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Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105992] Re: algebraic numbers
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Wed, 30 Dec 2009 04:10:38 -0500 (EST)
  • References: <hhc7a1$2o2$1@smc.vnet.net>

Andre Hautot <ahautot at ulg.ac.be> wrote:
> x= Sqrt[2] + Sqrt[3] + Sqrt[5]   is an algebraic number
>
> MinimalPolynomial[Sqrt[2] + Sqrt[3] + Sqrt[5], x]
>
> returns the polynomial :  576 - 960 x^2 + 352 x^4 - 40 x^6 + x^8  as
> expected
>
> Now suppose we only know the N first figures of x (N large enough), say
> :  N[x,50] = 5.3823323474417620387383087344468466809530954887989
>
> is it possible to recognize x as a probably algebraic number and to
> deduce its minimal polynomial ?

In[1]:= RootApproximant[5.3823323474417620387383087344468466809530954887989]

Out[1]= Root[576 - 960*#1^2 + 352*#1^4 - 40*#1^6 + #1^8 & , 8]

David


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