Logical Kronecker delta

Let us define a generalization of the Kronecker delta symbol and call it a Logical Kronecker Delta (LKD). This symbol is written as 5(L) and corresponds to a function that can return two possible values 1 if the logieal argument L is true or 0... 

The logical Kronecker delta, which appears when integration is performed over the coordinates of the remaining n-r electrons, can be easily substituted by the equivalent logical expression ... 

The same expression can be used with the appropriate restrictions to obtain matrix elements over Slater determinants made from non-orthogonal one-electron functions. The logical Kronecker delta expression, appearing in equation (15) as defined in (16)] must he substituted by a product of overlap integrals between the involved spinorbitals. 

A logical Kronecker delta S( L]) is a symbolic factor which is unity when the logical expression L is true and zero otherwise. ... 

With all this conditioning principles in mind, the present work tries to describe in a first place the definition and properties of two fundamental symbols Logical Kronecker Deltas (LKD s) and Nested Sums. The authors hope these symbol forms turn to be as useful to the scientific community as they had been in the development of their quest of a valid computational scheme based on PC machinery, whose main features had been already explained by one of us, see for example reference [3]. 

Otherwise. The Kronecker delta symbol is a particular case of a LKD, where in the logical expression L there is involved an equivalence symbol. 

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