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TitleVerification of Gr\"obner basis candidates.
Author(s) Masayuki Noro, Kazuhiro Yokoyama
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe propose a modular method for verifying the correctness of a Gröbner basis candidate. For an inhomogeneous ideal I, we propose to check that a Gröbner basis candidate G is a subset of I by computing an exact generating relation for each g in G by the given generating set of I via a modular method. The whole procedure is implemented in Risa/Asir, which is an open source general computer algebra system. By applying this method we succeeded in verifying the correctness of a Gröbner basis candidate computed in Romanovski et al (2007). In their paper the candidate was computed by a black-box software system and it has been necessary to verify the candidate for ensuring the mathematical correctness of the paper.
KeywordsGröbner basis, modular algorithm, verification
URL http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_64
PublisherBerlin: Springer
Translation No
Refereed No