IsRightInvolutary - Maple Help

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Magma

 IsRightInvolutary
 test whether a finite magma is right involutary

 Calling Sequence IsRightInvolutary( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A magma is right involutary if it satisfies the law (XY)Y = X.
 • The IsRightInvolutary command returns true if the given magma is right involutary.  It returns false otherwise.

Examples

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

Compatibility

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