On the links between triangular sets and dynamic constructible closure

Two kinds of triangular systems are studied: normalized triangular polynomial systems (a weaker form of Lazardʹs triangular sets (Discrete Appl. Math. 33 (1991) 33)) and constructible triangular systems (involved in the dynamic constructible closure programs of Gómez-Díaz (Quelques applications de l’évaluation dynamique, Ph.D. Thesis, Université de Limoges, 1994)). This paper shows that these notions are strongly related. In particular, combining the two points of view (constructible and polynomial) on the subject of square-free conditions, it allows us to effect dramatic improvements in the dynamic constructible closure programs.