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Magma

 HasZero
 test for the existence of a (two-sided) zero element in a finite magma

 Calling Sequence HasZero( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The HasZero command returns true if the given magma has a zero element; that is, an element z such that z*x = x*z = z, for all x in m. It returns false otherwise.

Examples

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

Compatibility

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