[Date Index]
[Thread Index]
[Author Index]
Re: Re: Re: Factoring question
*To*: mathgroup at smc.vnet.net
*Subject*: [mg35493] Re: [mg35470] Re: [mg35458] Re: Factoring question
*From*: Garry Helzer <gah at math.umd.edu>
*Date*: Tue, 16 Jul 2002 04:49:58 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
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 cox-internet.com> wrote in message
>> news:agbfhl$je9$1 at smc.vnet.net...
>>> 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 mindspring.com]
To: mathgroup at smc.vnet.net
>>> 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
Prev by Date:
**RE: Changing delayed formula**
Next by Date:
**Re: Changing delayed formula**
Previous by thread:
**Re: Factoring question**
Next by thread:
**Re: Re: Re: Factoring question**
| |