Intrinsic Near Quadratic Complexity Bounds for Real Multivariate Root Counting

@inproceedings{Rojas1998IntrinsicNQ,
  title={Intrinsic Near Quadratic Complexity Bounds for Real Multivariate Root Counting},
  author={J. Maurice Rojas},
  booktitle={ESA},
  year={1998}
}
  • J. M. Rojas
  • Published in ESA 24 August 1998
  • Mathematics, Computer Science
We give a new algorithm, with three versions, for computing the number of real roots of a system of n polynomial equations in n unknowns. The rst version is of Monte Carlo type and, neglecting logarithmic factors, runs in time quadratic in the average number of complex roots of a closely related system. The other two versions run nearly as fast and progressively remove a measure zero locus of failures present in the rst version. Via a slight simpliication of our algorithm, we can also count… 
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