NumberTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Number Theory : Queries : NumberTheory/IsCyclotomicPolynomial

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

withNumberTheory:

CyclotomicPolynomial2,x

x+1

(1)

By default

IsCyclotomicPolynomialx+1,x

true

(2)

IsCyclotomicPolynomialx+2,x

false

(3)

IsCyclotomicPolynomialx12,x,output=order

FAIL

(4)

IsCyclotomicPolynomialCyclotomicPolynomial33,x,x,output=result,order

true,33

(5)

pCyclotomicPolynomial7,x

px6+x5+x4+x3+x2+x+1

(6)

zeroessolvep=0,x:

qmulxzeroesi,i=1..6

qxcos2π7Isin2π7x+cos3π7Isin3π7x+cosπ7Isinπ7x+cosπ7+Isinπ7x+cos3π7+Isin3π7xcos2π7+Isin2π7

(7)

IsCyclotomicPolynomialq,x

true

(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]