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Magma

 IsSzasz
 test whether a given magma is a Szasz magma

 Calling Sequence IsSzasz( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A Szasz magma M is one in which there is exactly one nonassociative ordered triple of members of the magma.
 • The IsSzasz command returns true if the given magma is a Szasz magma. It 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)
 > $\mathrm{IsSzasz}\left(m\right)$
 ${\mathrm{false}}$ (2)
 > $m≔⟨⟨⟨1|1|3⟩,⟨1|2|3⟩,⟨1|2|3⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {1}& {3}\\ {1}& {2}& {3}\\ {1}& {2}& {3}\end{array}\right]$ (3)
 > $\mathrm{IsSzasz}\left(m\right)$
 ${\mathrm{true}}$ (4)

Compatibility

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