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Topic: algebraic numbers
Replies: 17   Last Post: Jan 8, 2010 4:16 AM

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DrMajorBob

Posts: 1,448
Registered: 11/3/08
Re: algebraic numbers
Posted: Dec 31, 2009 3:16 AM
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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@gmail.com> wrote:

>
> "Andre Hautot" <ahautot@ulg.ac.be> ha scritto nel messaggio
> news:hhc7a1$2o2$1@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@yahoo.com




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