REVIEW 1 cited by
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Certifying a probabilistic parallel modular algorithm for rational univariate representation
read the original 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.
Forward citations
Cited by 1 Pith paper
-
Fast Rational Univariate Representation via Gaussian Elimination
A Julia package using dense Gaussian elimination computes certified rational univariate representations of polynomial systems with thousands of solutions in seconds, outperforming msolve on several benchmarks.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.