test whether a magma is a band - Maple Help

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Magma[IsBand] - test whether a magma is a band

 Calling Sequence IsBand( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A band is an idempotent semigroup, that is, an associative magma in which the identity XX = X is satisfied.
 • The IsBand command returns true if the given magma is a band. It returns false otherwise.

Examples

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