Symbolic Computation Group

This talk presents joint work with J. Rosenkilde and G. Solomatov, about new algorithms for bivariate multi-point evaluation, interpolation and modular composition, which under certain assumptions have quasi-linear complexity. For multi-point evaluation and interpolation we assume that the set of points is generic and available for precomputation. In the case of modular composition, similar assumptions are made on a bivariate ideal which depends on part of the input. The key tool is an algorithm that reshapes the degree bounds of a given bivariate polynomial while preserving its membership in a coset of some fixed bivariate ideal available for precomputation.