Decomposition of x^4+x^3+x^2+x+1 (Yu Hsiung Huang)



> From: maxima-request at math.utexas.edu
> Subject: Maxima Digest, Vol 46, Issue 29
> To: maxima at math.utexas.edu
> Date: Sat, 15 May 2010 08:34:39 -0500
> 
> Send Maxima mailing list submissions to
> 	maxima at math.utexas.edu
> 
> To subscribe or unsubscribe via the World Wide Web, visit
> 	http://www.math.utexas.edu/mailman/listinfo/maxima
> or, via email, send a message with subject or body 'help' to
> 	maxima-request at math.utexas.edu
> 
> You can reach the person managing the list at
> 	maxima-owner at math.utexas.edu
> 
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Maxima digest..."
> 
> 
> Today's Topics:
> 
>    1. Re: Decomposition of rationnal fractions (Michel Talon)
>    2. check if a number is rational (Christian Stengg)
>    3. Re: check if a number is rational (Barton Willis)
>    4. Re: Question concerning sum (Dieter Kaiser)
>    5. Describe issue? (Raymond Toy)
>    6. Navier-Stokes equations and itensor package. (Grigory Sarnitskiy)
>    7. Re: Describe issue? (Dieter Kaiser)
>    8. Q in solve Chinese Remainder Theroem or inequality equation (? ??)
>    9. Q in wxMaxima0.8.2 in ubuntu9.10 (? ??)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Fri, 14 May 2010 09:31:52 +0200
> From: Michel Talon <talon at lpthe.jussieu.fr>
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] Decomposition of rationnal fractions
> Message-ID: <hsiu98$pgb$1 at dough.gmane.org>
> Content-Type: text/plain; charset=iso-8859-15
> 
> Nicolas FRANCOIS wrote:
> 
> > Le Thu, 13 May 2010 23:05:12 +0100,
> > Jaime Villate <villate at fe.up.pt> a ?crit :
> > 
> >> On Thu, 2010-05-13 at 23:00 +0100, Jaime Villate wrote:
> >> > (to obtain its formal series equivalent \sum a_nX^n, a_n being the
> >> > > number of ways to pay n? using 1, 2 and 5? corners (no, there
> >> > > is no such thing as a 5? corner, but there's a 5? banknote !)).
> >> Oops, sorry; I did not read this part before my previous reply to your
> >> message. Then the partial fractions expansion that I told you is not
> >> what you need.
> > 
> > Yes it is, and I'm aware of the partfrac function. My problem is it
> > does only work in Q[X] : I would like to force the use of complex
> > roots, to decompose 1+x+x^2+x^3+x^4 into a product of factors X-w,
> > where w is one of the fifth roots of 1 distinct from 1.
> > 
> > So my question is : is there a way to work in an extension of Q(X) ?
> > 
> > \bye
> > 
> 
> You can work in an extension by first using "factor" in an extension.
> For example:
> 
> (%i6) factor(x^4+1,w^2+1);
>                                  2        2
> (%o6)                          (x  - w) (x  + w)
> 
> So all you need is first adjoint the appropriate roots.
> 
> 
> --
> 
> Michel Talon
> 

I don' t know to decomposition of x^4+x^3+x^2+x+1 in maxima
but we  know 
x^5-1=0
(x-1)(x^4+x^3+x^2+x+1)=0

divide(x^5-1,x-1);
(%o1) [x^4+x^3+x^2+x+1,0]

so, we can 
solve(x^5-1);
(%o1) [x=%e^((2*%i*%pi)/5),x=%e^((4*%i*%pi)/5),x=%e^(-(4*%i*%pi)/5),x=%e^(-(2*%i*%pi)/5),x=1]
the answer is the factors of x^4+x^3+x^2+x+1


Yu Hsiung Huang

 		 	   		  
_________________________________________________________________
Hotmail ????????????
https://signup.live.com/signup.aspx?id=60969