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Re: Re: Re: Factoring question

  • To: mathgroup at
  • Subject: [mg35493] Re: [mg35470] Re: [mg35458] Re: Factoring question
  • From: Garry Helzer <gah at>
  • Date: Tue, 16 Jul 2002 04:49:58 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

The polynomial factoring algorithm is described briefly in the 
implementation notes to the Mathematica book. The basic idea is that if 
a polynomial factors over the integers it also factors modulo any prime. 
Factorization is easier in a finite field. Factorizations modulo enough 
primes may be put together to get a factorization over the integers. You 
need to understand at least this much or no trace will make sense.

--Garry Helzer

On Sunday, July 14, 2002, at 06:19  AM, Ken Levasseur wrote:

> Steve:
> I assume that the problem was  to solve x^7 + x^5 + x^4 + -x^3 + x + 
> 1=0.  If
> so, one of the basic factoring theorems is that if a polynomial over the
> integers  like this one has a rational root r/s, then r must divide the
> constant term and s must divide the leading coefficient.   So in this 
> problem,
> +/-1 are the only possible rational roots and so the (x+1) factor would 
> be
> found this way.   I'm sure that Mathematica checks this almost 
> immediately.
> As for the remaining 6th degree factor, I'm not certain how Mathematica
> proceeds, but if you plot it, it clearly has no linear factors.
> Ken Levasseur
> Steven Hodgen wrote:
>> "DrBob" <majort at> wrote in message
>> news:agbfhl$je9$1 at
>>> Factor[x^7 + x^5 + x^4 + -x^3 + x + 1] // Trace
>> This doesn't do it.  It only traces the initial evaluation, and then 
>> simply
>> displays the factored result with no intermediate factoring steps.
>> Thanks for the suggestion though.
>>> Bobby
>>> -----Original Message-----
>>> From: Steven Hodgen [mailto:shodgen at]
To: mathgroup at
>>> Subject: [mg35493] [mg35470] [mg35458]  Factoring question
>>> Hello,
>>> I just purchased Mathematica 4.1.  I'm taking precalculus and wanted 
>>> to
>> try
>>> a tough factoring problem, since the teacher couldn't do it either.
>>> Mathematica get's the correct answer, but I'm interrested in seeing 
>>> how it
>>> got there.  Is there a way to turn on some sort of trace feature 
>>> where it
>>> shows each step it used to get the the final result?
>>> Thanks!
>>> --Steven
Garry Helzer
Department of  Mathematics
University of Maryland
1303 Math Bldg
College Park, MD 20742-4015

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