Re: algebraic numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg105992] Re: algebraic numbers
- From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
- Date: Wed, 30 Dec 2009 04:10:38 -0500 (EST)
- References: <hhc7a1$2o2$1@smc.vnet.net>
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 ? In[1]:= RootApproximant[5.3823323474417620387383087344468466809530954887989] Out[1]= Root[576 - 960*#1^2 + 352*#1^4 - 40*#1^6 + #1^8 & , 8] David