Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Gröbner bases of symmetric ideals
 Journal of symbolic computation 54 (2013), pp.7286 ISSN: 07477171 ISSN: 1095855X 

 English 
 Journal Article 
 Fraunhofer ITWM () 
Abstract
In this article we present two new algorithms to compute the Grobner 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 Grobner 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 Grobner basis of the famous ideal of cyclic 9roots (cf. Bjorck and Froberg, 1991) over the rationals with SINGULAR.