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Magma

 IsAssociative
 test whether a given magma is associative
 IsSemigroup
 test whether a given magma is a semigroup

 Calling Sequence IsAssociative( m ) IsSemigroup( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The IsAssociative command returns true if the given magma satisfies the associativity identity (XY)Z = X(YZ).  It returns false otherwise.
 • The IsSemigroup command is an alias for IsAssociative. A semigroup is an associative magma.

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)
 > $\mathrm{IsAssociative}\left(m\right)$
 ${\mathrm{true}}$ (2)
 > $m≔⟨⟨⟨1|2|3⟩,⟨2|3|3⟩,⟨3|1|2⟩⟩⟩$
 ${m}{:=}\left[\begin{array}{rrr}{1}& {2}& {3}\\ {2}& {3}& {3}\\ {3}& {1}& {2}\end{array}\right]$ (3)
 > $\mathrm{IsSemigroup}\left(m\right)$
 ${\mathrm{false}}$ (4)

Compatibility

 • The Magma[IsAssociative] and Magma[IsSemigroup] commands were introduced in Maple 15.