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Magma

 HasIdentity
 test whether a finite magma has a (two-sided) identity element

 Calling Sequence HasIdentity( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The HasIdentity command returns true if the given magma has a two-sided identity element. That is, an element i such that i*x = x*i = x, for all x in m.  Otherwise, it returns the value false.

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

Compatibility

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