The commutant of a magma is the set of its members that commute with every member of the magma.

The Commutant command returns the commutant of the magma m as a set.

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

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

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

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

$\left\{1\,2\,3\right\}$

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

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

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

$\left\{1\,4\right\}$

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

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

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

$\left\{1\,3\,4\right\}$

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

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