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Magma

 IsLoop
 test whether a finite magma is a loop

 Calling Sequence IsLoop( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A loop is a quasigroup with an identity element.
 • The IsLoop command returns true if the given magma is a loop, and returns false otherwise.

Examples

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

Compatibility

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