Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces

@article{Loera2015RandomSI,
  title={Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces},
  author={Jes{\'u}s A. De Loera and Sonja Petrovic and Despina Stasi},
  journal={ArXiv},
  year={2015},
  volume={abs/1503.08804}
}
Abstract This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems and finding small generating sets of graded ideals. The cornerstone of our work is showing that the theory of violator spaces of Gartner et al. applies to polynomial ideal problems. To show this, one utilizes a… CONTINUE READING
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