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MathGroup Archive 2000

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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


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