Bar Code: A Visual Representation for Finite Sets of Terms and Its Applications

The Bar Code is a bidimensional diagram representing a finite set of terms in any number of variables. In particular, one can represent the (lexicographical) Groebner escalier of a zerodimensional monomial ideal and use this representation to desume many of its properties. The aim of this paper is to give a general description of the Bar Code and it construction, giving then an overview of all the applications studied so far.