Just to pick up on a comment from William's message earlier

On 13 May 2012 12:46, William Stein <[email protected]> wrote:
>
> It might be useful to work with floating point approximations to the
> algebraic numbers and ask for the minpoly of any particular one later.

This is exactly what is done by Sage's (IMHO excellent and rather
under-appreciated) QQbar module. At the moment this is not terribly
well integrated with either the number fields code or the symbolics
stuff, though; it could be made much more useful with a bit of work on
the coercion code.

David

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