Quaternion operations

GTQAbs — gives the absolute value of the quaternion.

GTConjugate — gives the conjugate element of the quaternion.

GTQInverse — gives the inverse element of the quaternion.

GTQMultiplication — multiplication of quaternions.

GTQPolar — gives the polar angle of the quaternion.

Logical operations

GTEulerAngelsQ — tests if input is a list with Euler angles.

GTQuaternionQ — tests if input is a quaternion.

GTSymbolQ — tests if input is a symbol.

Graphical representation of point group relationships

GTGroupConnection — illustrates the connection of several group, given in a list of groups.

GTGroupHierarchy — gives a graph containing all subgroups of a certain group as well as all group a certain group is a subgroup of.

GTPointGroups — plots a graph according to the subgroup relationships of the 32 point groups.

GTCayleyGraph — Cayley graph of a point group.

Spherical Harmonics

GTCartesianSphericalHarmonicY — gives the spherical harmonics in Cartesian coordinates.

GTCartesianTesseralHarmonicY — gives the tesseral harmonic in Cartesian form.

GTGauntCoefficient — calculates the integral over three spherical harmonics.

GTTesseralHarmonicY — gives the tesseral harmonic (real spherical harmonic).

Input and Output operations

GTExtractDatasets — extracts various sample data used in the documentation.

GTFermiSurfaceXSF — calculates the Fermi surface and writes it to a file readable by XCrySDen.

GTReadFromFile — reads an object from file.

GTWriteToFile — writes object to file.

GTSetMessage — messages to Notebook or Message window.

Handling of cluster data

GTClusterFilter — removes certain types of atoms from a given cluster.

GTCompactStore — allows to store sparse matrices in a compact form.

GTNeighborPlot — gives the information about the input of GTAdjacencyMatrix

Special matrices

GTDiracMatrix — gives the Dirac matrix.

GTSU2Matrix — gives the SU(2) matrix for a rotation around a vector.

GTReorderMatrix — gives a matrix to reorder a matrix.

Presentation of other data

GTBlueRed — defines a ColorFunction based on the MBP color code.

GTSetTableColors — used to change the color scheme of the tables.

GTCharacterTableP — pretty print of a character table given in list form.

GTGetIrepMatrix — prints a selection of representation matrices.

Other functions

GTAllSymbols — lists all implemented symbols.