Re: algebraic numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg106020] Re: [mg105989] algebraic numbers
- From: Carl Woll <carlw at wolfram.com>
- Date: Wed, 30 Dec 2009 04:16:00 -0500 (EST)
- References: <200912290620.BAA02732@smc.vnet.net>
Andre Hautot 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 > > > That's what RootApproximant is for: In[6]:= RootApproximant[5.3823323474417620387383087344468466809530954887989] Out[6]= Root[576 - 960 #1^2 + 352 #1^4 - 40 #1^6 + #1^8 &, 8] Carl Woll Wolfram Research
- References:
- algebraic numbers
- From: Andre Hautot <ahautot@ulg.ac.be>
- algebraic numbers