Details:
Title  Gröbner bases of symmetric ideals  Author(s)  Stefan Steidel  Type  Article in Journal  Abstract  In this article we present two new algorithms to compute the Gröbner basis of an ideal that is invariant under certain permutations of the ring variables and which are both implemented in Singular (cf. Decker et al., 2012). The first and major algorithm is most performant over finite fields whereas the second algorithm is a probabilistic modification of the modular computation of Gröbner bases based on the articles by Arnold (cf. Arnold, 2003), Idrees, Pfister, Steidel (cf. Idrees et al., 2011) and Noro, Yokoyama (cf. Noro and Yokoyama, in preparation; Yokoyama, 2012). In fact, the first algorithm that mainly uses the given symmetry, improves the necessary modular calculations in positive characteristic in the second algorithm. Particularly, we could, for the first time even though probabilistic, compute the Gröbner basis of the famous ideal of cyclic 9roots (cf. Björck and Fröberg, 1991) over the rationals with Singular.  Keywords  Gröbner bases, Symmetry, Modular computation, Parallel computation  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771711300014X 
Language  English  Journal  Journal of Symbolic Computation  Volume  54  Number  0  Pages  72  86  Year  2013  Edition  0  Translation 
No  Refereed 
No 
