Re: Mirror polynomial

*To*: mathgroup at smc.vnet.net*Subject*: [mg25370] Re: [mg25342] Mirror polynomial*From*: BobHanlon at aol.com*Date*: Sun, 24 Sep 2000 03:01:37 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 9/23/2000 3:55:59 AM, gorazd at e5.ijs.si writes: >Anyboby familiar with "mirror polynomials" and "mirror arrays"? > >My assumption: >x^n*P(1/x) is mirror polynomial to P(x) >Am I right ? > I have never heard of a mirror polynomial; however, given your definition, either mP1 or mP2 below will mirror a polynomial without having to know its order in advance. mP1[poly_, sym_Symbol:x] := Expand[Fold[#1 sym + #2 &, 0, CoefficientList[poly, sym]]]; mP2[poly_, sym_Symbol:x] := Expand[(poly /. sym :> (1/sym))* sym^(Length[CoefficientList[poly, sym]] - 1)]; n = Random[Integer, {1, 10}]; P[x_] := Evaluate[Sum[Random[]*x^k, {k, 0, n}]]; x^n P[1/x] == mP1[P[x]] == mP2[P[x]] // Simplify True Bob Hanlon