Magma - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Magma : Magma/IsQuasigroup

Magma

  

IsQuasigroup

  

test whether a finite magma is a quasigroup

  

IsLeftQuasigroup

  

test whether a finite magma is a left quasigroup

  

IsRightQuasigroup

  

test whether a finite magma is a right quasigroup

 

Calling Sequence

Parameters

Description

Thread Safety

Examples

Compatibility

Calling Sequence

IsQuasigroup( m )

IsLeftQuasigroup( m )

IsRightQuasigroup( m )

Parameters

m

-

Array representing the Cayley table of a finite magma

Description

• 

A left quasigroup is a magma in which the rows of the Cayley table are permutations of the elements.

• 

The IsLeftQuasigroup command returns true if the given magma is a left quasigroup, and returns false otherwise.

• 

A right quasigroup is a magma in which the columns of the Cayley table are permutations of the elements.

• 

The IsRightQuasigroup command returns true if the given magma is a right quasigroup, and returns false otherwise.

• 

A quasigroup is a magma whose Cayley table is a Latin square.  That is, each row and column is a permutation of the integers from 1 to n, where n is the order of the magma.  Thus, a magma is a quasigroup if, and only if, it is both a left quasigroup and a right quasigroup.

• 

The IsQuasigroup command returns true if the given magma is a quasigroup, and returns false otherwise.

Thread Safety

• 

The Magma[IsQuasigroup] command is thread-safe as of Maple 16.

• 

The Magma[IsLeftQuasigroup] and Magma[IsRightQuasigroup] commands are thread-safe as of Maple 17.

• 

For more information on thread safety, see index/threadsafe.

Examples

withMagma:

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

m123231312

(1)

IsQuasigroupm

true

(2)

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

m123233312

(3)

IsQuasigroupm

false

(4)

Compatibility

• 

The Magma[IsQuasigroup], Magma[IsLeftQuasigroup] and Magma[IsRightQuasigroup] commands were introduced in Maple 15.

• 

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

See Also

Magma