1 HOW TO USE GR OBNER - MATHEMATICA 2 Global Variable Semantics Possible Values

In this paper we report on GR OBNER-Mathematica, an experimental implementation for computing Grr obner bases in Mathematica. This implementation in its current form ooers three diierent versions of the Grr obner bases algorithm and is generic with respect to the ordering of power products, the domain of coeecients of the polynomials, and the representation of power products, monomials, polynomials, and other domains. The package GR OBNER-Mathematica implements the author's Grr obner bases algorithm (see Buchberger 85]) in Mathematica. In order to start GR OBNER-Mathematica one has to load the start-up le Groebner.m into the Mathematica system by entering the command <<Groebner.m. This le also contains some settings of global variables to initialize a default version of the Grr obner bases algorithm (global variables always begin with $). By changing these global variables one can choose a particular variant of the Grr obner bases algorithm. The global variables and their possible values are listed in Table 1, the exact meaning of the possible values of the global variables is explained in Section 2.5. An evaluation of the performance of the package is given in Buchberger 91]. Calling the function GB with one parameter, a set of polynomials, causes the system to call the version of the Grr obner bases algorithm that is stored in $GroebnerBasisPN. The result is the reduced Grr obner basis with respect to the ordering $GreaterEL. The normal form algorithm used during computation is the one stored in $NormalFormDNP, interreduction of the basis depends on the value of $InterReducedPN. To read in a polynomial set, the most comfortable way is to enter a list of polyno-mials in Mathematica format (preferable from a le) and then convert it to a desired 1