IsomorphicCopy - Maple Help

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Magma

 IsomorphicCopy
 produce an isomorphic copy of a magma

 Calling Sequence IsomorphicCopy( src, p )

Parameters

 src - Array; source magma whose Cayley table is to be moved p - permlist; permutation of 1..n to effect the isomorphic copy

Description

 • The IsomorphicCopy( 'src', 'p' ) command uses the permutation p to produce an isomorphic copy of the source magma src, in such a way that the permutation p is then an isomorphism from src to the isomorphic copy. The isomorphic copy is returned.
 • The operation of this command is effected by calling TransportStructure.
 • If you want to generate a number of isomorphic copies of a magma (or several magmas), you can use the TransportStructure command instead, which allows you to re-use an Array which you pass to the command.
 • If the permutation p is not supplied, then a randomly generated permutation is used.

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)
 > $p≔\left[2,1,3\right]$
 ${p}{≔}\left[{2}{,}{1}{,}{3}\right]$ (2)
 > $\mathrm{m2}≔\mathrm{IsomorphicCopy}\left(m,p\right)$
 ${\mathrm{m2}}{≔}\left[\begin{array}{ccc}{3}& {1}& {2}\\ {1}& {2}& {3}\\ {2}& {3}& {1}\end{array}\right]$ (3)
 > $\mathrm{AreIsomorphic}\left(m,\mathrm{m2}\right)$
 ${\mathrm{true}}$ (4)

Compatibility

 • The Magma[IsomorphicCopy] command was introduced in Maple 16.