Definitions of the tensor functions

For all possible values of their arguments, the discrete delta functions and , Kronecker delta functions and , and signature (Levi–Civita symbol) are defined by the formulas:

In other words, the Kronecker delta function is equal to 1 if all its arguments are equal.

In the case of one variable, the discrete delta function coincides with the Kronecker delta function . In the case of several variables, the discrete delta function coincides with Kronecker delta function :

where is the number of permutations needed to go from the sorted version of to .