Article View: sci.math.num-analysis
Article #1199Re: Polynomials
From: Virgil
Date: Fri, 06 Aug 2004 08:23
Date: Fri, 06 Aug 2004 08:23
41 lines
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3550 bytes
In article <953c225f.0408052335.15dce37f@posting.google.com>, proginoskes@email.msn.com (Proginoskes) wrote: > Gregory Toomey <nospam@bigpond.com> wrote in message > news:<2ned6lFvud2uU1@uni-berlin.de>... > > Proginoskes wrote: > > > > > Gregory Toomey <nospam@bigpond.com> wrote in message > > > news:<2n8jqpFtbojkU1@uni-berlin.de>... > > >> Jon wrote: > > >> > > >> > Polynomial Roots to any Degree > > >> > Vector Calculus Method > > >> > > >> We has enough of this nonsense last month. > > >> > > >> http://mathworld.wolfram.com/QuinticEquation.html > > >> Unlike quadratic, cubic, and quartic polynomials, the general quintic > > >> cannot be solved algebraically in terms of a finite number of additions, > > >> subtractions, multiplications, divisions, and root extractions, as > > >> rigorously demonstrated by Abel (Abel's impossibility theorem) and > > >> Galois. > > > > > > That argument doesn't work, since he's now thrown in the natural log > > > function ... > > > -- Christopher Heckman > > > > Its not an argument like you hear at the pub, its a proof thats been around > > since the 1800s. > > > > You can throw in logarithms as well but it makes no difference. > > I hadn't heard that (about Abel's proof also working with logarithms). What > else can you add and still be unable to find the roots of general > polynomials? > -- Christopher Heckman Just about anything short of elliptic functions will leave some general polynomial functions unsolvable, but I don't think that Abel's or Galois' proofs cover anything beyond a finite number of additions, subtractions, multiplications, divisions, and root extractions.
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X-Google-Thread: 107079,1597f9db3cddef58 X-Google-Thread: 109d8a,1597f9db3cddef58 X-Google-Thread: f72df,1597f9db3cddef58 X-Google-Thread: 103471,1597f9db3cddef58 X-Google-Thread: 1139f8,1597f9db3cddef58 X-Google-Thread: 10d67e,1597f9db3cddef58 X-Google-Thread: 1130d6,1597f9db3cddef58 X-Google-Thread: f6df2,1597f9db3cddef58 X-Google-Attributes: gid107079,gid109d8a,gidf72df,gid103471,gid1139f8,gid10d67e,gid1130d6,gidf6df2,public X-Google-Language: ENGLISH,ASCII-7-bit Path: arc1-ca.pugleaf.net!g2news1.google.com!news2.google.com!news.maxwell.syr.edu!border1.nntp.dca.giganews.com!nntp.giganews.com!local1.nntp.dca.giganews.com!nntp.comcast.com!news.comcast.com.POSTED!not-for-mail NNTP-Posting-Date: Fri, 06 Aug 2004 03:23:26 -0500 From: Virgil <ITSnetNOTcom#virgil@COMCAST.com> Newsgroups: sci.math.num-analysis,sci.math,japan.sci.math,han.sci.math,fr.sci.maths,aus.mathematics,alt.math.recreational,bln.sci.mathematik Subject: Re: Polynomials References: <J2EPc.23857$iK.8050@newsread2.news.atl.earthlink.net> <2n8jqpFtbojkU1@uni-berlin.de> <953c225f.0408031956.6d6f3cff@posting.google.com> <2ned6lFvud2uU1@uni-berlin.de> <953c225f.0408052335.15dce37f@posting.google.com> User-Agent: MT-NewsWatcher/3.4 (PPC Mac OS X) Date: Fri, 06 Aug 2004 02:23:26 -0600 Message-ID: <ITSnetNOTcom#virgil-1024C1.02232606082004@comcast.dca.giganews.com> Lines: 41 NNTP-Posting-Host: 24.9.121.215 X-Trace: sv3-zavdDqFd8KdF6zQWONukkaMVKx0jVpxMb7l/noYxNFdNXHNhmNC3rRdyJOgE0IdqeiTE2LAP7Dkm1L/!tPO97zgDI2T8qYlegLMDLu82XxdknsXgg4/jggrfqDT+RRCskSG0PGVK3+ZAq14SmbROc+0hvhoo!v6vaHmF3GVpU3mSkiSCrD+WSOUY= X-Complaints-To: abuse@comcast.net X-DMCA-Complaints-To: dmca@comcast.net X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.13