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Magma

 IsSubMagma
 test whether a set is a submagma of a given magma

 Calling Sequence IsSubMagma( ss, m )

Parameters

 ss - subset of the domain of the magma m m - Array representing the Cayley table of a finite magma

Description

 • A submagma of a magma is a subset that is closed under the specified binary operation.  Note that the empty set is vacuously a submagma of any magma.  Also, every magma is a submagma of itself.
 • The IsSubMagma( ss, m ) command returns true if the set ss is a submagma of the magma m, and returns false otherwise.

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)
 > IsSubMagma( { 1, 2, 3 }, m );
 ${\mathrm{false}}$ (3)
 > IsSubMagma( { 1, 2, 3, 4, 5 }, m );
 ${\mathrm{true}}$ (4)
 > IsSubMagma( {}, m );
 ${\mathrm{true}}$ (5)

Compatibility

 • The Magma[IsSubMagma] command was introduced in Maple 15.
 • For more information on Maple 15 changes, see Updates in Maple 15.

 See Also