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Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties

Abstract : We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynomials almost uniformly at random. The statistical distance between the output distribution of the algorithm and the uniform distribution on the set of common zeros is polynomially small in the field size, and the running time of the algorithm is polynomial in the description of the polynomials and their degrees provided that the number of the polynomials is a constant.
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https://hal.inria.fr/inria-00359299
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Submitted on : Friday, February 6, 2009 - 3:06:41 PM
Last modification on : Monday, October 2, 2017 - 4:06:04 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:00:40 PM

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  • HAL Id : inria-00359299, version 1
  • ARXIV : 0902.1254

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Mahdi Cheraghchi, Amin Shokrollahi. Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. pp.277-288. ⟨inria-00359299⟩

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