  This paper belongs to a group of work in the intersection of symbolic
computation and group analysis aiming for the symbolic analysis of differential
equations. The goal is to extract important properties without finding the
explicit general solution. In this contribution, we introduce the algorithmic
verification of nonlinear superposition properties and its implementation. More
exactly, for a system of nonlinear ordinary differential equations of first
order with a polynomial right-hand side, we check if the differential system
admits a general solution by means of a superposition rule and a certain number
of particular solutions. It is based on the theory of Newton polytopes and
associated symbolic computation. The developed method provides the basis for
the identification of nonlinear superpositions within a given system and for
the construction of numerical methods which preserve important algebraic
properties at the numerical level.
