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Magma

 Commutant
 compute the commutant of a magma

 Calling Sequence Commutant( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $m≔⟨⟨⟨1|2|3⟩,⟨2|3|1⟩,⟨3|1|2⟩⟩⟩$
 ${m}{:=}\left[\begin{array}{rrr}{1}& {2}& {3}\\ {2}& {3}& {1}\\ {3}& {1}& {2}\end{array}\right]$ (1)
 > $\mathrm{Commutant}\left(m\right)$
 $\left\{{1}{,}{2}{,}{3}\right\}$ (2)
 > $m≔⟨⟨⟨1|1|1|1|1⟩,⟨1|1|1|1|1⟩,⟨1|1|1|1|1⟩,⟨1|1|1|2|4⟩,⟨1|2|2|4|5⟩⟩⟩$
 ${m}{:=}\left[\begin{array}{rrrrr}{1}& {1}& {1}& {1}& {1}\\ {1}& {1}& {1}& {1}& {1}\\ {1}& {1}& {1}& {1}& {1}\\ {1}& {1}& {1}& {2}& {4}\\ {1}& {2}& {2}& {4}& {5}\end{array}\right]$ (3)
 > $\mathrm{Commutant}\left(m\right)$
 $\left\{{1}{,}{4}\right\}$ (4)
 > $m≔⟨⟨⟨1|1|1|1|1⟩,⟨1|1|1|1|1⟩,⟨1|1|1|1|1⟩,⟨1|1|1|2|4⟩,⟨1|2|1|4|5⟩⟩⟩$
 ${m}{:=}\left[\begin{array}{rrrrr}{1}& {1}& {1}& {1}& {1}\\ {1}& {1}& {1}& {1}& {1}\\ {1}& {1}& {1}& {1}& {1}\\ {1}& {1}& {1}& {2}& {4}\\ {1}& {2}& {1}& {4}& {5}\end{array}\right]$ (5)
 > $\mathrm{Commutant}\left(m\right)$
 $\left\{{1}{,}{3}{,}{4}\right\}$ (6)

Compatibility

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