Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory

Problems connected with ideals generated by finite sets F of multivariate polynomials occur, as mathematical subproblems, in various branches of systems theory, see, for example, [5]. The method of Grobner bases is a technique that provides algorithmic solutions to a variety of such problems, for instance, exact solutions of F viewed as a system of algebraic equations, computations in the residue class ring modulo the ideal generated by F, decision about various properties of the ideal generated by F, polynomial solution of the linear homogeneous equation with coefficients in F, word problems modulo ideals and in commutative semigroups (reversible Petri nets), the bijective enumeration of all polynomial ideal over a given coefficient domain etc.