2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72597We show that a convex pyramid in R^n with apex at 0 can be brought to the first quadrant by a finite sequence of monomial blowing-ups if and only if its intersection with the opposite of the first quadrant is 0. The proof is non-trivially derived from the theorem of Farkas-Minkowski. Then, we apply this theorem to show how the Newton diagrams of the roots of any Weierstrass polynomial are contained in a pyramid of this type. Finally, if n = 2, this fact is equivalent to the Jung-Abhyankar theorem.12 pagesCommutative AlgebraOptimization and Control15A39 (Primary), 13H99 (Secondary)text