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Re: Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106053] Re: [mg105999] Re: algebraic numbers
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Thu, 31 Dec 2009 03:17:10 -0500 (EST)
  • References: <hhc7a1$2o2$1@smc.vnet.net> <200912300912.EAA17052@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

Strictly speaking, you're right. The following results (if they were to be  
minimal polynomials EXACTLY) should be different:

5.3823323474417620387383087344468466809530954887989 // RootApproximant

Root[576 - 960 #1^2 + 352 #1^4 - 40 #1^6 + #1^8 &, 8]

5.38233234744176203873830873444684668095309548879891 // RootApproximant

Root[576 - 960 #1^2 + 352 #1^4 - 40 #1^6 + #1^8 &, 8]

This is a little like those idiotic SAT and GRE questions that ask "What's  
the next number in the following series?"... where any number will do.  
Test writers don't seem to know there's an interpolating polynomial (for  
instance) to fit the given series with ANY next element.

Bobby

On Wed, 30 Dec 2009 03:12:00 -0600, Francesco <fracix at gmail.com> wrote:

>
> "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.
>
>
>
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-- 
DrMajorBob at yahoo.com


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