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On the computation of parametric Gröbner bases for modules and syzygies

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Abstract

This 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.

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  1. Graduate School of Information Science and Technology, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan

    Katsusuke Nabeshima

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  1. Katsusuke Nabeshima
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Nabeshima, K. On the computation of parametric Gröbner bases for modules and syzygies. Japan J. Indust. Appl. Math. 27, 217–238 (2010). https://doi.org/10.1007/s13160-010-0003-z

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  • DOI: https://doi.org/10.1007/s13160-010-0003-z

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