• Corpus ID: 239017020

Faster Modular Composition

@article{Neiger2021FasterMC,
  title={Faster Modular Composition},
  author={Vincent Neiger and Bruno Salvy and {\'E}ric Schost and Gilles Villard},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.08354}
}
A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by $n$, the algorithm uses $O(n^{1.43})$ field operations, breaking through the $3/2$ barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require $O(n^{1.63})$ field operations in general, and ${n^{3/2+o(1)}}$ field operations in the particular case of power… 

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