  We present a numerical solution of the dynamical mean field theory of
infinite-dimensional equilibrium liquids established in [Phys. Rev. Lett. 116,
015902 (2016)]. For soft sphere interactions, we obtain the numerical solution
by an iterative algorithm and a straightforward discretization of time. We also
discuss the case of hard spheres, for which we first derive analytically the
dynamical mean field theory as a non-trivial limit of the soft sphere one. We
present numerical results for the memory function and the mean square
displacement. Our results reproduce and extend kinetic theory in the dilute or
short-time limit, while they also describe dynamical arrest towards the glass
phase in the dense strongly-interacting regime.
