The AreIsomorphic( 'm1', 'm2' ) command returns true if the magmas m1 and m2 are isomorphic, and returns false otherwise.

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

$\mathrm{m1}≔⟨⟨⟨1\left|2\right|3⟩\,⟨2\left|3\right|1⟩\,⟨3\left|1\right|2⟩⟩⟩$

$\mathrm{m1}≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]$

$\mathrm{m2}≔⟨⟨⟨2\left|3\right|1⟩\,⟨3\left|1\right|2⟩\,⟨1\left|2\right|3⟩⟩⟩$

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

$\mathrm{AreIsomorphic}\left(\mathrm{m1}\,\mathrm{m2}\right)$

$\mathrm{true}$

$\mathrm{m3}≔⟨⟨⟨1\left|2\right|1⟩\,⟨2\left|3\right|2⟩\,⟨3\left|1\right|3⟩⟩⟩$

$\mathrm{m3}≔\left[\begin{array}{ccc}1& 2& 1\\ 2& 3& 2\\ 3& 1& 3\end{array}\right]$

$\mathrm{AreIsomorphic}\left(\mathrm{m1}\,\mathrm{m3}\right)$

$\mathrm{false}$

The Magma[AreIsomorphic] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.