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Magma

  

IsSubMagma

  

test whether a set is a submagma of a given magma

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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 >>;

m3534325233431423211152454

(1)

IsSubMagma( { 1, 3, 4 }, m );

true

(2)

IsSubMagma( { 1, 2, 3 }, m );

false

(3)

IsSubMagma( { 1, 2, 3, 4, 5 }, m );

true

(4)

IsSubMagma( {}, m );

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

Magma