determine whether a polynomial is self-reciprocal
IsSelfReciprocal(a, x, 'p')
The IsSelfReciprocal(a, x) function determines whether a is a "self-reciprocal" polynomial in x. This property holds if and only if coeff⁡a,x,k=coeff⁡a,x,d−k for all k=0..d, where d=degree⁡a,x.
If d is even and if the optional third argument p is specified, p is assigned the polynomial P of degree 12⁢d such that x12⁢d⁢P⁡x+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](..).
Download Help Document
What kind of issue would you like to report? (Optional)
Thank you for submitting feedback on this help document. Your feedback will be used
to improve Maple's help in the future.