polytools
recipoly
determine whether a polynomial is self-reciprocal
Calling Sequence
Parameters
Description
Examples
recipoly(a, x)
recipoly(a, x, 'p')
a
-
expression
x
indeterminate
p
(optional) name
Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[IsSelfReciprocal] instead.
Determine 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 second argument p is specified, p is assigned the polynomial P of degree d2 such that xd2⁢P⁡x+1x=a.
Note that if d is odd, a being self-reciprocal implies a is divisible by x+1. In this case, if p is specified then the result computed is for ax+1.
with⁡polytools
minpoly,recipoly,shorten,sort_poly,split,splits,translate
recipoly⁡x4+x3+x+1,x,p
true
x2+x−2
recipoly⁡x5−3⁢x4+x3+x2−3⁢x+1,x,p
x2−4⁢x+3
See Also
PolynomialTools[IsSelfReciprocal]
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