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Microcomputer‐aided instruction and research in group theory
Author(s) -
Trindle Carl
Publication year - 1984
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540050206
Subject(s) - schematic , group (periodic table) , permutation (music) , generator (circuit theory) , computer science , algebra over a field , permutation group , character (mathematics) , group theory , arithmetic , theoretical computer science , mathematics , pure mathematics , geometry , engineering , chemistry , physics , power (physics) , organic chemistry , quantum mechanics , electronic engineering , acoustics
A collection of programs which aid in the use of group theory has been developed for the Apple II. The programs automate much of the tedious algebra necessary to generate character tables and representation matrices from the properties of the operators chosen to generate the group. At the same time, the presentation of intermediate results provides a schematic guide to the procedures by which groups are constructed. The choice of generators is not limited to the reflections, rotations, and inversions, which are the familiar features of chemical group theory. Any generator representable as a permutation may be treated; thus general permutation groups and Longuet‐Higgins groups may be studied. As an illustration we describe the states of beryllium borohydride, which require a form of Longuet‐Higgins group theory.