  The paper presents a REDUCE program for the simplification of tensor
expressions that are considered as formal indexed objects. The proposed
algorithm is based on the consideration of tensor expressions as vectors in
some linear space. This linear space is formed by all the elements of the group
algebra of the corresponding tensor expression. Such approach permits us to
simplify the tensor expressions possessing symmetry properties, summation
(dummy) indices and multiterm identities by unify manner. The canonical element
for the tensor expression is defined in terms of the basic vectors of this
linear space. The main restriction of the algorithm is the dimension of the
linear space that is equal to N!, where N is a number of indices of the tensor
expression. The program uses REDUCE as user interface.
