The center of a magma is the set of its members that both commute and associate with every member of the magma. Alternatively, it is the intersection of the nucleus and the commutant.

The Center command returns the center of the magma m as a set.  The spelling Centre is also supported as a synonym.

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

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

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

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

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

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

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

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

$\left\{1\right\}$

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

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

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

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

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

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