Open AccessAn algorithm for the arithmetic classification of multilattices
Author(s) -
Indelicato Giuliana
Publication year - 2013
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
eISSN - 1600-5724
pISSN - 0108-7673
DOI - 10.1107/s010876731203629x
Subject(s) - dimension (graph theory) , symmetry (geometry) , reduction (mathematics) , algorithm , monatomic gas , matrix (chemical analysis) , dimensionality reduction , software package , arithmetic , mathematics , computer science , software , artificial intelligence , pure mathematics , physics , geometry , programming language , materials science , quantum mechanics , composite material
A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular the reduction to the Smith normal form, and can be coded to provide a classification software package.