The SubMagmaCayleyTable( s, m ) command returns a Cayley table for the submagma s of the magma represented by the Cayley table m.  The elements of s are renumbered to fall within the range 1..k, where k is the number of elements of s.

If the subset s of {1,2,...,n} is not a submagma of m, then an exception is raised.

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

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

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

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

$\mathrm{true}$

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

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

The Magma[SubMagmaCayleyTable] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.