Re: "Cascaded sums"?
- To: mathgroup at smc.vnet.net
- Subject: [mg59195] Re: "Cascaded sums"?
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Tue, 2 Aug 2005 00:42:21 -0400 (EDT)
- Organization: The Open University, Milton Keynes, U.K.
- References: <dckb96$o4j$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
AES wrote: > A Mathematic calculation is yielding a result of the form > > (x^4 + a (x^3 + a (x^2 + a ( x + a )))) > > for the case n = 4, and analogous results for larger n; and Mathematica > seems to be able to do some interesting simplifications and factoring of > these results. > > I'm sure I learned about this form in a math class somewhere along the > line, but this was 50+ years ago. Could some kind soul remind me of > what this form is called, and maybe some of its interesting properties? > > Thanks . . . > Hi, The polynomial is expressed in Horner, or nested, form, which is highly efficient for numeric computations. You will find hereunder some links that explained in more details how Horner?s method works and how you can use it within Mathematica: http://math.fullerton.edu/mathews/n2003/HornerMod.html http://www.algebra.com/algebra/about/history/Horner-scheme.wikipedia http://support.wolfram.com/mathematica/mathematics/algebra/horner.html http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Algebra/Horner.html Hopes this helps, /J.M.