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

 Messages: [ Previous | Next ]
 Francesco Posts: 2 Registered: 12/30/09
Re: algebraic numbers
Posted: Dec 30, 2009 4:14 AM

"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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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