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Magma

 IsKei
 test whether a magma is a kei (involutary quandle)

 Calling Sequence IsKei( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The IsKei command returns true if the given magma is a kei. It returns false otherwise.
 • A kei, also called an involutary quandle, is a quandle that satisfies the right involutary law (XY)Y = X.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $m≔⟨⟨⟨1,3,2⟩|⟨3,2,1⟩|⟨2,1,3⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {3}& {2}\\ {3}& {2}& {1}\\ {2}& {1}& {3}\end{array}\right]$ (1)
 > $\mathrm{IsKei}\left(m\right)$
 ${\mathrm{true}}$ (2)
 > $m≔⟨⟨⟨1,2,3⟩|⟨2,3,3⟩|⟨3,1,2⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {2}& {3}\\ {2}& {3}& {1}\\ {3}& {3}& {2}\end{array}\right]$ (3)
 > $\mathrm{IsKei}\left(m\right)$
 ${\mathrm{false}}$ (4)

Compatibility

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