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Program Orbit

Usage

Orbit 'file1' 'file2' [-i] [-r] [-l] [-k] [-t] [-L=n] [-S=n] [-p] [-u] [-g] [-R]
file1: matrix_TYP, contains a matrix X whose orbit is to be calculated
file2: bravais_TYP, contains generators of a group G

Description

Calulates the orbit of the matrix X in file1 under the group G in file2, where the action is specified by the options. Default option is action by left multiplication.

Options

-i     : Use the generators given in file2 and their
         inverses to calculate the orbit.
-r     : Operate from the right.
-l     : Operate from the left (default).
-k     : Operate via conjugation, ie.  x -> g x g^-1
-L=n   : Calculate at most n elements of the orbit.
         0 means infinity.
-S=n   : If given as -S or -S=0 a generating set for
         the stabilizer is calculated. If given as
         -S=n at most n matrices of the stabilizer
         are calculated.
         S=-1 means ONLY the stabilizer is calculated.
-p     : Operate on pairs of the form {M,-M}.
-u     : Operate on the set of rows of the matrix given
         in file1.
-f     : Operates on quadratic forms via x -> g^-tr x g^-1
-g     : Operate on sublattices of Z^n spanned by the columns
         (rows) of the matrices gX (Xg) with g in G. Brakets
         apply if given with the -r option.
-R     : Give representatives of the G-orbits at the end of
         the output.

Remarks

WARNING: If the orbit is infinite use option -L!

See also for Is_finite and Order.

Examples

  1. Find the stabilizer of a sublattice in the Bravais group of the unit form F=I6.

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