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

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Francesco

Posts: 2
Registered: 12/30/09
Re: algebraic numbers
Posted: Dec 30, 2009 4:14 AM
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"Andre Hautot" <ahautot@ulg.ac.be> ha scritto nel messaggio
news:hhc7a1$2o2$1@smc.vnet.net...
> 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 ?


I have the impression that in your case the MinimalPolynomial is simply
x-N.

If you add a figure to N, let say ......9891, you will get a different
polynomial.



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