  {We analyze a general Implicit-Explicit (IMEX) time discretization for the
compressible Euler equations of gas dynamics, showing that they are
asymptotic-preserving (AP) in the low Mach number limit. The analysis is
carried out for a general equation of state (EOS). We consider both a single
asymptotic length scale and two length scales. We then show that, when coupling
these time discretizations with a Discontinuous Galerkin (DG) space
discretization with appropriate fluxes, an all Mach number numerical method is
obtained. A number of relevant benchmarks for ideal gases and their non-trivial
extension to non-ideal EOS validate the performed analysis.
