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.

$\mathrm{with}\left(\mathrm{group}\right)\:$

$\mathrm{pg}≔\mathrm{permgroup}\left(8\,\left\{\left[\left[1\,2\right]\right]\,\left[\left[1\,2\,5\,6\,7\,8\right]\right]\right\}\right)\:$

$\mathrm{s1}≔\left\{\left[\left[1\,2\right]\right]\,\left[\left[5\,1\,8\right]\right]\right\}\:$

$\mathrm{orbit}\left(\mathrm{pg}\,1\right)$

$\left\{1\,2\,5\,6\,7\,8\right\}$

$\mathrm{orbit}\left(\mathrm{pg}\,5\right)$

$\left\{1\,2\,5\,6\,7\,8\right\}$

$\mathrm{orbit}\left(\mathrm{s1}\,1\right)$

$\left\{1\,2\,5\,8\right\}$