- 
      Write the two matrices in a file 'g' and add
      
         #g2
      as top line. Now 'g' has bravais_TYP as format.
- 
      Call
      
         Normalizer g > gn
      to produce a file 'gn' containing G, a basis of the space of
      invariant quadratic forms of G, generators for the normalizer
      of G in GL4(Z), and the order of G. Note 'gn' has bravais_TYP
      as format.
- 
      Call
      
         Vector_systems gn > gout
      to write a set of representatives of the vector systems under the
      normalizer action into the file 'out'. It turs out that the order
      of the extension group is 8 and that there are 6 orbits, i. e. one
      has 6 affine classes going with the Z-class of G.
- 
      For each of the 6 cozycles write it into a file 'coz' and call
      
         Extract -r gn coz > g.i
      to construct the affine classes in the Z-class of G in standard form (i.e. the translation
      lattice is Zn):
- 
      Call
      
         Tr_bravais gn > gn_tr
      to get the transposed group 'gn_tr of 'g'.
- 
      Call
      
         Sublattices -b gn_tr > gl
      to write the matrices representing the bases of the Gtr-sublattices
      of Z4 of 2-power index into file 'gl'.
      (Note G and Gtr have order 26.) These
      sublattices are ordered by inclusion and form a chain:
         L1 = Z4 > L2 > L3 > L4 > 2 L1
       
- 
      For each inverse write it into a file 'inv' call
      
         Tr inv > l.i
      to transpose it. So we get the G-invariant superlattices of Zn:
         l.1 = Zn < l.2 < l.3
         < l.4 < 1/2 Zn
       
- 
      The following is trivial:
      
         - 
            The first extension splits for every superlattice.
         
- 
            The first extension splits and the other extensions don't split for 1/2 Zn.
         
 So we only have to consider 'g.2' to 'g.6' with the lattices 'l.2' to 'l.4'.
- 
      Enlarge the matrices in the files 'l.2', 'l.3' and 'l.4', i.e. change
      
         4       /2              % tranposed of 1-th matrix of inv
          2  0  0  1
          0 -2  0 -1
          0  0 -2 -1
          0  0  0 -1
      to
          5       /2              % tranposed of 1-th matrix of inv
           2  0  0  1 0
           0 -2  0 -1 0
           0  0 -2 -1 0
           0  0  0 -1 0
           0  0  0  0 2
      
- 
      To decide for which superlattice each extension splits, one has to add the translations of a
      superlattice 'l.j' to a spacegroup 'g.i' and transform this group such that the translation
      lattice is Zn (Cf.
      Standard_affine_form). This can be done
      in one step by calling:
      
         for i in 2 3 4 5 6 ; do
            for j in 2 3 4 ; do
               Conj_bravais -i g.i l.j > g.i.j ;
            done ;
         done
      We get the following spacegroups:
- 
      For each of these groups, extract the cozycle and the point group:
      
         for i in 2 3 4 5 6 ; do
            for j in 2 3 4 ; do
               Extract -p g.i.j > pg.i.j ;
               Extract -c g.i.j > cg.i.j ;
            done ;
         done
      We get the following files:
- 
      Call
      
         for i in 2 3 4 5 6 ; do
            for j in 2 3 4 ; do
               Vector_systems -i pg.$i.$j cg.$i.$j ;
            done ;
         done
      to identify the spacegroups in the files 'g.i.j'. The name is 0 iff the extension splits.
      We get the following output:
         Name for the 1-th extension in pg.2.2: 1
         Name for the 1-th extension in pg.2.3: 1
         Name for the 1-th extension in pg.2.4: 0
         Name for the 1-th extension in pg.3.2: 2
         Name for the 1-th extension in pg.3.3: 0
         Name for the 1-th extension in pg.3.4: 0
         Name for the 1-th extension in pg.4.2: 2
         Name for the 1-th extension in pg.4.3: 0
         Name for the 1-th extension in pg.4.4: 0
         Name for the 1-th extension in pg.5.2: 3
         Name for the 1-th extension in pg.5.3: 1
         Name for the 1-th extension in pg.5.4: 0
         Name for the 1-th extension in pg.6.2: 0
         Name for the 1-th extension in pg.6.3: 0
         Name for the 1-th extension in pg.6.4: 0