test whether a given magma is associative - Maple Help

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Magma[IsAssociative] - test whether a given magma is associative

Magma[IsSemigroup] - test whether a given magma is a semigroup

Calling Sequence

IsAssociative( m )

IsSemigroup( m )

Parameters

m

-

Array representing the Cayley table of a finite magma

Description

• 

The IsAssociative command returns true if the given magma satisfies the associativity identity (XY)Z = X(YZ).  It returns false otherwise.

• 

The IsSemigroup command is an alias for IsAssociative. A semigroup is an associative magma.

Examples

withMagma:

m:=1|2|3,2|3|1,3|1|2

m:=123231312

(1)

IsAssociativem

true

(2)

m:=1|2|3,2|3|3,3|1|2

m:=123233312

(3)

IsSemigroupm

false

(4)

See Also

Magma


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