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Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105996] Re: [mg105989] algebraic numbers
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 30 Dec 2009 04:11:24 -0500 (EST)
  • Reply-to: hanlonr at cox.net

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 at 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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