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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: <22278@shlump.nac.dec.com>
Date: 23 Apr 91 12:06:46 GMT
References: <25744@hydra.gatech.EDU> <6230006@hplred.HP.COM>
Sender: newsdaemon@shlump.nac.dec.com
Reply-To: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Organization: Digital Equipment Corporation
Lines: 44

In article <6230006@hplred.HP.COM>, seroussi@hplred.HP.COM (Gadiel
Seroussi) writes:

>>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.
. . .
>
>However, the word "algebraic" has a well defined meaning in mathematics
>>(especially when talking about roots of polynomials), and the concept
>we are referring to here is precisely captured by the term
>"solvable by radicals". There is no need to start redefining standard 
>mathematical terms.

"Algebraic" has not just one meaning in mathematics, but several.  The
following is from James and James, _Mathematics Dictionary_ fourth
edition (Van Nostrand Reinhold Company, New York:  1976), under
"Algebraic":

         algebraic proofs and solutions.  Proofs and solutions which
         use algebraic symbols and no operations other than those
         which are algebraic.  See above, algebraic operations.

Above that, we find:

         algebraic operations.  Addition, subtraction, multiplication,
         division, evolution and involution (extracting roots and
         raising to powers).

The meaning I used is correct in the context "algebraic solution".  The
meaning you gave is for "algebraic number".

Is it dead yet?


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