ATENSOR - REDUCE PROGRAM FOR TENSOR SIMPLIFICATION

The paper presents a REDUCE program for the simplification of tensor e xpressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vect ors in some linear space. This linear space is formed by all the eleme nts of the group algebra of the corresponding tensor expression. Such approach permits us to simplify the tensor expressions possessing symm etry properties, summation (dummy) indices and multiterm identities by unify manner. The canonical element for the tensor expression is defi ned in terms of the basic vectors of this linear space. The main restr iction of the algorithm is the dimension of the linear space that is e qual to N!, where N is a number of indices of the tensor expression, T he program uses REDUCE as user interface.