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Magma

 IsRack
 test whether a magma is a rack

 Calling Sequence IsRack( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A rack is a right-distributive and right-invertible magma. In other words, the right action of the magma on itself by right translations is automorphic.  (Racks have, therefore, also been called automorphic sets in the literature.)
 • The IsRack command returns true if the given magma is a rack. It returns false otherwise.

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)
 > $\mathrm{IsRack}\left(m\right)$
 ${\mathrm{true}}$ (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)
 > $\mathrm{IsRack}\left(m\right)$
 ${\mathrm{false}}$ (4)

Compatibility

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