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Rewriting polynomials for computers

  1. Oct 13, 2010 #1
    Suppose I have a REALLY big polynomial:
    [tex]a_0 + a_1 x + a_2 x^2 + a_3 x^3+a_4 x^4+ \cdots + a_n x^n[/tex]
    I can rewrite the polynomial as a combination of multiplication and addition operators (instead of exponents) that a computer tends to like as such:
    [tex]a_0 + x \left( a_1 + x \left( a_2 + x \left( a_3 + x \left(a_4 + \cdots + a_n x \left)\right. \cdots \right)\right)\right)\right)[/tex]

    • Does this process have a name?
    • Is there an algorithm to do this?
    • Is there an implementation of this on Sage or MATLAB/Octave or Mathematica?
  2. jcsd
  3. Oct 13, 2010 #2


    Staff: Mentor

    I believe this is called Horner's Rule. I'm sure there's an algorithm, but I don't recall what it is. Check online for more information about it.

    I don't know what MATLAB and the others have for Horner's Rule.
  4. Oct 13, 2010 #3

    http://en.wikipedia.org/wiki/Horner_scheme" [Broken]

    Thanks! The information at the wiki page is more than plenty for me.
    Last edited by a moderator: May 5, 2017
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