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…
3 Citations
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