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NumberTheory

  

RootsOfUnity

  

modular roots of unity

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

RootsOfUnity(k, n)

Parameters

k

-

prime number

n

-

positive integer

Description

• 

The RootsOfUnity(k, n) command computes all the kth roots of unity modulo n.

• 

An integer x is said to be a kth root of unity modulo n if xk=1modn.

Examples

withNumberTheory:

unityRootsOfUnity5,8965

unity1,1631,2446,3261,6521

(1)

mapx→x5mod8965,unity

1

(2)

Distribution of the second roots of unity. A point x,y on the plot denotes that y is a second root of unity modulo x.

plots:-pointplotselectp→p22modp1=1,seqseqi,j,j=0..i1,i=1..1000,labels=Modulus,Second roots of unity,labeldirections=horizontal,vertical

Compatibility

• 

The NumberTheory[RootsOfUnity] command was introduced in Maple 2016.

• 

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

See Also

NumberTheory