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Magma

 IsIdentity
 test whether an element of a magma is a (two-sided) identity

 Calling Sequence IsIdentity( m, id )

Parameters

 m - Array; magma represented by its Cayley table id - posint; candidate identity element

Description

 • The IsIdentity command determines whether an element id of a magma m is an identity for m.  It returns true if id is an identity of m, and returns false otherwise.  The element id is an identity of m if id * x = x = x * id, for all x in m.

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)
 > $\mathrm{IsIdentity}\left(m,1\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{IsIdentity}\left(m,2\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{IsIdentity}\left(m,3\right)$
 ${\mathrm{false}}$ (4)

Compatibility

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