IsQuasitrivial - Maple Help

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Magma

 IsQuasitrivial
 test whether a given magma is quasitrivial

 Calling Sequence IsQuasitrivial( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A magma M is quasitrivial if x*y = x or x*y = y, for all x and y in M.
 • The IsQuasitrivial command returns true if the given magma is quasitrivial. It returns false otherwise.

Examples

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

Compatibility

 • The Magma[IsQuasitrivial] command was introduced in Maple 16.
 • For more information on Maple 16 changes, see Updates in Maple 16.