# 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…
9 Citations
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DIMACS Series in Discrete Mathematics and Theoretical Computer Science Erratum to : Lower Bounds and Real Algebraic Geometry
• Computer Science, Mathematics
• 2002
This work describes a method, based on the rational univariate reduction (RUR), for computing roots of systems of multivariate polynomials with rational coefficients that has been used successfully on certain degenerate boundary evaluation problems.
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• Computer Science, Mathematics
• 2003
A method, based on the rational univariate reduction (RUR), for computing roots of systems of multivariate polynomials with rational coefficients that enables exact algebraic computations with the root coordinates and works even if the underlying set of roots is positive dimensional.
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• J. M. Rojas
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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
• 1999
It is shown that the following two problems can be solved within PSPACE, and the truth of the Generalized Riemann Hypothesis implies that detecting roots in Q/sup n/ for the polynomial systems in problem (I) can be done via a two-round Arthur-Merlin protocol.

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