The HasZero command returns true if the given magma has a zero element; that is, an element z such that z*x = x*z = z, for all x in m. It returns false otherwise.

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

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

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

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

$\mathrm{false}$

$m≔⟨⟨⟨1\|1\|1⟩\,⟨1\|1\|1⟩\,⟨2\|1\|1⟩⟩⟩$

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

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

$\mathrm{true}$

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

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