MRC - A System for Computing Gröbner Bases in Monoid and Group Rings
Birgit Reinert, Dirk Zeckzer · 1998
Grobner bases and Buchberger's algorithm have been generalized to monoid and group rings. In this paper we summarize procedures from this field and present a description of their implementation in the system Mrc V 1.0. Keywords Monoid and group rings, Grobner bases, prefix reduction Mrc stands for Monoid Ring Completion. y This author was supported by the Deutsche Forschungsgemeinschaft (DFG). 1 Introduction In 1965 Buchberger introduced the theory of Grobner bases for ideals in commutative polynomial rings over fields [4], which allows solving many problems related to polynomial ideals in a computational fashion using rewriting methods. The most familiar problem is the ideal membership problem, i.e. the problem of deciding whether a given polynomial lies in an ideal specified by a generating set. In case the generating set is a Grobner basis this problem becomes solvable by checking whether the polynomial reduces to zero with the computed Grobner basis. Nowadays implementati...