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