MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105999] Re: algebraic numbers
  • From: "Francesco" <fracix at gmail.com>
  • Date: Wed, 30 Dec 2009 04:12:00 -0500 (EST)
  • References: <hhc7a1$2o2$1@smc.vnet.net>

"Andre Hautot" <ahautot at ulg.ac.be> ha scritto nel messaggio 
news:hhc7a1$2o2$1 at smc.vnet.net...
> 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 ?

I have the impression that in your case the MinimalPolynomial is simply
x-N.

If  you add a figure to N, let say ......9891, you will get a different 
polynomial. 



__________ Information from ESET Smart Security, version of virus signature database 4725 (20091229) __________

The message was checked by ESET Smart Security.

http://www.eset.com






  • Prev by Date: Re: simplifying a system of equations
  • Next by Date: Re: simplifying a system of equations
  • Previous by thread: Re: algebraic numbers
  • Next by thread: Re: Re: algebraic numbers