An algorithm to simplify tensor expressions

The problem of simplifying tensor expressions is addressed in two parts. Th e 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 spli t into classes and a natural place for them is defined. The canonical form is the closest configuration to the natural configuration. In the second pa rt, the Grobner basis method is used to simplify tensor expressions which o bey the linear identities that come from cyclic symmetries (or more general tensor identities, including nonlinear identities). The algorithm is suita ble for implementation in general purpose computer algebra systems. Some ti mings of an experimental implementation over the Riemann package are shown. (C) 1998 Published by Elsevier Science B.V.