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

Let K be a field; let P ⊂ Kn be a finite set and let (P) ⊂ K[x1 ,…, xn] be the ideal of P. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K[x1, … , xn]/(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.t.. 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 Gröbner basis of (P) with respect to ⩽i.t. without using Buchbergerʹs algorithm).