Certifying a probabilistic parallel modular algorithm for rational univariate representation

06/21/2021

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by   Bernard Parisse, et al.

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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>) 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.