  Lie point symmetries of the one-dimensional gas dynamics equations of a
polytropic gas in Lagrangian coordinates are considered. Complete Lie group
classification of these equations reduced to a scalar second-order PDE is
performed. The classification parameter is the entropy. Noether theorem is
applied for constructing conservation laws. The conservation laws can be
represented in the gas dynamics variables. For the basic adiabatic case
invariant and conservative difference schemes are discussed.
