On 10/11/15 10:45, John Cremona wrote:
Two ideas:
(1) As in your first construction but replace each field constructed
after the forst with the corresponding absolute field.
(2) Let a = sqrt(2)+sqrt(3)+... as a real number and use LLL to find
its mimimum polynomial.
(2) is easily done in Sage using algdep (which uses PARI/GP). Here is an
example
sage: a = QQbar(2).sqrt() + QQbar(3).sqrt() + QQbar(5).sqrt()
sage: p = algdep(a.n(digits=100), 8)
sage: p
x^8 - 40*x^6 + 352*x^4 - 960*x^2 + 576
sage: p(a)
0.?e-12
Though on the huge initial example of Pierre it does not work very well...
Vincent
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