On 11/20/23 20:48, Waldek Hebisch wrote:

Extra remark: it should be possible to get much of effect
of RealClosure by considering pairs of AlgebraicNumber
and floating point approximation.  Namely, we can compute
minimal polynomial of algebraic number and moderately
accurate floating point approximation uniquely determines
corresponding exact root.  In case when we get reducible
polynomials we could use floating point approximations to
find right factor.


Does this mean the right thing to do is to have two kinds
of algebraic numbers?  For first kind, its position is not
fixed (like current status of 'rootOf), for the other kind,
the position is fixed (you described above).

Because some computation doesn't care which root is which
(for example sum of all roots or a polynomial), while other
computation cares.

- Qian

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