  For a finite index sublattice $L$ of the root lattice $A_{n}$, we construct a
deterministic algorithm to deform the lattice ideal $I_L$ to a nearby generic
lattice ideal, answering a question posed by Miller and Sturmfels. Our
algorithm is based on recent results of Perkinson, Perlman and Wilmes
concerning commutative algebraic aspects of chip firing on directed graphs. As
an application of our deformation algorithm, we construct a cellular resolution
of the lattice ideal $I_L$ by degenerating the Scarf complex of its
deformation.
