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From: gsmith@garnet.berkeley.edu (Gene W. Smith)
Newsgroups: sci.math,comp.theory,sci.logic
Subject: Re: Reflections on 50,000 digits of "e"
Message-ID: <1990Feb13.092111.10078@agate.berkeley.edu>
Date: 13 Feb 90 09:21:11 GMT
References: <1528@milton.acs.washington.edu> <906@imec.UUCP> <31369@shemp.CS.UCLA.EDU> <15889@well.UUCP> <1990Feb3.062130.25362@cadence.com> <14353@cs.yale.edu> <1990Feb7.002735.8746@cadence.com> <3981@ucrmath.UCR.EDU>
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In-reply-to: baez@x.ucr.edu (john baez)

In article <3981@ucrmath.UCR.EDU>, baez@x.ucr (john baez) writes:

>1) is there a decision procedure for rationality of
>algebraic numbers (i.e., given a polynomial with
>integer coefficients, can one tell which roots are
>rational and which not?

  This is actually pretty easy. For one thing, there are good
algorithms for factoring over Q(x), and for another, one can
clear denominators and consider a related *monic* polynomial with
integer coefficients. The roots of this will be algebraic
integers, and hence rational only if rational integers.
--
ucbvax!garnet!gsmith          Gene Ward Smith/Brahms Gang/Berkeley CA 94720
"I am quite prepared to prove in court that I am neither stupid nor insane."
quoted from ONE FOR THE BOOKS, the authorized biography of Captain Carnage.