CARAT Introduction / Programs / Bravais_catalog

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## Program Bravais_catalog

### Usage

    Bravais_catalog [file]

file: (OPTIONAL) contains a set of commands for Bravais_catalog, which are otherwise asked from stdin.

### 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 and Symbol.

Bravais_catalog is a synonym for Datei!

### 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.

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