Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation

@article{Neiger2020GenericBM,
  title={Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation},
  author={Vincent Neiger and Johan Sebastian Rosenkilde and Grigory Solomatov},
  journal={Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation},
  year={2020}
}
Suppose K is a large enough field and P ⊂ K2 is a fixed, generic set of points which is available for precomputation. We introduce a technique called reshaping which allows us to design quasi-linear algorithms for both: computing the evaluations of an input polynomial f ∈ K [x, y] at all points of P and computing an interpolant f ∈ K[x, y] which takes prescribed values on P and satisfies an input y-degree bound. Our genericity assumption is explicit and we prove that it holds for most point… 
6 Citations

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