Program Datei

Usage

Datei [file]

Description

Accesses the catalog of bravais groups up to dimension 6.

The first input for the catalog is the family symbol, whose grammar is described in detail in the CARAT manual. It is build up from atomic symbols which are seperated by `,' or `;' to indicate diagonals and direct products. We just state the two important rules here:

 LIST OF 'ATOMS':
 dim1: 1
 dim2: 2-1  2-1'  2-2  2-2'
 dim3: 3
 dim4: 4-1  4-1'  4-2  4-2'  4-3  4-3'
 dim5: 5-1  5-2
 dim6: 6-1  6-2  6-2'  6-3  6-3'  6-4  6-4'

Meaning of `,':                        (X 0 0)
 A,A,A stands for groups of the form   (0 X 0) with X in A
                                       (0 0 X)
Meaning of `;':
 A;B stands for groups of the form (X 0)
                                   (0 Y) with X in A and Y in B.
NOTE: The primed atoms 2-1' and 2-2' only occur in multiples, seperated by `,'.
Examples: 2-1,2-1;2-1     (degree 6)
          1;1;1           (degree 3)
          3,3             (degree 6)
          4-1;1           (degree 5)

Remarks

See also for Bravais_type/Symbol.

Datei is a synonym for Bravais_catalog!

Examples

1. List all names of Bravais groups of degree 4.
2. How do the Z-classes in the Q-class of a given group distribute into their Bravais flocks?
3. Determine the maximal finite subgroups of GL₅(Z)
4. Find the dual pairs of Bravais groups in family 1;1;1;1
5. Find the stabilizer of a sublattice in the Bravais group of the unit form F=I₆.