  The problem of simplifying tensor expressions is addressed in two parts. The
first part presents an algorithm designed to put tensor expressions into a
canonical form, taking into account the symmetries with respect to index
permutations and the renaming of dummy indices. The tensor indices are split
into classes and a natural place for them is defined. The canonical form is the
closest configuration to the natural configuration. In the second part, the
Groebner basis method is used to simplify tensor expressions which obey the
linear identities that come from cyclic symmetries (or more general tensor
identities, including non-linear identities). The algorithm is suitable for
implementation in general purpose computer algebra systems. Some timings of an
experimental implementation over the Riemann package are shown.

General Relativity and Quantum Cosmology