R. Carbo et E. Besalu, DEFINITION, MATHEMATICAL EXAMPLES AND QUANTUM-CHEMICAL APPLICATIONS OF NESTED SUMMATION SYMBOLS AND LOGICAL KRONECKER DELTAS, Computers & chemistry, 18(2), 1994, pp. 117-126
Two mathematical symbols are introduced and their applications to comp
utational chemistry and to artificial intelligence are described. The
first symbol is called a nested summation symbol (NSS). After a discus
sion of its properties, we insist on the significance of this symbol i
n developing sequential and parallel computational algorithms. Another
group of symbols, related to logical expressions, are defined under t
he name logical Kronecker deltas (LKDs). Application examples of the N
SS 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 th
at both symbols constitute a powerful link between mathematical formal
ism and programming in high level languages.