| Previous Example | Introduction | Next Example | 
| A. | 7 0 1 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 7 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 | B. | 6 /2 -1 1 0 0 -1 -2 -3 1 2 0 -1 -2 3 1 0 0 1 -4 3 -1 2 0 1 -2 0 0 2 -2 2 0 0 0 0 0 0 2 6 /2 -2 0 0 0 -1 -1 -4 0 2 0 -1 -1 2 -2 0 2 -1 -1 2 -2 2 0 1 -1 2 0 2 0 0 0 0 0 0 0 0 2 | 
#g2or
#2as top row.
Extract group > linear_partto write the linear part of the affine group, whose generators are in the file 'group', to the file 'linear_part' in bravais_TYP as format. At the same time invariant forms are calculated.
Is_finite linear_partto find that the potential point group has finite order, 12 in this case. The output is
The order of the group is: 12
Presentation linear_part > presto get a presentation of the group in file 'linear_part' and to write this to the file 'pres' in matrix_TYP as format.
Standard_affine_form group presto find that the rank of the translation lattice of the affine group in 'g' is not full, i. e. 6, but only 3. Hence one has a subperiodic group and not a space group. The output is
The rank of the translation lattice is 3
#g2or
#2as top row.
Extract group > linear_partto write the linear part of the affine group, whose generators are in the file 'group', to the file 'linear_part' in bravais_TYP as format. At the same time invariant forms are calculated.
Order linear_partto find that the potential point group has finite order, 720 in this case (Here we use "Order" in contrast to part A. because "Is_finite" only works for integral matrices). The output is
The order of the group is 720
Presentation linear_part > presto get a presentation of the group in file 'linear_part' and to write this to the file 'pres' in matrix_TYP as format.
Standard_affine_form group pres > Sto get the space group in standard form in file 'S'. So the given matrices really generate a space group.
Name -o Sto get the CARAT name and the CARAT representative for this affine class:
   #g2 % standard group for S
   6       /2              % generator
     0 2  0 0 -2 -2
     0 0  2 0  0  0
     2 0  0 0  2 -1
    -2 2 -2 0 -2  0
     0 0  2 2  2  0
     0 0  0 0  0  2
   6       /2              % generator
    -2  0  0  0 -2 -1
     0  0  2  0  0  0
     2 -2  0 -2  0  0
    -2  2 -2  0 -2  0
     2  0  2  0  0  0
     0  0  0  0  0  2
   % order of the group unknown
   qname: group.1040 zname: 3 1 aff_name: 1
   
| Previous Example | Introduction | Next Example |