Re: Factorising polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg63983] Re: [mg63970] Factorising polynomials
- From: gardyloo <gardyloo at mail.wsu.edu>
- Date: Thu, 26 Jan 2006 03:43:08 -0500 (EST)
- References: <200601251346.IAA25881@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, Tony,
I don't think that my technique is very elegant (it certainly won't
generalize very well for similar polynomials), but it should work for
your problem:
In[1]:=
factoredForm = (Factor[x^#1 + 1] & ) /@ Range[6]
Out[1]=
{1 + x, 1 + x^2, (1 + x)*(1 - x + x^2), 1 + x^4,
(1 + x)*(1 - x + x^2 - x^3 + x^4),
(1 + x^2)*(1 - x^2 + x^4)}
In[2]:=
(If[Head[#1] === Times, List @@ #1, {1}] & ) /@
factoredForm
Out[2]=
{{1}, {1}, {1 + x, 1 - x + x^2}, {1},
{1 + x, 1 - x + x^2 - x^3 + x^4},
{1 + x^2, 1 - x^2 + x^4}}
In[3]:=
Length /@ %
Out[3]=
{1, 1, 2, 1, 2, 2}
Good luck,
Curtis O.
Tony King wrote:
>I am trying to find the number of irreducible polynomials over the integers
>in the factorisation of x^n+1
>
>I used the following code
>
>data = Factor[x^# + 1] & /@ Range[6]
>
>Followed by
>
>Table[Length[data[[k]]], {k, 1, 6}]
>
>And Mathematica returned {2,2,2,2,2,2}, one assumes because it was counting
>terms such as 1+x as 2 terms. However, when the number of factors exceeds 1,
>Mathematica returns them as a list and counts them correctly. The output
>that I was looking for should have been {1,1,2,1,2,2}.
>
>Does anyone have any ideas how I might modify the above code so that it
>returns the correct number of terms
>
>Many thanks
>
>Tony
>
>
>
>
- References:
- Factorising polynomials
- From: "Tony King" <mathstutoring@ntlworld.com>
- Factorising polynomials