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Topic: algebraic numbers
Replies: 17   Last Post: Jan 8, 2010 4:16 AM

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 dh Posts: 651 Registered: 11/26/08
Re: algebraic numbers
Posted: Dec 30, 2009 4:19 AM

Hi,
algebraic numbers are dense in R. Therefore there are an infinite
number of algebraic numbers "close" to any rational (here even :
finite decimal representation).
Therefore, you must give a more stringent condition, to choose one.
Daniel

On 29 Dez., 07:24, Andre Hautot <ahau...@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 ?
>
> Thanks for a hint,
> ahautot

Date Subject Author
12/29/09 André Hautot
12/30/09 David W. Cantrell
12/30/09 Bob Hanlon
12/30/09 Francesco
12/30/09 dh
12/31/09 DrMajorBob
1/1/10 Noqsi
1/2/10 DrMajorBob
1/3/10 Noqsi
1/3/10 Andrzej Kozlowski
1/4/10 DrMajorBob
1/4/10 DrMajorBob
1/5/10 Noqsi
1/5/10 DrMajorBob
1/6/10 DrMajorBob
1/8/10 DrMajorBob