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From: edp@jareth.enet.dec.com (Always mount a scratch monkey.)
Newsgroups: comp.sys.handhelds
Subject: Re: Finding roots of Tertiary and above equations?
Message-ID: <22117@shlump.nac.dec.com>
Date: 17 Apr 91 15:18:39 GMT
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Organization: Digital Equipment Corporation
Lines: 27

In article <6230005@hplred.HP.COM>, seroussi@hplred.HP.COM (Gadiel Seroussi)
writes...

>> I gusss what I am asking is, what does it meen to say something
>> has an algebraic soloution and
>> is ther any thing realy special about 5'th and above degree
>> polynomials.
> 
>A number is "algebraic" if it is the root of a polynomial with rational 
>coefficients.

In regard to previous messages, "algebraic solution" did not refer to the
numbers that were zeroes of the polynomial being algebraic numbers; it referred
to the solution itself being algebraic.  In that context, "algebraic" means
composed of only finite numbers of additions, subtractions, multiplications,
divisions, raisings to powers, and extractions of roots.

And to answer the previous questions, yes, there is something special about
polynomials that are quintic and above:  Their solutions cannot be written
as algebraic (in the sense I have given above) formulae of their coefficients.
Quartic polynomials and below can be solved with finite numbers of the listed
operations; quintic polynomials and above cannot, in the general case.


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