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Magma

 SubMagmaCayleyTable
 compute the Cayley table of a submagma

 Calling Sequence SubMagmaCayleyTable( s, m )

Parameters

 s - subset of {1,2,...,n} m - Array representing the Cayley table of a finite magma of order n

Description

 • The SubMagmaCayleyTable( s, m ) command returns a Cayley table for the submagma s of the magma represented by the Cayley table m.  The elements of s are renumbered to fall within the range 1..k, where k is the number of elements of s.
 • If the subset s of {1,2,...,n} is not a submagma of m, then an exception is raised.

Examples

 > with( Magma ):
 > m := << 3, 5, 3, 4, 3 ;        2, 5, 2, 3, 3 ;        4, 3, 1, 4, 2 ;        3, 2, 1, 1, 1 ;        5, 2, 4, 5, 4 >>;
 ${m}{≔}\left[\begin{array}{ccccc}{3}& {5}& {3}& {4}& {3}\\ {2}& {5}& {2}& {3}& {3}\\ {4}& {3}& {1}& {4}& {2}\\ {3}& {2}& {1}& {1}& {1}\\ {5}& {2}& {4}& {5}& {4}\end{array}\right]$ (1)
 > IsSubMagma( { 1, 3, 4 }, m );
 ${\mathrm{true}}$ (2)
 > SubMagmaCayleyTable( { 1, 3, 4 }, m );
 $\left[\begin{array}{ccc}{2}& {2}& {3}\\ {3}& {1}& {3}\\ {2}& {1}& {1}\end{array}\right]$ (3)

Compatibility

 • The Magma[SubMagmaCayleyTable] command was introduced in Maple 17.