CARAT Introduction / Programs / Normalizer

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## Program Normalizer

### Usage

    Normalizer 'file1' ['file2' ['file3']] [-p=prime] [-o]

file1: bravais_TYP containing the group G.
file2: (OPTIONAL) bravais_TYP containing the transposed of G. (cf. Tr_bravais)
file3: (OPTIONAL) matrix_TYP of a G-perfect form. (cf. First_perfect)

### Description

Calculates a set of matrices which together with G generate the normalizer NGLn(Z)(G) of G in GLn(Z).
NOTE: the output echoes any input information about G, except input about generators of the normalizer.
NOTE: The dimension of the space of invariant forms is a measure for the complexity of the algorithm. Up to degree 6 the only infeasible case are <I6> and <-I6>. Here the generators of the normalizer can be taken from Bravais_catalog.html/Datei with family 1,1,1,1,1,1.

### Options

    -b      :  The normalizer of the bravais group B(G) is calculated. With this
               option the program is much faster. (The normalizer of G is a
               subgroup of N_GL_n(Z) (B(G)). )
    -p=prime:  The determinants of the perfect forms are
               calculated module prime. The default is 1949.
    -o      :  The G-perfect forms are given as additional output.

### Remarks

See also for Bravais_catalog.html/Datei, First_perfect and Tr_bravais.

### Examples

1. Find all space groups with a given point group and decide for which superlattices each extension splits.
2. Is the normalizer of a given group finite?

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