  We study gradient Ricci solitons warped products whose base is the Euclidean
space. We show that the warping functions of these manifolds are invariant
under the (n-1)-dimensional translation group. We characterize the potential
function when the torsion function depends only on one variable, which is a
particular case of invariance by translation. From this study, we derive
complete examples of expanding gradient Ricci solitons.
