EVALUATION OF GROUP THEORETICAL CHARACTERISTICS USING THE SYMBOLIC MANIPULATION LANGUAGE MAPLE

Relying on theoretical developments exploiting quasispin and the pseud o-orthogonal group in the Hubbard model of cyclic polyenes, the genera l expressions for generating polynomials, providing the dimensional in formation for relevant irreducible representations, were derived (M. D . Gould, J. Paldus, and J. Cizek, Int, J. Quantum Chem., in press). Th ese generating polynomials result from g-dimensional formulas through rather tedious algebraic manipulations involving ratios of polynomials with fractional powers. It is shown that these expressions may be eff iciently handled using the symbolic manipulation language MAPLE and th e dimensional information for an arbitrary spin, isospin, and quasimom entum obtained. Exploitation of symbolic computation for other group t heoretical problems that are relevant in quantum chemical calculations and their relationship with Gaussian polynomial based combinatorial a pproaches is also briefly addressed and various possible applications outlined. (C) 1994 John Wiley and Sons, Inc.