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group(deprecated)

 orbit
 Compute the orbit of a point

 Calling Sequence orbit(pg, i)

Parameters

 pg - permutation group or a set of permutations i - point

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[Orbit] instead.
 • This function computes the orbit of i under the group action of pg. The orbit is returned as a set of points.
 • The command with(group,orbit) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[Orbit] instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $\mathrm{pg}≔\mathrm{permgroup}\left(8,\left\{\left[\left[1,2\right]\right],\left[\left[1,2,5,6,7,8\right]\right]\right\}\right):$
 > $\mathrm{s1}≔\left\{\left[\left[1,2\right]\right],\left[\left[5,1,8\right]\right]\right\}:$
 > $\mathrm{orbit}\left(\mathrm{pg},1\right)$
 $\left\{{1}{,}{2}{,}{5}{,}{6}{,}{7}{,}{8}\right\}$ (1)
 > $\mathrm{orbit}\left(\mathrm{pg},5\right)$
 $\left\{{1}{,}{2}{,}{5}{,}{6}{,}{7}{,}{8}\right\}$ (2)
 > $\mathrm{orbit}\left(\mathrm{s1},1\right)$
 $\left\{{1}{,}{2}{,}{5}{,}{8}\right\}$ (3)