Re: algebraic numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg106026] Re: algebraic numbers
- From: dh <dh at metrohm.com>
- Date: Wed, 30 Dec 2009 04:17:10 -0500 (EST)
- References: <hhc7a1$2o2$1@smc.vnet.net>
Hi, algebraic numbers are dense in R. Therefore there are an infinite number of algebraic numbers "close" to any rational (here even : finite decimal representation). Therefore, you must give a more stringent condition, to choose one. Daniel On 29 Dez., 07:24, Andre Hautot <ahau... 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