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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Verification of Gröbner Basis Candidates
verfasst von : Masayuki Noro, Kazuhiro Yokoyama
Erschienen in: Mathematical Software – ICMS 2014
Verlag: Springer Berlin Heidelberg
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We 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.