A magma is simple if it has no homomorphic images other than itself and the single magma.

The function IsSimple( m ) returns true if the magma m is simple and returns false otherwise.

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

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

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

$\mathrm{IsSimple}\left(m\right)$

$\mathrm{true}$

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

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

$\mathrm{IsSimple}\left(m\right)$

$\mathrm{false}$

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

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