calculate cyclotomic polynomial - Maple Help

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numtheory[cyclotomic] - calculate cyclotomic polynomial

Calling Sequence

cyclotomic(n, t)

Parameters

n

-

non-negative integer

t

-

variable

Description

• 

The function cyclotomic(n, t) returns the nth cyclotomic  polynomial in t.

  

By definition, cyclotomic(n, t) =

  

 

ζtζ:ζisaprimitiventhrootofunity

• 

With the exception of small values of n, for which a table lookup is used, cyclotomicn,t is computed using an algorithm based on the fact that cyclotomicn,t=tn1d=divisorsnncyclotomicd,t.

• 

The degree of the nth cyclotomic polynomial is given by the totient function numtheory[phi].

Examples

withnumtheory:

cyclotomic1,x

x1

(1)

cyclotomic20,z

z8z6+z4z2+1

(2)

See Also

numtheory, numtheory[divisors], numtheory[iscyclotomic]


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