Notations and notes

Package-wise notations

• g,h::{Matrix,[Matrix,Vector]} group element, g*h is group multiplication, gi is inverse.
• p::Vector point of a linear space where the group acts, g*p is group action.
• nd=Dim2(g)[1]=Dim2(p) matrix size or spatial dimension.
• nt::nonnegint number of translation vectors.
• T::{Matrix,[Matrix,Vector],Vector} transformation defined as g'=Ti*g*T and p'=Ti*p and M'=M.T.
• SG,PG,RG,LG::string symmetry/space, point, rod, layer group name.
• G,H::list(g) group.
• S::list(g) any set of elements.
• preS::list(g) repeating elements are allowed.

Notes

• See sections Conventions and Frequently used code in FiniteGroups.mw.
• Currently implemented is matrix algebra only, other algebras can be added by expanding FG_GroupAlgebra command.
• In many package commands it is assumed that G[1] is the unit element.