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Magma

  

DirectProduct

  

compute the direct product of two magmas

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DirectProduct( A, B )

Parameters

A

-

Array representing the Cayley table of a finite magma

B

-

Array representing the Cayley table of a finite magma

Description

• 

The direct product of two magmas A and B is the set of pairs (a,b), with a in A and b in B, and with binary operation defined componentwise.

• 

The DirectProduct( A, B ) command returns the Cayley table of the direct product of the magmas A and B.

Examples

withMagma:

A1|2,2|1

A1221

(1)

B1|1|2,2|3|2,3|2|1

B112232321

(2)

DirectProductA,B

112445232565321654445112565232654321

(3)

AreIsomorphicDirectProductA,B,DirectProductB,A

true

(4)

C1|2|3,2|3|1,3|1|2

C123231312

(5)

AreIsomorphicDirectProductDirectProductA,B,C,DirectProductA,DirectProductB,C

true

(6)

Compatibility

• 

The Magma[DirectProduct] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

Magma