Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An algorithm for the determination of space groups
HTML articles powered by AMS MathViewer

by Harold Brown PDF
Math. Comp. 23 (1969), 499-514 Request permission

Abstract:

This semiexpository paper presents in detail a numerical formulation of an algorithm for the determination of all $n$-dimensional, crystallographic space groups. The implementation of this algorithm on a digital computer is also described.
References
  • Edgar Ascher and Aloysio Janner, Algebraic aspects of crystallography. Space groups as extensions, Helv. Phys. Acta 38 (1965), 551–572. MR 199271
  • L. Bieberbach, "Über die Bewegungsgruppen der Euklidischen Räume. I," Math. Ann., v. 70, 1910, pp. 297–336.
  • Ludwig Bieberbach, Über die Bewegungsgruppen der Euklidischen Räume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich, Math. Ann. 72 (1912), no. 3, 400–412 (German). MR 1511704, DOI 10.1007/BF01456724
  • L. Bieberbach, "Über die Minkowskische Reduktion der positiven quadratischen Formen und die endlichen Gruppen linear ganzzahliger Substitutionen," Nachr. Akad. Wiss. Göttingen, 1912, pp. 207–216. H. Brown, J. Neubüser & H. Zassenhaus, "The 4-dimensional finite unimodular groups." (To appear.) M. Buerger, Elementary Crystallography, Wiley, New York, 1956.
  • H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 14, Springer-Verlag, Berlin-Göttingen-New York, 1965. MR 0174618
  • M. A. Jaswon, An introduction to mathematical crystallography, American Elsevier Publishing Co., Inc., New York, 1965. MR 0198917
  • Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
  • Hans Zassenhaus, Über einen Algorithmus zur Bestimmung der Raumgruppen, Comment. Math. Helv. 21 (1948), 117–141 (German). MR 24424, DOI 10.1007/BF02568029
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 20.60, 65.00
  • Retrieve articles in all journals with MSC: 20.60, 65.00
Additional Information
  • © Copyright 1969 American Mathematical Society
  • Journal: Math. Comp. 23 (1969), 499-514
  • MSC: Primary 20.60; Secondary 65.00
  • DOI: https://doi.org/10.1090/S0025-5718-1969-0246975-6
  • MathSciNet review: 0246975