TTC: Symbolic tensor calculus with indices

In an earlier paper [P. Castellvi, X. Jaen, and E. Llanta, Comput. Phys. 9, 3 (1995)] we presented the capabilities of TTC (Tools of Tensor Calculus, a Mathematica package, see http:// baldufa.upc.es/ttc) when inputs are made in index notation. In that article inputs were merely an effective way to indicate explicit operations to be performed on tensors. Here we describe the way TTC operates with index notation at a symbolic level, that is, when inputs and outputs are expressed in index notation and tensors are not explicitly declared. The operations are performed only at a symbolic level. This is not just an appearance of symbolic computing supplemented with a limited collection of rules. TTC makes algorithm simplifications on symbolic indexed expressions while using the symmetry properties of tensors. (C) 1998 American Institute of Physics. [S0894-1866(98)01603-4].