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Magma

 IsAlternative
 test whether a magma is alternative

 Calling Sequence IsAlternative( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The IsAlternative command returns true if the given magma satisfies the laws (X*X)*Y = X*(X*Y) and X*(Y*Y) = (X*Y)*Y. It returns false otherwise.

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)
 > $\mathrm{IsAlternative}\left(m\right)$
 ${\mathrm{true}}$ (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)
 > $\mathrm{IsAlternative}\left(m\right)$
 ${\mathrm{false}}$ (4)

Compatibility

 • The Magma[IsAlternative] command was introduced in Maple 15.
 • For more information on Maple 15 changes, see Updates in Maple 15.