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Complexity bounds for many problems on matrices with univariate polynomialentries have been improved in the last few years. Still, for most relatedalgorithms, efficient implementations are not available, which leaves open thequestion of the practical impact of these algorithms, e.g. on applications suchas decoding some error-correcting codes and solving polynomial systems orstructured linear systems. In this paper, we discuss implementation aspects formost fundamental operations: multiplication, truncated inversion, approximants,interpolants, kernels, linear system solving, determinant, and basis reduction.We focus on prime fields with a word-size modulus, relying on Shoup's C++library NTL. Combining these new tools to implement variants of Villard'salgorithm for the resultant of generic bivariate polynomials (ISSAC 2018), weget better performance than the state of the art for large parameters.

Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants