The IsAssociative command returns true if the given magma satisfies the associativity identity (XY)Z = X(YZ).  It returns false otherwise.

The IsSemigroup command is an alias for IsAssociative. A semigroup is an associative magma.

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

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

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

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

$\mathrm{true}$

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

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

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

$\mathrm{false}$

The Magma[IsAssociative] and Magma[IsSemigroup] commands were introduced in Maple 15.

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