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Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106022] Re: [mg105989] algebraic numbers
  • From: Artur <grafix at csl.pl>
  • Date: Wed, 30 Dec 2009 04:16:24 -0500 (EST)
  • References: <200912290620.BAA02732@smc.vnet.net>
  • Reply-to: grafix at csl.pl

RootApproximant[5.3823323474417620387383087344468466809530954887989]
Root[576 - 960 #1^2 + 352 #1^4 - 40 #1^6 + #1^8 &, 8]

If you have older version 5 you can use inspite RootApproximant function 
Recognize

Best wishes
Artur

Andre Hautot pisze:
> 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 ?
>
> Thanks for a hint,
> ahautot
>
>
>
>   


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