Indices

The indexed objects (tensors, symbols) are denoted as operators and the indices are written in the arguments in the case of non-scalar indexed objects:

A $A$ 0-indexed object (scalar)

A(I) $Ai$ 1-indexed object

A(I,J) $Aij$ 2-indexed object

... ... ...

Arbitrary integers (inclusive of zero) and identifiers may be used as indices. The reserved identifiers T (boolean variable) and I (imaginary unit) of REDUCE can be used as indices, in this case they lose their original meaning in the arguments of the indexed objects.

The indices are divided into two groups:

• concrete indices (e.g. integer indices and identifier indices undeclared as abstract indices).
• abstract indices (e.g. identifiers declared as abstract indices)

Concrete indices denote the elements of a given indexed object. Abstract indices are applied in tensorial relations or in component equations referring to the components in the given slot of the object. If they play the rôle of dummy indices then they can be arbitrarily renamed to other abstract indices.

Abstract indices can be introduced by the command INDEX

It may occur that calculating certain expressions there are not enough predefined abstract index identifiers introduced by the user to use them as dummy indices. In such cases the program declares new ones by the letter I and by a serial number, e.g. I0, I1, I2, ... Therefore these identifiers should be avoided as concrete indices in the expressions because it could lead to wrong results.

Identifiers as abstract indices can be removed by the command CLEAR INDEX

All the properties of the identifiers remain unchanged but from now on the system treats them in the arguments of indexed objects as concrete indices.