Certifying a probabilistic parallel modular algorithm for rational univariate representation
Symbolic Computation
2021-09-01 v3
Abstract
This paper is about solving polynomial systems. It first recalls how to do that efficiently with a very high probability of correctness by reconstructing a rational univariate representation (rur) using Groebner revlex computation, Berlekamp-Massey algorithm and Hankel linear system solving modulo several primes in parallel. Then it introduces a new method (theorem \ref{prop:check}) for rur certification that is effective for most polynomial systems.These algorithms are implemented in https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.html 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.
Cite
@article{arxiv.2106.10912,
title = {Certifying a probabilistic parallel modular algorithm for rational univariate representation},
author = {Bernard Parisse},
journal= {arXiv preprint arXiv:2106.10912},
year = {2021}
}