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Re: algebraic numbers
Posted:
Dec 31, 2009 3:16 AM


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 > xN. > > 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 > > > > >
 DrMajorBob@yahoo.com



