2F978-3-642-04103-7_13
PublisherBerlin: Springer
Translation No
Refereed No