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# 1 Introduction

The Cryst package, previously known as CrystGAP, provides functions for the computation with affine crystallographic groups, in particular space groups. For the definition of the standard crystallographic notions we refer to the International Tables Hah95, in particular the chapter by Wondratschek Won95, and to the introductory chapter in BBNWZ78. The principal algorithms used in this package are described in EGN97.

The present version for GAP 4 has been considerably reworked from an earlier version for GAP 3.4.4. Most of the porting to GAP 4 has been done by Franz Gähler. Besides affine crystallographic groups acting from the right, also affine crystallographic groups acting from the left are now fully supported. Many algorithms have been added, extended, or improved in other ways.

Our warmest thanks go the Max Neunhöffer, whose extensive testing of the GAP 4 version of Cryst in connection with XGAP uncovered several bugs and led to many performance improvements.

Cryst is implemented in the GAP 4 language, and runs on any system supporting GAP 4. However, certain commands may require that other GAP packages such as CARAT or XGAP are installed. In particular, the routines in Section Normalizers are likely to require CARAT, and the function WyckoffGraph (see WyckoffGraph) requires XGAP. Both CARAT and XGAP are available only under Unix.

The Cryst package is loaded with the command

    gap> RequirePackage( "cryst" );
    true

Cryst has been developed by

Bettina Eick
  Fachbereich Mathematik und Informatik
  Technische Universität Braunschweig
  Pockelsstr. 14, D-38106 Braunschweig, Germany
  e-mail: b.eick@tu-bs.de

Franz Gähler
  Institut für Theoretische und Angewandte Physik,
  Universität Stuttgart, D-70550 Stuttgart, Germany
  e-mail: gaehler@itap.physik.uni-stuttgart.de

Werner Nickel
  Fachbereich Mathematik, AG2, Technische Universität Darmstadt,
  Schlossgartenstraße 7, D-64289 Darmstadt, Germany
  e-mail: nickel@mathematik.tu-darmstadt.de

Please send bug reports, suggestions and other comments to any of these e-mail addresses.

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