Groebner Bases of Symmetric Ideals

Details Groebner Bases of Symmetric Ideals Groebner Bases of Symmetric Ideals

2012-01-27

arxiv.org/abs/1201.5792v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

In this paper we present a new algorithm to compute the Gr\"obner basis of an ideal that is invariant under certain permutations of the ring-variables. Furthermore, we introduce a second algorithm which is a modification of the modular computation of Gr\"obner bases as introduced by Idrees, Pfister, Steidel in the symmetric case. In fact, the algorithm that uses the given symmetry, improves the modular calculations in positive characteristic. In particular, we could, for the first time, compute the Gr\"obner basis of the famous ideal of cyclic 9-roots over the rationals with SINGULAR. Both new algorithms are implemented in SINGULAR.

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