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General Solution for Polynomial Equations?

Posted by michael on from the higher-order-geekdom dept.

An anonymous reader writes "On september 9, several media reported that a young Dutch student found a formula to determine the roots of any polynomial equation. Does this conflict with Abel's proof that such a formula cannot exist? Here is the news item (in Dutch) on his school's homepage." Another reader writes "A Dutch student at the Fontys school of physics has solved a math problem of several centuries old: finding the roots of any polynomial equation. Arxciv copy here. Although an exact solution has been proven impossible for higher orders, this is not the case for numeric solutions."

3 of 482 comments (clear)

  1. The fish by leonmergen · · Score: 5, Informative

    http://babelfish.altavista.com/babelfish/trurl_pag econtent?url=http%3A%2F%2Fwww.fontys.nl%2Fnieuws%2 Fnieuws_artikel.asp%3Fdocid%3D3487&lp=nl_en

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    - Leon Mergen
    http://www.solatis.com
  2. Mirror by avalys · · Score: 5, Informative

    Apparently some people can't get to the site, which is funny because I'm having no problem, but here is a mirror.

    The Roots of any Polynomial Equation

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    This space intentionally left blank.
  3. Its no big deal by moss1956 · · Score: 5, Informative

    The theorem of Abel (or Galois) that is being referred to merely claims that you can't find a general formula built from just the arithmetic operations plus taking nth roots. It has been known for a long time that there is a general formula using elliptic functions.

    The student just used the method of formal power series to solve the equation. This approach dates back at least to Cauchy ~1850 and probably can be found in the works of Euler.