Block-Krylov techniques in the context of sparse-FGLM algorithms

Abstract : Consider a zero-dimensional ideal $I$ in $\mathbb{K}[X_1,\dots,X_n]$. Inspired by Faugère and Mou's Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of $I$ in order to compute a description of its zero set by means of univariate polynomials. Steel recently showed how to use Coppersmith's block-Wiedemann algorithm in this context; he describes an algorithm that can be easily parallelized, but only computes parts of the output in this manner. Using generating series expressions going back to work of Bostan, Salvy, and Schost, we show how to compute the entire output for a small overhead, without making any assumption on the ideal I other than it having dimension zero. We then propose a refinement of this idea that partially avoids the introduction of a generic linear form. We comment on experimental results obtained by an implementation based on the C++ libraries LinBox, Eigen and NTL.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

Littérature citée [52 références]  Voir  Masquer  Télécharger

https://hal-unilim.archives-ouvertes.fr/hal-01661690
Contributeur : Vincent Neiger <>
Soumis le : mardi 12 décembre 2017 - 10:07:08
Dernière modification le : jeudi 11 janvier 2018 - 06:27:36

Fichier

blockKrylov-sparseFGLM.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01661690, version 1

Collections

Citation

Seung Gyu Hyun, Vincent Neiger, Hamid Rahkooy, Éric Schost. Block-Krylov techniques in the context of sparse-FGLM algorithms. 2017. 〈hal-01661690〉

Partager

Métriques

Consultations de la notice

226

Téléchargements de fichiers

57