The notion of H-lattice concave functions defined on the whole $N_{\mathbb{R}}$ coincides with the notion of tropical Laurent polynomials over the integers, that is, the elements of the group semi-algebra $\mathbb{Z}_{\text{trop}}[N]$, where the arithmetic operations of the base semi-ring $\mathbb{Z}_{\text{trop}}=(\mathbb{Z},\oplus,\odot)$ are defined as $x\oplus y=\min(x,y)$ and $x\odot y=x+y$.