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Magma

 IsRightDistributive
 test whether a finite magma is right distributive

 Calling Sequence IsRightDistributive( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A magma is right distributive if it satisfies the right distributive law (XY)Z = (XZ)(YZ).
 • The IsRightDistributive command returns true if the given magma is right distributive. It returns false otherwise.

Examples

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

Compatibility

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