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Program Extract

Usage

Extract 'file1' ['file2'] [-c] [-p] [-f] [-r [-D]] [-t=n]
file1: bravais_TYP containing a space or (in case of option -r) a point group.
file2: matrix_TYP only used with options -r and -t.

Description

Extracts the linear part of the affine (space) group in file1. Note this is the point group of the space group in case the space group is given in standard form.

Options

-p    : extracts the linear part (default).
-c    : extracts the translational part as a vector system (1-cozycle).
-f    : do not calculate the formspace of the point group.
-r    : reverses the process: Reads in the generators of the point group
        of file1 and multiple vector systems for these generators from file2
        and outputs the resulting space groups. Overwrites any other option.
-D    : this option only works together with '-r'. The spacegroups are written
        to 'file.i' with i = 1, ...
-t=n  : transform the space group with generators in  file1 into standard
        form, ie. the translation lattice is transformed to Z^n. If a
        parameter n>0 is specified, the transforming matrix will be
        given as well.  NOTE: For the -t-option file2 must contain a
        presentation for the point group.  If the translation lattice
        is of smaller rank, it will give the rank. Synonymous command:
        Standard_affine_form
-T    : RESERVED

Remarks

See also for Extensions and Vector_systems. A synonym for Extract -t is Standard_affine_form.

Examples

  1. Find all space groups with a given point group and decide for which superlattices each extension splits.
  2. Do given matrices generate a space group? If so, find its name and normal representation.
  3. Find all Z-classes, affine classes and torsion free space groups in a given Q-class.

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