The IsLeftIdentity command determines whether an element id of a magma m is a left identity for m.  It returns true if id is a left identity of m, and returns false otherwise.  The element id is a left identity of m if id * x = x, for all x in m.

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

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

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

$\mathrm{IsLeftIdentity}\left(m\,1\right)$

$\mathrm{false}$

$\mathrm{IsLeftIdentity}\left(m\,2\right)$

$\mathrm{false}$

$\mathrm{IsLeftIdentity}\left(m\,3\right)$

$\mathrm{true}$

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

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