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

 Messages: [ Previous | Next ]
 André Hautot Posts: 18 Registered: 12/8/04
algebraic numbers
Posted: Dec 29, 2009 1:24 AM

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

Date Subject Author
12/29/09 André Hautot
12/30/09 David W. Cantrell
12/30/09 Bob Hanlon
12/30/09 Francesco
12/30/09 dh
12/31/09 DrMajorBob
1/1/10 Noqsi
1/2/10 DrMajorBob
1/3/10 Noqsi
1/3/10 Andrzej Kozlowski
1/4/10 DrMajorBob
1/4/10 DrMajorBob
1/5/10 Noqsi
1/5/10 DrMajorBob
1/6/10 DrMajorBob
1/8/10 DrMajorBob