The procedure Operations returns a module exporting procedures that implement the group operations for the elements of g. The module is in the same format that Group accepts for specifying the operations on a custom group:

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

$\mathrm{gens1}≔\left[\mathrm{Perm}\left(\left[\left[1\,2\right]\,\left[3\,4\,5\right]\right]\right)\,\mathrm{Perm}\left(\left[\left[1\,2\,3\right]\,\left[4\,5\right]\right]\right)\right]$

$\mathrm{gens1}≔\left[\left(1\,2\right)\left(3\,4\,5\right)\,\left(1\,2\,3\right)\left(4\,5\right)\right]$

$\mathrm{g1}≔\mathrm{PermutationGroup}\left(\mathrm{gens1}\right)$

$\mathrm{g1}≔⟨\left(1\,2\right)\left(3\,4\,5\right)\,\left(1\,2\,3\right)\left(4\,5\right)⟩$

$\mathrm{ops1}≔\mathrm{Operations}\left(\mathrm{g1}\right)$

$\mathrm{ops1}≔\mathbf{module}\left(\right)\mathbf{local}\mathrm{ModuleApply}\&comma;\mathrm{ModuleLoad}\&semi;\mathbf{export}\mathrm{`.`}\&comma;\mathrm{`/`}\&comma;\mathrm{`=`}\&comma;\mathrm{`<`}\&comma;\mathrm{print}\&comma;1\&semi;\mathbf{end\; module}$

$\mathrm{ops1}:-\mathrm{`.`}\left(\mathrm{gens1}\left[1\right]\&comma;\mathrm{gens1}\left[2\right]\right)$

$\left(1\&comma;3\&comma;5\right)$

$\mathrm{ops1}:-\mathrm{`/`}\left(\mathrm{gens1}\left[1\right]\right)$

$\left(1\&comma;2\right)\left(3\&comma;5\&comma;4\right)$

$\mathrm{ops1}:-\mathrm{`.`}\left(\mathrm{gens1}\left[1\right]\&comma;\mathrm{ops1}:-\mathrm{`/`}\left(\mathrm{gens1}\left[1\right]\right)\right)$

$\mathrm{ops1}:-\mathrm{`=`}\left(\mathrm{ops1}:-\mathrm{`1`}\&comma;\right)$

$\left(\right)=\left(\right)$

$\mathrm{evalb}\left(\right)$

$\mathrm{true}$

The GroupTheory[Operations] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.