README.lattice

README FOR THE SUBLATTICE DATABASE:

The following example is taken for the file 
   lattice_3_3_1
to explain the data structure involved.
Firstly concerning the filename itself:
   CARAT_DIR/tables/lattices/dim3/lattice_3_3_1
                             ^            ^
                             |            | Symbol of the group is "3", and
                             |              it's position in the catalog is
                             |              3rd almost decomposable group,
                             |              1st Zclass
                             dimension of the group


#7                    <= the group has 7 bravais Z-classes of Bravais subgroups

3 3 1                 <= Symbol of the class "3", position 3,1
1                     <= number of subgroups Z-equivalent to the group this grp
#1                    <= number of orbits of normalizer of G this groups
3	%             <= for each orbit a matrix, which conjugates the
 1 0 0                   group in the catalog to a subgroup of G in the i-th
 0 1 0                   orbit
 0 0 1
1,1,1 1 1
1 
#1 
3	% 
 1 0 0
 0 1 0
 0 0 1
1,1;1 1 2
9 
#2 
3	% 
  0 -1 -1
 -1 -1  0
  1  1  1
3	% 
 -1 -1 -1
  0 -1  0
  0  1  1
2-2;1 1 2
4 
#1 
3	% 
 0  0 -1
 1  0  0
 0 -1 -1
1;1;1 1 4
3 
#1 
3	% 
  1 0 1
 -1 0 0
  0 1 0
1;1;1 1 3
1 
#1 
3	% 
  0 -1  0
  0  0 -1
 -1  0 -1
2-1;1 1 2
3 
#1 
3	% 
  1 1  1
  0 0 -1
 -1 0 -1