Computing Complex Dimension Faster and Deterministically

Details Computing Complex Dimension Faster and Deterministically Computing Complex Dimension Faster and Deterministically

2000-05-03

arxiv.org/abs/math/0005028v1

Mathematics

Algebraic Geometry

A mild revision of an earlier version submitted to a conference proceedings. Latex file needs acmconf.cls to compile

Scientific paper

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper quantitative estimates on rational univariate representations of roots of polynomial systems. As a corollary of the latter bounds, we considerably improve a recent algorithm of Koiran for deciding the emptiness of a hypersurface intersection over the complex numbers, given the truth of the Generalized Riemann Hypothesis (GRH).

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