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Magma

 TransportStructure
 produce an isomorphic copy of a magma

 Calling Sequence TransportStructure( dst, src, p )

Parameters

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

Description

 • The TransportStructure( 'dst', 'src', 'p' ) command uses the permutation p to produce an isomorphic copy of the source magma src in the array dst, in such a way that the permutation p is then an isomorphism from src to dst.
 • A more convenient, but less efficient interface to this functionality is provided by the IsomorphicCopy command, which allocates storage for the resulting Cayley table automatically.

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)
 > $\mathrm{m2}≔\mathrm{TransportStructure}\left(\mathrm{Array}\left(1..3,1..3,':-\mathrm{order}'=':-\mathrm{C_order}',':-\mathrm{datatype}'=':-\mathrm{integer}'\left[4\right]\right),m,p\right)$
 ${\mathrm{m2}}{≔}\left[\begin{array}{ccc}{3}& {1}& {2}\\ {1}& {2}& {3}\\ {2}& {3}& {1}\end{array}\right]$ (3)
 > $\mathrm{AreIsomorphic}\left(m,\mathrm{m2}\right)$
 ${\mathrm{true}}$ (4)

Compatibility

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