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

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David W. Cantrell

Posts: 3,395
Registered: 12/3/04
Re: algebraic numbers
Posted: Dec 30, 2009 4:13 AM
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Andre Hautot <ahautot@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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