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PolynomialTools

  

IsSelfReciprocal

  

determine whether a polynomial is self-reciprocal

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsSelfReciprocal(a, x, 'p')

Parameters

a

-

expression

x

-

indeterminate

p

-

(optional) name

Description

• 

The IsSelfReciprocal(a, x) function determines whether a is a "self-reciprocal" polynomial in x. This property holds if and only if coeffa,x,k=coeffa,x,dk for all k=0..d, where d=degreea,x.

• 

If d is even and if the optional third argument p is specified, p is assigned the polynomial P of degree 12d such that x12dPx+1x=a.

• 

Note that if d is odd, a being self-reciprocal implies that a is divisible by x+1. In this case, if p is specified then the result computed is for ax+1.

• 

This function is part of the PolynomialTools package, and so it can be used in the form IsSelfReciprocal(..) only after executing the command with(PolynomialTools). However, it can always be accessed through the long form of the command by using PolynomialTools[IsSelfReciprocal](..).

Examples

withPolynomialTools:

IsSelfReciprocalx4+x3+x+1,x,'p'

true

(1)

p

x2+x2

(2)

IsSelfReciprocalx53x4+x3+x23x+1,x,'p'

true

(3)

p

x24x+3

(4)

See Also

coeff

degree

PolynomialTools

 


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