  The article presents computer algebra procedures and routines applied to the
study of the Dirac field on curved spacetimes. The main part of the procedures
is devoted to the construction of Pauli and Dirac matrices algebra on an
anholonomic orthonormal reference frame. Then these procedures are used to
compute the Dirac equation on curved spacetimes in a sequence of special
dedicated routines. A comparative review of such procedures obtained for two
computer algebra platforms (REDUCE + EXCALC and MAPLE + GRTensorII) is carried
out. Applications for the calculus of Dirac equation on specific examples of
spacetimes with or without torsion are pointed out.
