A submagma of a magma is a subset that is closed under the specified binary operation.  Note that the empty set is vacuously a submagma of any magma.  Also, every magma is a submagma of itself.

The IsSubMagma( ss, m ) command returns true if the set ss is a submagma of the magma m, and returns false otherwise.

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

$m≔⟨⟨⟨3\left|5\right|3\left|4\right|3⟩\,⟨2\left|5\right|2\left|3\right|3⟩\,⟨4\left|3\right|1\left|4\right|2⟩\,⟨3\left|2\right|1\left|1\right|1⟩\,⟨5\left|2\right|4\left|5\right|4⟩⟩⟩$

$m≔\left[\begin{array}{ccccc}3& 5& 3& 4& 3\\ 2& 5& 2& 3& 3\\ 4& 3& 1& 4& 2\\ 3& 2& 1& 1& 1\\ 5& 2& 4& 5& 4\end{array}\right]$

$\mathrm{IsSubMagma}\left(\left\{1\,3\,4\right\}\,m\right)$

$\mathrm{true}$

$\mathrm{IsSubMagma}\left(\left\{1\,2\,3\right\}\,m\right)$

$\mathrm{false}$

$\mathrm{IsSubMagma}\left(\left\{1\,2\,3\,4\,5\right\}\,m\right)$

$\mathrm{true}$

$\mathrm{IsSubMagma}\left(\varnothing \,m\right)$

$\mathrm{true}$

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

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