Applications of Bar Code to Involutive Divisions and a “Greedy” Algorithm for Complete Sets - Ceria, Michela (Mathematics in computer science, 2022)
Given a finite set of terms U in n variables, we describe an algorithm which finds – if it exists – an ordering on the variables such that U is a complete set according to Janet involutive division. The algorithm, based on Bar Codes for monomial ideals, is able to adjust the variables ordering with a sort of backtracking technique, thus allowing to find the desired ordering without trying all the n ! possible ones.