The IsomorphicCopy( 'src', 'p' ) command uses the permutation p to produce an isomorphic copy of the source magma src, in such a way that the permutation p is then an isomorphism from src to the isomorphic copy. The isomorphic copy is returned.

The operation of this command is effected by calling TransportStructure.

If you want to generate a number of isomorphic copies of a magma (or several magmas), you can use the TransportStructure command instead, which allows you to re-use an Array which you pass to the command.

If the permutation p is not supplied, then a randomly generated permutation is used.

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

$m≔⟨⟨⟨1\left|2\right|3⟩\,⟨2\left|3\right|1⟩\,⟨3\left|1\right|2⟩⟩⟩$

$m≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]$

$p≔\left[2\,1\,3\right]$

$p≔\left[2\,1\,3\right]$

$\mathrm{m2}≔\mathrm{IsomorphicCopy}\left(m\,p\right)$

$\mathrm{m2}≔\left[\begin{array}{ccc}3& 1& 2\\ 1& 2& 3\\ 2& 3& 1\end{array}\right]$

$\mathrm{AreIsomorphic}\left(m\,\mathrm{m2}\right)$

$\mathrm{true}$

The Magma[IsomorphicCopy] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.