GetIsomorphism - Maple Help

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Magma

 GetIsomorphism
 return an isomorphism between isomorphic magmas

 Calling Sequence GetIsomorphism( m1, m2 )

Parameters

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

Description

 • The GetIsomorphism( 'm1', 'm2' ) command returns an isomorphism, in the form of a permutation of 1..n, where m1 and m2 are of order n, which effects an isomorphism from m1 to m2.  In case m1 and m2 are not isomorphic, then the value false is returned.

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)
 > $\mathrm{GetIsomorphism}\left(\mathrm{m1},\mathrm{m2}\right)$
 $\left[{3}{,}{1}{,}{2}\right]$ (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)
 > $\mathrm{GetIsomorphism}\left(\mathrm{m1},\mathrm{m3}\right)$
 ${\mathrm{false}}$ (5)

Compatibility

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