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

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Bob Hanlon

Posts: 2,604
Registered: 1/29/05
Re: algebraic numbers
Posted: Dec 30, 2009 4:14 AM
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Use RootApproximant. In this case it takes at least 33-digit precision

x = Sqrt[2] + Sqrt[3] + Sqrt[5];

RootApproximant /@ Table[N[x, n], {n, 30, 35}] // ColumnForm


Bob Hanlon

---- 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 ?

Thanks for a hint,
ahautot






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