Block-Krylov techniques in the context of sparse-FGLM algorithms

@article{Hyun2020BlockKrylovTI,
  title={Block-Krylov techniques in the context of sparse-FGLM algorithms},
  author={S. G. Hyun and Vincent Neiger and Hamid Rahkooy and {\'E}. Schost},
  journal={J. Symb. Comput.},
  year={2020},
  volume={98},
  pages={163-191}
}
  • S. G. Hyun, Vincent Neiger, +1 author É. Schost
  • Published 2020
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • Consider a zero-dimensional ideal $I$ in $\mathbb{K}[X_1,\dots,X_n]$. Inspired by Faugere and Mou's Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of $I$ in order to compute a description of its zero set by means of univariate polynomials. Steel recently showed how to use Coppersmith's block-Wiedemann algorithm in this context; he describes an algorithm that can be easily parallelized, but only computes parts of the output in this manner. Using generating… CONTINUE READING

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