Details:
Title  On the computation of parametric Gr\"obner bases for modules and syzygies.  Author(s)  Katsusuke Nabeshima  Type  Article in Journal  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.  Keywords  Gröbner bases, Comprehensive Syzygies, Modules  ISSN  09167005; 1868937X/e 
URL 
http://link.springer.com/article/10.1007%2Fs131600100003z 
Language  English  Journal  Japan J. Ind. Appl. Math.  Volume  27  Number  2  Pages  217238  Publisher  Springer Japan, Tokyo  Year  2010  Edition  0  Translation 
No  Refereed 
No 
