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Magma

 AreIsomorphic
 test isomorphism of magmas

 Calling Sequence AreIsomorphic( m1, m2 )

Parameters

 m1 - Array; Cayley table of a magma m2 - Array; Cayley table of a magma

Description

 • The AreIsomorphic( 'm1', 'm2' ) command returns true if the magmas m1 and m2 are isomorphic, and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $\mathrm{m1}≔⟨⟨⟨1|2|3⟩,⟨2|3|1⟩,⟨3|1|2⟩⟩⟩$
 ${\mathrm{m1}}{≔}\left[\begin{array}{ccc}{1}& {2}& {3}\\ {2}& {3}& {1}\\ {3}& {1}& {2}\end{array}\right]$ (1)
 > $\mathrm{m2}≔⟨⟨⟨2|3|1⟩,⟨3|1|2⟩,⟨1|2|3⟩⟩⟩$
 ${\mathrm{m2}}{≔}\left[\begin{array}{ccc}{2}& {3}& {1}\\ {3}& {1}& {2}\\ {1}& {2}& {3}\end{array}\right]$ (2)
 > $\mathrm{AreIsomorphic}\left(\mathrm{m1},\mathrm{m2}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{m3}≔⟨⟨⟨1|2|1⟩,⟨2|3|2⟩,⟨3|1|3⟩⟩⟩$
 ${\mathrm{m3}}{≔}\left[\begin{array}{ccc}{1}& {2}& {1}\\ {2}& {3}& {2}\\ {3}& {1}& {3}\end{array}\right]$ (4)
 > $\mathrm{AreIsomorphic}\left(\mathrm{m1},\mathrm{m3}\right)$
 ${\mathrm{false}}$ (5)

Compatibility

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