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Re: Re: Interpreting the solutions... better this time

• To: mathgroup at smc.vnet.net
• Subject: [mg75279] Re: [mg75258] Re: [mg75225] Interpreting the solutions... better this time
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 23 Apr 2007 05:43:16 -0400 (EDT)
• References: <200704220306.XAA25855@smc.vnet.net> <200704220912.FAA20543@smc.vnet.net>

On 22 Apr 2007, at 18:12, bsyehuda at gmail.com wrote:

> You cannot find (except for special cases) the exact roots for  
> polynomials
> with degrees greater than 5.

This may be a little pedantic and not  relevant here to the issue at  
hand, but it may of some interest to note that the correct statement  
of the above is that one cannot express, in general, the roots of a  
polynomial of degree greater or equal to 5 in terms of radicals of  
the coefficients of the polynomial. There are, however, "exact"  
expressions for these roots in terms of theta functions of several  
variables. These expressions generalize the famous one for the roots  
of a quintic found by Hermite already in 1858.

Andrzej Kozlowski 

• References:
  • Interpreting the solutions... better this time
    • From: "Apostolos E. A. S. Evangelopoulos" <a.e.a.evangelopoulos@sms.ed.ac.uk>