Example 1

Used Programs

Solution

1. Call

      Bravais_catalog

   and insert

      1,1,1,1

   Calculate the Bravais groups and choose the filename 1111. Print all Bravais groups now (there is only one). Screenshot

   Now 1111 contains the Bravais group <-I₄>.

   Note the normalizer N of <-I_4> in GL₄(Z) is GL₄(Z) itself.

2. Call

      Bravais_inclusions -S 1111 > b4
   

   to get all the Bravais supergroups of <-I₄>, up to conjugacy under N = GL₄(Z). The result is written on the file with name b4.