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