Algebraic programming of Hamiltonian formalism in general relativity: Application to inhomogeneous space-times

We describe the structure and the use of a program written in the algebraic programming languagereduce 2, giving the super-Hamiltonian and supermomenta constraints, as well as Hamilton's canonical equations in terms of the canonical variables, for vacuum relativistic space-times. The program uses as input the components of the spatial metric tensor and of the corresponding canonically conjugate momenta in a coordinate or in a spatial Cartan basis. The results of the application of the program to a series of inhomogeneous (cosmological as well as noncosmological) space-times are given: in particular, the constraints, the Dirac Hamiltonian and the canonical equations are explicitly written for axisymmetric space-times, constituting the starting point for the study of the dynamics and of the canonical quantization of these configurations.