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TitleOn the computation of parametric Gr\"obner bases for modules and syzygies.
Author(s) Katsusuke Nabeshima
TypeArticle in Journal
AbstractThis paper presents algorithms to compute parametric Gröbner bases for modules and parametric syzygies. The theory of Gröbner basis is by far the most important tool for computations in commutative algebra and algebraic geometry. The theory of parametric Gröbner basis is also important to solve problems of ideals generated by parametric polynomials and submodule generated by parametric vectors. Several algorithms are known for computing parametric Gröbner bases in polynomial rings. However, nobody has studied the extension of parametric Gröbner bases to modules yet. In this paper we extend the theory of parametric Gröbner bases to modules, and we describe an algorithm for computing syzygies of parametric polynomials (vectors). These algorithms have been implemented in the computer algebra system Risa/Asir.
KeywordsGröbner bases, Comprehensive Syzygies, Modules
ISSN0916-7005; 1868-937X/e
URL http://link.springer.com/article/10.1007%2Fs13160-010-0003-z
JournalJapan J. Ind. Appl. Math.
PublisherSpringer Japan, Tokyo
Translation No
Refereed No