Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry

@article{Bates2013RecoveringER,
  title={Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry},
  author={Daniel J. Bates and Jonathan D. Hauenstein and Timothy M. McCoy and Chris Peterson and Andrew J. Sommese},
  journal={Experimental Mathematics},
  year={2013},
  volume={22},
  pages={38 - 50}
}
Let be a set of homogeneous polynomials. Let Z denote the complex projective algebraic set determined by the zero locus of . Numerical-continuation-based methods can be used to produce arbitrary-precision numerical approximations of generic points on each irreducible component of Z. Consider the ideal and the prime decomposition over . This article illustrates how lattice-reduction algorithms may take as input numerically approximated generic points on Z and effectively extract exact elements… 
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