Numerically intersecting algebraic varieties via witness sets

  title={Numerically intersecting algebraic varieties via witness sets},
  author={Jonathan D. Hauenstein and Charles W. Wampler},
  journal={Applied Mathematics and Computation},
The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F , for which A is an irreducible component of V(F ), a generic linear space L of complementary dimension to A, and a numerical approximation to the set of witness points, L ∩A. Given F , methods exist for computing a numerical irreducible decomposition, which consists of a collection of witness sets, one for each… CONTINUE READING
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