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Magma

  

IsRack

  

test whether a magma is a rack

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsRack( m )

Parameters

m

-

Array representing the Cayley table of a finite magma

Description

• 

A rack is a right-distributive and right-invertible magma. In other words, the right action of the magma on itself by right translations is automorphic.  (Racks have, therefore, also been called automorphic sets in the literature.)

• 

The IsRack command returns true if the given magma is a rack. It returns false otherwise.

Examples

withMagma:

m1|3|2,3|2|1,2|1|3

m132321213

(1)

IsRackm

true

(2)

m1|2|3,2|3|3,3|1|2

m123233312

(3)

IsRackm

false

(4)

Compatibility

• 

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

• 

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

See Also

IsRightDistributive

IsRightInvertible

Magma