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Magma

 IsCrossedSet
 test whether a finite magma is a crossed set

 Calling Sequence IsCrossedSet( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A crossed set is a quandle Q such that, for all x and y in Q, we have x * y = x if, and  only if, y * x = y.
 • The IsCrossedSet command returns true if the given magma is a crossed set.  It returns false otherwise.
 • Note that it is not assumed that the magma m is a quandle, so this check is applied first.

Examples

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

Compatibility

 • The Magma[IsCrossedSet] command was introduced in Maple 16.