Description of FiniteGroups package

by Andriy Zhugayevych

FiniteGroups is a package for manipulating discrete groups whose elements are represented as affine transformations.

If you have comments, suggestions, or have found a bug, please email me.

Tested for Maple 17 on Windows 7 and 10.

Highlighted features

• Support of custom group algebras. Predefined are matrices and affine transformations.
• Support of symbolic lattice coordinates.
• Large list of predefined groups: space, layer, rod, point (also 5- and 8-fold axes), in different settings.
• Representations of point groups.
• Sites and dimers: black-box construction of a tight-binding Hamiltonian.

Installation

• Download source files FiniteGroups.zip, unzip to any location, open install.mw and follow the instructions.
• Windows users: If failed to install or you don't need the source, download FiniteGroups_lib.zip and unzip to Maple library folder MapleXX/lib.
• Experienced users: the package can be initialized by reading FiniteGroups.ini with Maple "read" command.
• The documentation is built into the Maple Help system. Individual help pages are also available as individual mw-files.

Credits

• Bilbao Crystallographic Server – group tables
• Artem Naumov – rod groups

Requires implementation

• Symmetry groups in all ITA settings.
• Support of nonscalar objects such as multiple degenerate orbitals per site.