From algebraic sets to monomial linear bases by means of combinatorial algorithms

Let K be a eld; let P K n be a nite set and let =(P) Kx 1 ; : : :; x n ] be the ideal of P. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra Kx 1 ; : : :; x n ]==(P) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order i:l:. It is also shown how this algorithm can be extended to the case in which P is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grr obner basis of =(P) with respect to i:l: without using Buchberger's algorithm).