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Magma

  

Nucleus

  

compute the nucleus of a magma

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Nucleus( m )

Parameters

m

-

Array representing the Cayley table of a finite magma

Description

• 

The nucleus of a magma is the set of its members that associate with every member of the magma. That is, an element x is in the nucleus if all of the equations (xy)z = x(yz), (yx)z = y(xz) and (yz)x = y(zx) are satisfied, for all y and z from the magma.

• 

The Nucleus command returns the nucleus of the magma m as a set.

Examples

with( Magma ):

m := << 1, 2, 3 ; 2, 3, 1 ; 3, 1, 2 >>;

m123231312

(1)

Nucleus( m );

1&comma;2&comma;3

(2)

m := << 1, 1, 1, 1, 1; 1, 1, 1, 1, 1 ; 1, 1, 1, 1, 1 ; 1, 1, 1, 2, 4 ; 1, 2, 2, 4, 5 >>;

m1111111111111111112412245

(3)

Nucleus( m );

1&comma;2&comma;3

(4)

m := << 1, 1, 1, 1, 1 ; 1, 1, 1, 1, 1 ; 1, 1, 1, 1, 1 ; 1, 1, 1, 2, 4 ; 1, 2, 1, 4, 5 >>;

m1111111111111111112412145

(5)

Nucleus( m );

1&comma;2&comma;3

(6)

Compatibility

• 

The Magma[Nucleus] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

See Also

Center

Magma