Elias' Article

Separation bounds for real roots of polynomial systems.
Kristoffer Arnsfelt Hansen, Michal Koucky, Niels Lauritzen, Peter Bro Miltersen, and Elias P. Tsigaridas.
In Proc. 11th Int'l Symp. on Effective Methods in Algebraic Geometry (MEGA), 2011.

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Abstract:

Given a system of $m$ polynomials in $n$ variables (where $m$ is in general different from $n$) of degree bounded by $d$, whose coefficients have bitsizes at most $\tau$, and an isolated (in the Euclidean topology) real root of the system, what is an upper bound on its algebraic degree as a function of $d$ and $n$? What is the separation bound of the system, that is the minimum distance between any two isolated real roots? How close can a non-zero isolated real root be to zero?

@InProceedings{hklmt-mega-2011,
  author =       {Kristoffer Arnsfelt Hansen and Michal Koucky and
                  Niels Lauritzen and Peter Bro Miltersen and Elias~P.
                  Tsigaridas},
  title =        { Separation bounds for real roots of polynomial
                  systems},
  booktitle =    {Proc. 11th Int'l Symp. on Effective Methods in
                  Algebraic Geometry (MEGA)},
  year =         2011,
  abstract =     " Given a system of $m$ polynomials in $n$ variables
                  (where $m$ is in general different from $n$) of
                  degree bounded by $d$, whose coefficients have
                  bitsizes at most $\tau$, and an {\em isolated} (in
                  the Euclidean topology) real root of the system,
                  what is an upper bound on its algebraic degree as a
                  function of $d$ and $n$? What is the separation
                  bound of the system, that is the minimum distance
                  between any two isolated real roots? How close can a
                  non-zero isolated real root be to zero? ",
}

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