Covariant and contravariant indices

The covariant (lower) and contravariant (upper) indices are distinguished simply by a minus sign in the case of indices of any type:

All the information about indexed objects are crammed into the operator notation and the indices from the arguments. For example $Aij$ is distinguished from other objects by

• its identifier:
• the number of its indices:
• the position of its indices: _{\>\> j}, A_i^{\>\> j}, A_ij
• the type of its indices:

The components of a tensor or symbol are regarded as different objects and there is no possibility to store the elements in an array like

$Aij=(Ai,\; Bi,\; Ci,\; Di).$

All the elements or subtensors can only be given as independent objects:

$Ai0=Ai,Ai1=Bi,Ai2=Ci,Ai3=Di.$

(The primary goal in developing the system was to solve the manipulation of the abstract indices - storing in arrays can be achieved by improving the program.)