The nucleus of a magma is the set of its members that associate with every member of the magma. That is, an element x is in the nucleus if all of the equations (xy)z = x(yz), (yx)z = y(xz) and (yz)x = y(zx) are satisfied, for all y and z from the magma.

The Nucleus command returns the nucleus of the magma m as a set.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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