Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers

@article{Lecerf2003ComputingTE,
  title={Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers},
  author={Gr{\'e}goire Lecerf},
  journal={J. Complexity},
  year={2003},
  volume={19},
  pages={564-596}
}
We present a new probabilistic method for solving systems of polynomial equations and inequations. Our algorithm computes the equidimensional decomposition of the Zariski closure of the solution set of such systems. Each equidimensional component is encoded by a generic fiber, that is a finite set of points obtained from the intersection of the component with a generic transverse affine subspace. Our algorithm is incremental in the number of equations to be solved. Its complexity is mainly… CONTINUE READING
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