polytools(deprecated)/recipoly - Maple Help

polytools

 recipoly
 determine whether a polynomial is self-reciprocal

 Calling Sequence recipoly(a, x) recipoly(a, x, 'p')

Parameters

 a - expression x - indeterminate p - (optional) name

Description

 • 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 $\mathrm{coeff}\left(a,x,k\right)=\mathrm{coeff}\left(a,x,d-k\right)$ for all $k=0..d$, where $d=\mathrm{degree}\left(a,x\right)$.
 • If d is even and if the optional second argument p is specified, p is assigned the polynomial P of degree $\frac{d}{2}$ such that ${x}^{\frac{d}{2}}P\left(x+\frac{1}{x}\right)=a$.
 • 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 $\frac{a}{x+1}$.

Examples

Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[IsSelfReciprocal] instead.

 > $\mathrm{with}\left(\mathrm{polytools}\right)$
 $\left[{\mathrm{minpoly}}{,}{\mathrm{recipoly}}{,}{\mathrm{shorten}}{,}{\mathrm{sort_poly}}{,}{\mathrm{split}}{,}{\mathrm{splits}}{,}{\mathrm{translate}}\right]$ (1)
 > $\mathrm{recipoly}\left({x}^{4}+{x}^{3}+x+1,x,'p'\right)$
 ${\mathrm{true}}$ (2)
 > $p$
 ${{x}}^{{2}}{+}{x}{-}{2}$ (3)
 > $\mathrm{recipoly}\left({x}^{5}-3{x}^{4}+{x}^{3}+{x}^{2}-3x+1,x,'p'\right)$
 ${\mathrm{true}}$ (4)
 > $p$
 ${{x}}^{{2}}{-}{4}{}{x}{+}{3}$ (5)