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algebraic numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg105989] algebraic numbers
• From: Andre Hautot <ahautot at ulg.ac.be>
• Date: Tue, 29 Dec 2009 01:20:33 -0500 (EST)

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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