On the complexity of the multivariate resultant

@article{Grenet2012OnTC,
  title={On the complexity of the multivariate resultant},
  author={Bruno Grenet and Pascal Koiran and Natacha Portier},
  journal={ArXiv},
  year={2012},
  volume={abs/1210.1451}
}
View PDF on arXiv
11 Citations
Highly Influential Citations
1
Background Citations
7
Methods Citations
2

11 Citations

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Sparse resultants and straight-line programs

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References

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The main result is that testing the resultant for zero is NP-hard under deterministic reductions in any characteristic, for systems of low-degree polynomials with coefficients in the ground field (rather than in an extension).

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It will be shown in the sequel that the parallel arithmetic complexity of all these four problems is upper bounded by O(log2n) and the algorithms that establish this bound use a number of processors polynomial in n, disproves I. Munro's conjecture.

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