DEFINITION, MATHEMATICAL EXAMPLES AND QUANTUM-CHEMICAL APPLICATIONS OF NESTED SUMMATION SYMBOLS AND LOGICAL KRONECKER DELTAS

Two mathematical symbols are introduced and their applications to computational chemistry and to artificial intelligence are described. The first symbol is called a nested summation symbol (NSS). After a discussion of its properties, we insist on the significance of this symbol in developing sequential and parallel computational algorithms. Another group of symbols, related to logical expressions, are defined under the name logical Kronecker deltas (LKDs). Application examples of the NSS and LKD technique to several computational quantum chemistry topics are given. It is shown how some standard formulae become shorter and easier to write, generalize, program and evaluate. It is emphasized that both symbols constitute a powerful link between mathematical formalism and programming in high level languages.