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Re: Factorising polynomials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63987] Re: [mg63970] Factorising polynomials
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 26 Jan 2006 03:43:21 -0500 (EST)
  • References: <200601251346.IAA25881@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 25 Jan 2006, at 13:46, 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
>


You should use FactorList instead of Factor.

data = FactorList[x^# + 1] & /@ Range[6];


Length/@data-1

{1,1,2,1,2,2}



Andrzej Kozlowski


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