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From: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Newsgroups: comp.sys.handhelds
Subject: Re: Finding roots of Tertiary and above equations?
Message-ID: <21917@shlump.nac.dec.com>
Date: 9 Apr 91 12:42:45 GMT
References: <25744@hydra.gatech.EDU> <21858@shlump.nac.dec.com> <40686@netnews.upenn.edu> <40731@netnews.upenn.edu>
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Reply-To: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Organization: Digital Equipment Corporation
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In article <40731@netnews.upenn.edu>, hoford@sequoia.circ.upenn.edu
(John Hoford) writes:

>>In short, no.  For polynomials up to degree four, there are exact
>>algebraic solutions.  Beyond that, numerical methods must be used. 

>Is this true in the sense that, a solution involving a square root
>is a numerical solution.
>That is to find SQRT(x) programs implement some form of ('x = y^2' 'y' solve)

I'm not quite sure what you are asking.  However, my statement did not
mean to exclude square roots.  For example, sqrt(2) is considered an
exact algebraic solution to x^2=2.  For quadratic, cubic, and quartic
polynomials, one can always find an exact algebraic solution, even if
the answer is complex and involves square roots, cube roots, or quartic
roots.  The solution may be irrational, so it will not have an exact
numerical representation, but the algebraic solution can be found.

Many polynomials above degree four do have algebraic solutions, but in
the general case, there is no exact algebraic solution for all
polynomials of degree five, or of any higher degree.


				-- edp (Eric Postpischil)
				"Always mount a scratch monkey."
				edp@jareth.enet.dec.com