The IsKei command returns true if the given magma is a kei. It returns false otherwise.

A kei, also called an involutary quandle, is a quandle that satisfies the right involutary law (XY)Y = X.

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

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

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

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

$\mathrm{true}$

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

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

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

$\mathrm{false}$

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

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