Is Cyclotomic Polynomial - Maple Help
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NumberTheory

  

IsCyclotomicPolynomial

  

test whether a polynomial is cyclotomic

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsCyclotomicPolynomial(p, x)

IsCyclotomicPolynomial(p, x, output_opt)

Parameters

p

-

univariate polynomial in x

x

-

name

output_opt

-

(optional) an equation of the form output = result, output = order, output = [result, order], or output = [order, result]; the default is output = result 

Description

• 

The IsCyclotomicPolynomial function determines whether p is a cyclotomic polynomial, and, optionally, the order of p if p is cyclotomic.

• 

The IsCyclotomicPolynomial(p, x) calling sequence returns true if p(x) is a cyclotomic polynomial, and false otherwise.

• 

Use output_opt to specify whether to return the result, the order, or both:

– 

output = result: Returns true if p is cyclotomic and false otherwise. This is the default behavior for IsCyclotomicPolynomial.

– 

output = order: Returns the order of p as a cyclotomic polynomial if p is cyclotomic. Returns FAIL otherwise.

– 

output = [result, order] (or output = [order, result]): Returns an expression sequence with result and then order (or with order and then result).

• 

If p is the nth cyclotomic polynomial, then p is said to be the order of n.

Examples

(1)

By default

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Compatibility

• 

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

• 

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

See Also

Names

NumberTheory

NumberTheory[CyclotomicPolynomial]

 


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