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Magma

 IsLeftDistributive
 test whether a finite magma is left distributive

 Calling Sequence IsLeftDistributive( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The IsLeftDistributive command returns true if the given magma satisfies the left distributive law X(YZ) = (XY)(XZ).  It returns false otherwise.

Examples

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

Compatibility

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