2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121586We provide explicit conditions for a real polynomial $f$ of degree 2d to be a sum of squares (s.o.s.), stated only in terms of the coefficients of $f$, i.e. with no lifting. All conditions are simple and provide an explicit description of a convex polyhedral subcone of the cone of s.o.s. polynomials of degree at most 2d. We also provide a simple condition to ensure that $f$ is s.o.s., possibly modulo a constant.9 pagesAlgebraic GeometryCommutative Algebra12E05 12Y05text