Abstract
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.
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Noro, M., Yokoyama, K. (2014). Verification of Gröbner Basis Candidates. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_64
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DOI: https://doi.org/10.1007/978-3-662-44199-2_64
Publisher Name: Springer, Berlin, Heidelberg
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