Basic

Classes

GTClasses — gives the conjugacy classes of a group.

GTClassMult — calculates the class constants.

GTClassMultTable — calculates a table of class constants.

Characterization of groups and elements

GTCenter — determines the center of a group.

GTConjugacyClass — constructs the set of all subgroups conjugated to the subgroup of group.

GTConjugateElement — gives the conjugate element.

GTGenerators — gives the generators of a group.

GTGetInvSubGroup— gives an invariant subgroup of a specified order

GTGetSubGroups — finds subgroups of a group.

GTGroupOrder — gives the order of a group.

GTInverseElement — gives the inverse element.

GTInvSubGroups — gives the invariant subgroups of a group.

GTLeftCosets — gives the left coset of a group according to a subgroup.

GTMultTable — gives the multiplication table for a group.

GTNormalizer — constructs the normalizer of group with respect to its supergroup.

GTOrderOfElement — gives the order of a group element.

GTProductGroup — forms the product of two groups.

GTQuotientGroup — gives the multiplication table of the quotient group.

GTRightCosets — gives the right coset of a group according to a subgroup.

Logical operators

GTAbelianQ — tests if a group is an abelian group.

GTCyclicQ — tests if group is a cyclic group.

GTGroupQ — tests if a group of symmetry elements satisfies the "group axioms".

GTInvSubGroupQ — tests if the group with smaller order is an invariant subgroup of the group with larger order.

GTProductGroupQ — tests if group is a product group of two groups.

GTQuotientGroupQ — tests if two groups can form a quotient group.

GTSelfAdjointQ — tests if an element of a group is self-adjoint

GTSubGroupQ — tests if the group with smaller order is a subgroup of the group with larger order.

Symbols, matrices, quaternions and Euler angles

GTAllSymbols — gives a list of all implemented symbols.

GTGetEulerAngles — gives the Euler angles of a symmetry element.

GTGetMatrix — gives a representation matrix of a certain symmetry element.

GTGetQuaternion — gives the quaternion of a certain symmetry element.

GTGetRotationMatrix — gives the 3-dimensional rotation matrix of a certain symmetry element.

GTGetSU2Matrix — gives the SU(2) matrix of a certain symmetry element.

GTGetSymbol — gives the symbol of a certain symmetry element.

GTgmat — performs a group multiplication of two elements.

GTSetMultiplication — multiplications of sets of symmetry elements.

GTType — transforms a point group element to a space group element.

GTWhichInput — determines the type of an element.

GTWhichOutput — transforms an element to a certain type.

Coordinate transformation

GTTransformation — performs a coordinate transformation of a vector.

GTTransformationOperator — applies a coordinate transformation to a function.

Magnetic groups    

GTMagnetic — determines if magnetic point group are taken into account

GTMagneticQ — gives True if if magnetic groups are taken into account