A probabilistic parallel modular algorithm for rational univariate representation
Résumé
Version 1 of this preprint did not introduce new mathematical ideas, it was more a state of the art June 2021 picture about solving polynomial systems efficiently by reconstructing a rational univariate representation (rur) with a very high probability of correctness using Groebner revlex computation, Berlekamp-Massey algorithm and Hankel linear system solving modulo several primes in parallel.
Version 2 introduces an algorithm for rur certification that is effective for most systems (the cost of this algorithm
being bounded in theorem \ref{prop:check}), something new as far as I know.
These algorithms are implemented in \href{https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.html}{Giac/Xcas} (\cite{giac})since version 1.7.0-13 or 1.7.0-17 for certification, it has (July 2021) leading performances on multiple CPU, at least for an open-source software.
Domaines
Calcul formel [cs.SC]
Origine : Fichiers produits par l'(les) auteur(s)