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Evaluation of group theoretical characteristics using the symbolic manipulation language MAPLE
Author(s) -
Taneri U.,
Paldus J.
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560520816
Subject(s) - maple , symbolic computation , group (periodic table) , algebraic number , algebra over a field , polynomial , computation , gaussian , algebraic expression , pure mathematics , computer science , mathematics , physics , algorithm , quantum mechanics , botany , biology , mathematical analysis
Abstract Relying on theoretical developments exploiting quasispin and the pseudo‐orthogonal group in the Hubbard model of cyclic polyenes, the general expressions for generating polynomials, providing the dimensional information for relevant irreducible representations, were derived (M.D. Gould, J. Paldus, and J. Cízek, Int. J. Quantum Chem., in press). These generating polynomials result from q ‐dimensional formulas through rather tedious algebraic manipulations involving ratios of polynomials with fractional powers. It is shown that these expressions may be efficiently handled using the symbolic manipulation language MAPLE and the dimensional information for an arbitrary spin, isospin, and quasimomentum obtained. Exploitation of symbolic computation for other group theoretical problems that are relevant in quantum chemical calculations and their relationship with Gaussian polynomial based combinatorial approaches is also briefly addressed and various possible applications outlined. © 1994 John Wiley & Sons, Inc.