Example 8

Used Programs

Solution

1. Prepare the following file 'f' containing a basis of the space of invariant forms of the Bravais group B of all permutation matrices and their negatives.

         #2
         6 d0
         1
         6x0
         1
         1 1
         1 1 1
         1 1 1 1
         1 1 1 1 1
         1 1 1 1 1 1
         

2. Call

            Aut_grp f > gf
         

   to get all the relevant data of the Bravais group B on file 'gf'.
3. Call

            Bravais_inclusions gf > gfi
         

   to get all the Bravais subgroups of B on the file 'gfi', more precisely a list of the representatives of their conjugacy classes under the normalizer of B in GL_n(Z), which is B itself.
   (Note, the above command only lists names. If one wants the actual groups, one has to call "Bravais_inclusions" with the option -G . This takes much longer.)
4. Call

            grep Symbol gfi | wc
         

   to count 27 subgroups.