Tables for
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

International Tables for Crystallography (2011). Vol. A1, ch. 1.3, p. 25   | 1 | 2 |

Section 1.3.1. Introduction

Franz Gählera*

aFakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Correspondence e-mail:

1.3.1. Introduction

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Most of the data in Part 2[link] of this volume have been checked by a computer-algebra program. This program is built upon the package Cryst (Eick et al., 2001[link]), formerly known as CrystGAP (Eick et al., 1997[link]), which in turn is an extension of the computer-algebra program GAPGAP (computer algebra program) (The GAP Group, 2002[link]). GAP is a program system for computations involving general algebraic structures, in particular groups. Since space groups are infinite groups, the generic algorithms for finite groups often cannot be used for space groups. The Cryst package provides the special methods and algorithms needed for working with space groups, thereby extending the field of applicability of GAP. The algorithms used in Cryst have been described by Eick et al. (1997[link]).


Eick, B., Gähler, F. & Nickel, W. (1997). Computing maximal subgroups and Wyckoff positions of space groups. Acta Cryst. A53, 467–474.
Eick, B., Gähler, F. & Nickel, W. (2001). The `Cryst' Package. Version 4.1. .
The GAP Group (2002). GAP – Groups, Algorithms and Programming. Version 4.3. .

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